Patent Publication Number: US-2023163878-A1

Title: Transmitter apparatus and signal processing method thereof

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This is a Continuation of U.S. application Ser. No. 17/333,520 filed May 28, 2021, which is a Continuation of U.S. application Ser. No. 16/424,481 filed May 29, 2019, now U.S. Pat. No. 11,082,159 issued Aug. 3, 2021, which is a Continuation of U.S. application Ser. No. 15/264,057 filed Sep. 13, 2016, now U.S. Pat. No. 10,367,606 issued on Jul. 30, 2019, which is a Continuation of U.S. application Ser. No. 14/324,436 filed Jul. 7, 2014, now U.S. Pat. No. 9,484,957 issued on Nov. 1, 2016, which claims the benefit under 35 U.S.C. § 119 from U.S. Provisional Application 61/843,114 filed on Jul. 5, 2013, U.S. Provisional Application 61/864,758 filed on Aug. 12, 2013, and U.S. Provisional Application 61/897,480 filed on Oct. 30, 2013, in the United States Patent and Trademark Office, and Korean Patent Application 10-2013-0125664 filed on Oct. 21, 2013, Korean Patent Application 10-2014-0026298 filed on Mar. 5, 2014, and Korean Patent Application 10-2014-0083647 filed on Jul. 4, 2014, in the Korean Intellectual Property Office, the disclosures of which are incorporated herein by reference in their entireties. 
    
    
     BACKGROUND 
     1. Technical Field 
     Apparatuses and methods consistent with exemplary embodiments relate to a transmitter apparatus and a signal processing method thereof, and more particularly, to a transmitter apparatus which processes data and transmits the data, and a signal processing method thereof. 
     2. Description of the Related Art 
     In the 21st century information-oriented society, broadcasting communication services are moving into the era of digitalization, multi-channel, wideband, and high quality. In particular, as more high quality digital televisions, portable multimedia players (PMPs) and portable broadcasting equipment are used in recent years, there is an increasing demand for various methods for receiving digital broadcasting services. 
     Many standard groups have established various standards to meet such a demand for providing a variety of services to satisfy the user&#39;s needs. Still, however, there is a demand for a method for providing an improved service with more robust encoding and decoding performance. 
     SUMMARY 
     One or more exemplary embodiments may overcome the above disadvantages and other disadvantages not described above. However, it is understood that one or more exemplary embodiment are not required to overcome the disadvantages described above, and may not overcome any of the problems described above. 
     One or more exemplary embodiments provide a transmitter apparatus which can map a bit included in a predetermined group from among a plurality of groups of a Low Density Parity Check (LDPC) codeword onto a predetermined bit of a modulation symbol, and transmit the bit, and a signal processing method thereof. 
     According to an aspect of an exemplary embodiment, there is provided a transmitter apparatus including: an encoder configured to generate an LDPC codeword by performing LDPC encoding; an interleaver configured to interleave the LDPC codeword; and a modulator configured to map the interleaved LDPC codeword onto a modulation symbol, wherein the modulator maps a bit included in a predetermined group from among a plurality of groups constituting the LDPC codeword onto a predetermined bit in the modulation symbol. 
     Each of the plurality of groups may be formed of  360  bits. 
     The interleaver may include: a parity interleaver configured to interleave parity bits constituting the LDPC codeword; a group interleaver configured to perform group-interlaeving by dividing the parity-interleaved LDPC codeword into the plurality of groups and rearranging an order of the plurality of groups in; and a block interleaver configured to perform block-interleaving of the plurality of groups the order of which has been rearranged. 
     The group interleaver may rearrange the order of the plurality of groups based on Equation 11. 
     In Equation 11, π(j) may be determined based on at least one of a length of the LDPC codeword, a modulation method and a code rate. 
     The π(j) may be defined as in Table 37 when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 6/15. 
     The π(j) may be defined as in Table 38 when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 8/15. 
     The π(j) may be defined as in Table 39 when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 10/15. 
     The π(j) may be defined as in Table 40 when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 10/15. 
     The π(j) may be defined as in Table 41 when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 12/15. 
     The block interleaver may perform the block-interleaving by writing the plurality of groups in each of a plurality of columns in group units in a column direction, and reading each row of the plurality of columns in which the plurality of groups are written in group units in a row direction. 
     The block interleaver, for the writing the plurality of groups in each of the plurality of columns, may divide the plurality of columns in at least two parts, write at least some groups among the plurality of groups in a first part of each of the plurality of columns serially, and write the remaining of the plurality of groups in the other part of each of the plurality of columns. 
     The group interleaver may rearrange the order of the plurality of groups such that groups including a bit to be mapped onto a same location of different modulation symbols are serially arranged to be adjacent to one another so that the block interleaver writes a predetermined group among the plurality of groups in a predetermined column among the plurality of columns. 
     The modulator may generate the modulation symbol by mapping a bit output from the predetermined column onto a predetermined bit in the modulation symbol. 
     According to an aspect of another exemplary embodiment, there is provided a signal processing method of a transmitter apparatus, the signal processing method including: generating an LDPC codeword by performing LDPC encoding; interleaving the LDPC codeword; and mapping the interleaved LDPC codeword onto a modulation symbol, wherein the mapping the interleaved LDPC codeword onto the modulation symbol includes mapping a bit included in a predetermined group from among a plurality of groups constituting the LDPC codeword onto a predetermined bit in the modulation symbol. 
     Each of the plurality of groups may be formed of  360  bits. 
     The interleaving may include: interleaving parity bits constituting the LDPC codeword; group-interleaving by dividing the parity-interleaved LDPC codeword into the plurality of groups and rearranging an order of the plurality of groups; and block-interleaving the plurality of groups the order of which has been rearranged. 
     The rearranging the order of the plurality of groups in the group-wise fashion may include rearranging the order of the plurality of groups in the group-wise fashion based on Equation 11. 
     In Equation 11, π(j) may be determined based on at least one of a length of the LDPC codeword, a modulation method, and a code rate. 
     The π(j) may be defined as in Table 37 when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 6/15. 
     The π(j) may be defined as in Table 38 when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 8/15. 
     The π(j) may be defined as in Table 39 when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 10/15. 
     The π(j) may be defined as in Table 40 when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 10/15. 
     The π(j) may be defined as in Table 41 when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 12/15. 
     The block-interleaving the plurality of groups may include: performing the block-interleaving by writing the plurality of groups in each of a plurality of columns in group units in a column direction; and reading each row of the plurality of columns in which the plurality of groups are written in group units in a row direction. 
     The block-interleaving the plurality of groups may include: dividing the plurality of columns in at least two parts; writing at least some groups among the plurality of groups in a first part of each of the plurality of columns serially; and writing the remaining of the plurality of groups in the other part of each of the plurality of columns. 
     The rearranging the order of the plurality of groups on the group-wise fashion may be performed such that groups comprising a bit to be mapped onto a same location of different modulation symbols are serially arranged to be adjacent to one another so that a predetermined group among the plurality of groups is written on a predetermined column among the plurality of columns. 
     The mapping the LDPC codeword onto the modulation symbol may include generating the modulation symbol by mapping a bit output from the predetermined column onto a predetermined bit in the modulation symbol. 
     According to various exemplary embodiments described above, improved decoding and receiving performance maybe provided. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above and/or other aspects will be more apparent by describing in detail exemplary embodiments, with reference to the accompanying drawings, in which: 
         FIG.  1    is a block diagram to illustrate a configuration of a transmitter apparatus according to an exemplary embodiment; 
         FIGS.  2  and  3    are views to illustrate a configuration of a parity check matrix according to exemplary embodiments; 
         FIG.  4    is a block diagram to illustrate a configuration of an interleaver according to an exemplary embodiment; 
         FIGS.  5  to  7    are views illustrating a method for processing an LDPC codeword on a group basis according to exemplary embodiments; 
         FIGS.  8  to  11    are views to illustrate a configuration of a block interleaver and an interleaving method according to exemplary embodiments; 
         FIGS.  12  and  13    are views to illustrate an operation of a demultiplexer according to exemplary embodiments; 
         FIG.  14    is a view to illustrate an example of a uniform constellation modulation method according to an exemplary embodiment; 
         FIGS.  15  to  19    are views to illustrate an example of a non-uniform constellation modulation method according to exemplary embodiments; 
         FIGS.  20  to  22    are views to illustrate performance when a signal processing method according to exemplary embodiments are applied; 
         FIG.  23    is a block diagram to illustrate a configuration of an interleaver according to another exemplary embodiment; 
         FIGS.  24  to  26    are views to illustrate a configuration of a block-row interleaver and an interleaving method according to exemplary embodiments; 
         FIG.  27    is a block diagram to illustrate a configuration of a receiver apparatus according to an exemplary embodiment; 
         FIGS.  28  and  29    are block diagrams to illustrate a configuration of a deinterleaver according to exemplary embodiments; 
         FIG.  30    is a flowchart to illustrate a signal processing method according to an exemplary embodiment; and 
         FIG.  31    is a view provided to explain a block deinterleaver according to an exemplary embodiment. 
     
    
    
     DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS 
     Hereinafter, various exemplary embodiments will be described in greater detail with reference to the accompanying drawings. 
     In the following description, same reference numerals are used for the same elements when they are depicted in different drawings. The matters defined in the description, such as detailed construction and elements, are provided to assist in a comprehensive understanding of the exemplary embodiments. Thus, it is apparent that the exemplary embodiments can be carried out without those specifically defined matters. Also, functions or elements known in the related art are not described in detail since they would obscure the exemplary embodiments with unnecessary detail. 
       FIG.  1    is a block diagram to illustrate a configuration of a transmitter apparatus according to an exemplary embodiment. Referring to  FIG.  1   , the transmitter apparatus  100  includes an encoder  110 , an interleaver  120 , and a modulator  130  (or a constellation mapper). 
     The encoder  110  generates a Low Density Parity Check (LDPC) codeword by performing LDPC encoding. The encoder  110  may include an LDPC encoder (not shown) to perform the LDPC encoding. 
     Specifically, the encoder  110  LDPC-encodes input bits to information word bits to generate the LDPC codeword which is formed of the information word bits and parity bits (that is, LDPC parity bits). Here, since an LDPC code for the LDPC encoding is a systematic code, the information word bits may be included in the LDPC codeword as they are. 
     The LDPC codeword is formed of the information word bits and the parity bits. For example, the LDPC codeword is formed of N ldpc  number of bits, and includes K ldpc  number of information word bits and N parity =N ldpc −K ldpc  number of parity bits. 
     In this case, the encoder  110  may generate the LDPC codeword by performing the LDPC encoding based on a parity check matrix. That is, since the LDPC encoding is a process for generating an LDPC codeword to satisfy H.C T =0, the encoder  110  may use the parity check matrix when performing the LDPC encoding. Herein, H is a parity check matrix and C is an LDPC codeword. 
     For the LDPC encoding, the transmitter apparatus  100  may include a separate memory and may pre-store parity check matrices of various formats. 
     For example, the transmitter apparatus  100  may pre-store parity check matrices which are defined in Digital Video Broadcasting-Cable version 2 (DVB-C2), Digital Video Broadcasting-Satellite-Second Generation (DVB-S2), Digital Video Broadcasting-Second Generation Terrestrial (DVB-T2), etc., or may pre-store parity check matrices which are defined in the North America digital broadcasting standard system Advanced Television System Committee (ATSC) 3.0 standards, which are currently being established. However, this is merely an example and the transmitter apparatus  100  may pre-store parity check matrices of other formats in addition to these parity check matrices. 
     Hereinafter, a configuration of a parity check matrix will be explained in detail with reference to  FIGS.  2  and  3   . 
     First, referring to  FIG.  2   , a parity check matrix  200  is formed of an information word submatrix  210  corresponding to information word bits, and a parity submatrix  220  corresponding to parity bits. In the parity check matrix  200 , elements other than elements with 1 have 0. 
     The information word submatrix  210  includes K ldpc  number of columns and the parity submatrix  220  includes N parity =N ldpc −K ldpc  number of columns. The number of rows of the parity check matrix  200  is identical to the number of columns of the parity submatrix  220 , N parity =N ldpc −K ldpc . 
     In addition, in the parity check matrix  200 , N ldpc  is a length of an LDPC codeword, K ldpc  is a length of information word bits, and N parity =N ldpc −K ldpc  is a length of parity bits. The length of the LDPC codeword, the information word bits, and the parity bits mean the number of bits included in each of the LDPC codeword, the information bits, and the parity bits. 
     Hereinafter, the configuration of the information word submatrix  210  and the parity submatrix  220  will be explained in detail. 
     The information word submatrix  210  includes K ldpc  number of columns (that is, 0 th  column to (K ldpc -1) th  column), and follows the following rules: 
     First, M number of columns from among K ldpc  number of columns of the information word submatrix  210  belong to the same group, and K ldpc  number of columns is divided into K ldpc /M number of column groups. In each column group, a column is cyclic-shifted from an immediately previous column by Q ldpc  or Q ldpc  number of bits. 
     Herein, M is an interval at which a pattern of a column group, which includes a plurality of columns, is repeated in the information word submatrix  210  (e.g., M=360), and Q ldpc  is a size by which one column is cyclic-shifted from an immediately previous column in a same column group in the information word submatrix  210 . M and Q ldpc  are integers and are determined to satisfy Q ldpc =(N ldpc -K ldpc )/M. In this case, K ldpc /M is also an integer. M and Q ldpc  may have various values according to a length of the LDPC codeword and a code rate. 
     For example, when M=360 and the length of the LDPC codeword, N ldpc , is 64800, Q ldpc  may be defined as in table 1 presented below, and, when M=360 and the length N ldpc  of the LDPC codeword&#39; is 16200, Q ldpc  may be defined as in table 2 presented below. 
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Code Rate 
                 N ldpc   
                 M 
                 Q ldpc   
               
               
                   
                   
               
             
            
               
                   
                  5/15 
                 64800 
                 360 
                 120 
               
               
                   
                  6/15 
                 64800 
                 360 
                 108 
               
               
                   
                  7/15 
                 64800 
                 360 
                  96 
               
               
                   
                  8/15 
                 64800 
                 360 
                  84 
               
               
                   
                  9/15 
                 64800 
                 360 
                  72 
               
               
                   
                 10/15 
                 64800 
                 360 
                  60 
               
               
                   
                 11/15 
                 64800 
                 360 
                  48 
               
               
                   
                 12/15 
                 64800 
                 360 
                  36 
               
               
                   
                 13/15 
                 64800 
                 360 
                  24 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                 Code Rate 
                 N ldpc   
                 M 
                 Q ldpc   
               
               
                   
                   
               
             
            
               
                   
                  5/15 
                 16200 
                 360 
                 30 
               
               
                   
                  6/15 
                 16200 
                 360 
                 27 
               
               
                   
                  7/15 
                 16200 
                 360 
                 24 
               
               
                   
                  8/15 
                 16200 
                 360 
                 21 
               
               
                   
                  9/16 
                 16200 
                 360 
                 18 
               
               
                   
                 10/15 
                 16200 
                 360 
                 15 
               
               
                   
                 11/15 
                 16200 
                 360 
                 12 
               
               
                   
                 12/15 
                 16200 
                 360 
                  9 
               
               
                   
                 13/15 
                 16200 
                 360 
                  6 
               
               
                   
                   
               
            
           
         
       
     
     Second, when the degree of the 0 th  column of the i th  column group (i=0, 1, . . . , K ldpc /M-1) is D i  (herein, the degree is the number of value 1 existing in each column and all columns belonging to the same column group have the same degree), and a position (or an index) of each row where 1 exists in the 0 th  column of the i th  column group is R i,0   (0) , R i,0   (1) , . . . , R i,0   (D     i     -1) , an index R i,j   (k)  of a row where k th  weight-1 is located in the j th  column in the i th  column group group (that is, an index of a row where k th  1 is located in the j th  column in the i th  column group) is determined by following Equation 1: 
       R i,j   (k) =R i,(k-1)   (k) +Q ldpc mod(N ldpc -K ldpc )   (1)
 
     where k=0, 1, 2, . . . D i -1; i=0, 1, . . . , K ldpc /M-1; and j=1, 2, . . . , M-1. 
     Equation 1 can be expressed as following Equation 2: 
       R i,j   (k) ={R i,0   (k) +(j modM)×Q ldpc }mod(N ldpc -K ldpc )   (2)
 
     where k=0, 1, 2, . . . , D i -1; i=0, 1, . . . , K ldpc /M-1; and j=1, 2, . . . , M-1. 
     In the above equations, R i,j   (k)  is an index of a row where k th  weight-1 is located in the j th  column in the i th  column group, N ldpc  is a length of an LDPC codeword, K ldpc  is a length of information word bits, D i  is a degree of columns belonging to the i th  column group, M is the number of columns belonging to a single column group, and Q ldpc  is a size by which each column in the column group is cyclic-shifted. 
     As a result, referring to these equations, when only R i,0   (k)  is known, the index R i,j   (k)  of the row where the k th  weight-1 is located in the j th  column in the i th  column group can be known. Therefore, when the index value of the row where the k th  weight-1 is located in the first column of each column group is stored, a position of column and row where weight-1 is located in the parity check matrix  200  having the configuration of  FIG.  2    (that is, in the information word submatrix  210  of the parity check matrix 200) can be known. 
     According to the above-described rules, all of the columns belonging to the i th  column group have the same degree D i . Accordingly, the LDPC codeword which stores information on the parity check matrix according to the above-described rules may be briefly expressed as follows. 
     For example, when N ldpc  is 30, K ldpc  is 15, and Q ldpc  is 3, position information of the row where weight-1 is located in the 0 th  column of the three column groups may be expressed by a sequence of Equations 3 and may be referred to as “weight-1 position sequence”. 
       R 1,0   (1) =1, R 1,0   (2) =2, R 1,0   (3) =8, R 1,0   (4) =10, R 2,0   (1) =0, R 2,0   (2) =9, R 2,0   (3) =13, R 3,0   (1) =0R 3,0   (2) =14.   (3),
 
     where R i,j   (k)  is an index of a row where k th  weight-1 is located in the j th  column in the i th  column group. 
     The weight-1 position sequence like Equation 3 which expresses an index of a row where 1 is located in the 0 th  column of each column group may be briefly expressed as in Table 3 presented below: 
     
       
         
           
               
               
               
               
               
               
             
               
                   
                 TABLE 3 
               
               
                   
                   
               
             
            
               
                   
                   
                 1 
                 2 
                 8 
                 10 
               
               
                   
                   
                 0 
                 9 
                 13 
                   
               
               
                   
                   
                 0 
                 14 
               
               
                   
                   
               
            
           
         
       
     
     Table 3 shows positions of elements having weight-1, that is, the value 1, in the parity check matrix, and the i th  weight-1 position sequence is expressed by indexes of rows where weight-1 is located in the 0 th  column belonging to the i th  column group. 
     The information word submatrix  210  of the parity check matrix according to an exemplary embodiment may be defined as in Tables 4 to 26 presented below, based on the above descriptions 
     Specifically, Tables 4 to 26 show indexes of rows where 1 is located in the 0 th  column of the i th  column group of the information word submatrix  210 . That is, the information word submatrix  210  is formed of a plurality of column groups each including M number of columns, and positions of 1 in the 0 th  column of each of the plurality of column groups may be defined by Tables 4 to 26. 
     Herein, the indexes of the rows where 1 is located in the 0 th  column of the i th  column group mean “addresses of parity bit accumulators”. The “addresses of parity bit accumulators” have the same meaning as defined in the DVB-C2/S2/T2 standards or the ATSC 3.0 standards which are currently being established, and thus, a detailed explanation thereof is omitted. 
     For example, when the length N ldpc  of the LDPC codeword is 16200, the code rate R is 5/15, and M is 360, the indexes of the rows where 1 is located in the 0 th  column of the i th  column group of the information word submatrix  210  are as shown in Table 4 presented below: 
     
       
         
           
               
               
             
               
                 TABLE 4 
               
               
                   
               
               
                 i 
                 Index of row where 1 is located in the 0th column of the ith column group 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 0 
                 245 449 491 980 1064 1194 1277 1671 2026 3186 4399 4900  
               
               
                   
                 5283 5413 5558 6570 7492 7768 7837 7984 8306 8483 
               
               
                   
                 8685 9357 9642 10045 10179 10261 10338 10412 
               
               
                 1 
                 1318 1584 1682 1860 1954 2000 2062 3387 3441 3879 3931  
               
               
                   
                 4240 4302 4446 4603 5117 5588 5675 5793 5955 6097 6221  
               
               
                   
                 6449 6616 72187394 9535 9896 10009 10763 
               
               
                 2 
                 105 472 785 911 1168 1450 2550 2851 3277 3624 4128 4460  
               
               
                   
                 4572 4669 4783 5102 5133 5199 5905 6647 7028 7086 7703 
               
               
                   
                 8121 8217 9149 9304 9476 9736 9884 
               
               
                 3 
                 1217 5338 5737 8334 
               
               
                 4 
                 855 994 2979 9443 
               
               
                 5 
                 7506 7811 9212 9982 
               
               
                 6 
                 848 3313 3380 3990 
               
               
                 7 
                 2095 4113 4620 9946 
               
               
                 8 
                 1488 2396 6130 7483 
               
               
                 9 
                 1002 2241 7067 10418 
               
               
                 10 
                 2008 3199 7215 7502 
               
               
                 11 
                 1161 7705 8194 8534 
               
               
                 12 
                 2316 4803 8649 9359 
               
               
                 13 
                 125 1880 3177 
               
               
                 14 
                 1141 8033 9072 
               
               
                   
               
            
           
         
       
     
     In another example, when the length N ldpc  of the LDPC codeword is 16200, the code rate R is 6/15, and M is 360, the indexes of the rows where 1 is located in the 0 th  column of the i th  column group of the information word submatrix  210  are as shown in Table 5 presented below: 
     
       
         
           
               
               
             
               
                 TABLE 5 
               
               
                   
               
               
                 i 
                 Index of row where 1 is located in the 0th column of the ith column group 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 0 
                 13 88 136 188 398 794 855 918 954 1950 2762 2837 2847  
               
               
                   
                 4209 4342 5092 5334 5498 5731 5837 6150 6942 7127 
               
               
                   
                 7402 7936 8235 8307 8600 9001 9419 9442 9710 
               
               
                 1 
                 619 792 1002 1148 1528 1533 1925 2207 2766 3021  
               
               
                   
                 3267 3593 3947 4832 4873 5109 5488 5882 6079 6097 6276  
               
               
                   
                 6499 6584 6738 6795 7550 7723 7786 8732 9060 9270 9401 
               
               
                 2 
                 499 717 1551 1791 2535 3135 3582 3813 4047 4309  
               
               
                   
                 5126 5186 5219 5716 5977 6236 6406 6586 6591 7085 7199  
               
               
                   
                 7485 7726 7878 8027 8066 8425 8802 9309 9464 9553 9671 
               
               
                 3 
                 658 4058 7824 8512 
               
               
                 4 
                 3245 4743 8117 9369 
               
               
                 5 
                 465 6559 8112 9461 
               
               
                 6 
                 975 2368 4444 6095 
               
               
                 7 
                 4128 5993 9182 9473 
               
               
                 8 
                 9 3822 5306 5320 
               
               
                 9 
                 4 8311 9571 9669 
               
               
                 10 
                 13 8122 8949 9656 
               
               
                 11 
                 3353 4449 5829 8053 
               
               
                 12 
                 7885 9118 9674 
               
               
                 13 
                 7575 9591 9670 
               
               
                 14 
                 431 8123 9271 
               
               
                 15 
                 4228 7587 9270 
               
               
                 16 
                 8847 9146 9556 
               
               
                 17 
                 11 5213 7763 
               
               
                   
               
            
           
         
       
     
     In another example, when the length N ldpc  of the LDPC codeword is 16200, the code rate R is 7/15, and M is 360, the indexes of the rows where 1 is located in the 0 th  column of the i th  column group of the information word submatrix  210  are as shown in Table 6 presented below: 
     
       
         
           
               
               
             
               
                 TABLE 6 
               
               
                   
               
               
                 i 
                 Index of row where 1 is located in the 0th column of the ith column group 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 0 
                 432 655 893 942 1285 1427 1738 2199 2441 2565 2932  
               
               
                   
                 3201 4144 4419 4678 4963 5423 5922 6433 6564 6656 7478 7514 7892 
               
               
                 1 
                 220 453 690 826 1116 1425 1488 1901 3119 3182 3568 
               
               
                   
                 3800 3953 4071 4782 5038 5555 6836 6871 7131 7609 7850 8317 8443 
               
               
                 2 
                 300 454 497 930 1757 2145 2314 2372 2467 2819 3191 
               
               
                   
                 3256 3699 3984 4538 4965 5461 5742 5912 6135 6649 7636 8078 8455 
               
               
                 3 
                 24 65 565 609 990 1319 1394 1465 1918 1976 2463 2987 
               
               
                   
                 3330 3677 4195 4240 4947 5372 6453 6950 7066 8412 8500 8599 
               
               
                 4 
                 1373 4668 5324 7777 
               
               
                 5 
                 189 3930 5766 6877 
               
               
                 6 
                 3 2961 4207 5747 
               
               
                 7 
                 1108 4768 6743 7106 
               
               
                 8 
                 1282 2274 2750 6204 
               
               
                 9 
                 2279 2587 2737 6344 
               
               
                 10 
                 2889 3164 7275 8040 
               
               
                 11 
                 133 2734 5081 8386 
               
               
                 12 
                 437 3203 7121 
               
               
                 13 
                 4280 7128 8490 
               
               
                 14 
                 619 4563 6206 
               
               
                 15 
                 2799 6814 6991 
               
               
                 16 
                 244 4212 5925 
               
               
                 17 
                 1719 7657 8554 
               
               
                 18 
                 53 1895 6685 
               
               
                 19 
                 584 5420 6856 
               
               
                 20 
                 2958 5834 8103 
               
               
                   
               
            
           
         
       
     
     In another example, when the length N ldpc  of the LDPC codeword is 16200, the code rate R is 8/15, and M is 360, the indexes of the rows where 1 is located in the 0 th  column of the i th  column group of the information word submatrix  210  are as shown in Table 7, 8 or 9 presented below: 
     
       
         
           
               
               
             
               
                 TABLE 7 
               
               
                   
               
               
                 i 
                 Index of row where 1 is located in the 0th column of the ith column group 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 0 
                 32 384 430 591 1296 1976 1999 2137 2175 3638 4214 
               
               
                   
                 4304 4486 4662 4999 5174 5700 6969 7115 7138 7189 
               
               
                 1 
                 1788 1881 1910 2724 4504 4928 4973 5616 5686 5718 
               
               
                   
                 5846 6523 6893 6994 7074 7100 7277 7399 7476 7480 7537 
               
               
                 2 
                 2791 2824 2927 4196 4298 4800 4948 5361 5401 5688  
               
               
                   
                 5818 5862 5969 6029 6244 6645 6962 7203 7302 7454 7534 
               
               
                 3 
                 574 1461 1826 2056 2069 2387 2794 3349 3366 4951  
               
               
                   
                 5826 5834 5903 6640 6762 6786 6859 7043 7418 7431 7554 
               
               
                 4 
                 14 178 675 823 890 930 1209 1311 2898 4339 4600 5203  
               
               
                   
                 6485 6549 6970 7208 7218 7298 7454 7457 7462 
               
               
                 5 
                 4075 4188 7313 7553 
               
               
                 6 
                 5145 6018 7148 7507 
               
               
                 7 
                 3198 4858 6983 7033 
               
               
                 8 
                 3170 5126 5625 6901 
               
               
                 9 
                 2839 6093 7071 7450 
               
               
                 10 
                 11 3735 5413 
               
               
                 11 
                 2497 5400 7238 
               
               
                 12 
                 2067 5172 5714 
               
               
                 13 
                 1889 7173 7329 
               
               
                 14 
                 1795 2773 3499 
               
               
                 15 
                 2695 2944 6735 
               
               
                 16 
                 3221 4625 5897 
               
               
                 17 
                 1690 6122 6816 
               
               
                 18 
                 5013 6839 7358 
               
               
                 19 
                 1601 6849 7415 
               
               
                 20 
                 2180 7389 7543 
               
               
                 21 
                 2121 6838 7054 
               
               
                 22 
                 1948 3109 5046 
               
               
                 23 
                 272 1015 7464 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 8 
               
               
                   
               
               
                 i 
                 Index of row where 1 is located in the 0th column of the ith column group 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 0 
                 5 519 825 1871 2098 2478 2659 2820 3200 3294  
               
               
                   
                 3650 3804 3949 4426 4460 4503 4568 
               
               
                   
                 4590 4949 5219 5662 5738 5905 5911 6160 6404  
               
               
                   
                 6637 6708 6737 6814 7263 7412 
               
               
                 1 
                 81 391 1272 1633 2062 2882 3443 3503 3535 3908  
               
               
                   
                 4033 4163 4490 4929 5262 5399 
               
               
                   
                 5576 5768 5910 6331 6430 6844 6867 7201 7274 7290  
               
               
                   
                 7343 7350 7378 7387 7440 7554 
               
               
                 2 
                 105 975 3421 3480 4120 4444 5957 5971 6119 6617 6761 6810 7067 7353 
               
               
                 3 
                 6 138 485 1444 1512 2615 2990 3109 5604 6435 6513 6632 6704 7507 
               
               
                 4 
                 20 858 1051 2539 3049 5162 5308 6158 6391 6604 6744 7071 7195 7238 
               
               
                 5 
                 1140 5838 6203 6748 
               
               
                 6 
                 6282 6466 6481 6638 
               
               
                 7 
                 2346 2592 5436 7487 
               
               
                 8 
                 2219 3897 5896 7528 
               
               
                 9 
                 2897 6028 7018 
               
               
                 10 
                 1285 1863 5324 
               
               
                 11 
                 3075 6005 6466 
               
               
                 12 
                 5 6020 7551 
               
               
                 13 
                 2121 3751 7507 
               
               
                 14 
                 4027 5488 7542 
               
               
                 15 
                 2 6012 7011 
               
               
                 16 
                 3823 5531 5687 
               
               
                 17 
                 1379 2262 5297 
               
               
                 18 
                 1882 7498 7551 
               
               
                 19 
                 3749 4806 7227 
               
               
                 20 
                 2 2074 6898 
               
               
                 21 
                 17 616 7482 
               
               
                 22 
                 9 6823 7480 
               
               
                 23 
                 5195 5880 7559 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 9 
               
               
                   
               
               
                 i 
                 Index of row where 1 is located in the 0th column of the ith column group 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 0 
                 6 243 617 697 1380 1504 1864 1874 1883 2075 2122 2439  
               
               
                   
                 2489 3076 3715 3719 3824 4028 4807 5006 5196 5532  
               
               
                   
                 5688 5881 6216 6899 7000 7118 7284 7412 7417 7523 
               
               
                 1 
                 0 6 17 20 105 1279 2443 2523 2800 3458 3684 4257 4799  
               
               
                   
                 4819 5499 5665 5810 5927 6169 6536 6617 6669 7069  
               
               
                   
                 7127 7132 7158 7164 7230 7320 7393 7396 7465 
               
               
                 2 
                 2 6 12 15 2033 2125 3352 3382 5931 7024 7143 7358 7391 7504 
               
               
                 3 
                 5 17 1725 1932 3277 4781 4888 6025 6374 7001 7139 7510 7524 7548 
               
               
                 4 
                 4 19 101 1493 4111 4163 4599 6517 6604 6948 6963 7008 7280 7319 
               
               
                 5 
                 8 28 2289 5025 
               
               
                 6 
                 5505 5693 6844 7552 
               
               
                 7 
                 9 3441 7424 7533 
               
               
                 8 
                 917 1816 3540 4552 
               
               
                 9 
                 256 6362 6868 
               
               
                 10 
                 2125 3144 5576 
               
               
                 11 
                 3443 5553 7201 
               
               
                 12 
                 2219 3897 4541 
               
               
                 13 
                 6331 6481 7224 
               
               
                 14 
                 7 1444 5568 
               
               
                 15 
                 81 1325 3345 
               
               
                 16 
                 778 2726 7316 
               
               
                 17 
                 3512 6462 7259 
               
               
                 18 
                 768 3751 6028 
               
               
                 19 
                 4665 7130 7452 
               
               
                 20 
                 2375 6814 7450 
               
               
                 21 
                 7073 7209 7483 
               
               
                 22 
                 2592 6466 7018 
               
               
                 23 
                 3716 5838 7547 
               
               
                   
               
            
           
         
       
     
     In another example, when the length N ldpc  of the LDPC codeword is 16200, the code rate R is 9/15, and M is 360, the indexes of the rows where 1 is located in the 0 th  column of the i th  column group of the information word submatrix  210  are as shown in Table 10 presented below: 
     
       
         
           
               
               
             
               
                 TABLE 10 
               
               
                   
               
               
                 i 
                 Index of row where 1 is located in the 0th column of the ith column group 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 0 
                 350 462 1291 1383 1821 2235 2493 3328 3353 3772 3872  
               
               
                   
                 3923 4259 4426 4542 4972 5347 6217 6246 6332 6386 
               
               
                 1 
                 177 869 1214 1253 1398 1482 1737 2014 2161 2331 3108  
               
               
                   
                 3297 3438 4388 4430 4456 4522 4783 5273 6037 6395 
               
               
                 2 
                 347 501 658 966 1622 1659 1934 2117 2527 3168 3231  
               
               
                   
                 3379 3427 3739 4218 4497 4894 5000 5167 5728 5975 
               
               
                 3 
                 319 398 599 1143 1796 3198 3521 3886 4139 4453 4556  
               
               
                   
                 4636 4688 4753 4986 5199 5224 5496 5698 5724 6123 
               
               
                 4 
                 162 257 304 524 945 1695 1855 2527 2780 2902 2958  
               
               
                   
                 3439 3484 4224 4769 4928 5156 5303 5971 6358 6477 
               
               
                 5 
                 807 1695 2941 4276 
               
               
                 6 
                 2652 2857 4660 6358 
               
               
                 7 
                 329 2100 2412 3632 
               
               
                 8 
                 1151 1231 3872 4869 
               
               
                 9 
                 1561 3565 5138 5303 
               
               
                 10 
                 407 794 1455 
               
               
                 11 
                 3438 5683 5749 
               
               
                 12 
                 1504 1985 3563 
               
               
                 13 
                 440 5021 6321 
               
               
                 14 
                 194 3645 5923 
               
               
                 15 
                 1217 1462 6422 
               
               
                 16 
                 1212 4715 5973 
               
               
                 17 
                 4098 5100 5642 
               
               
                 18 
                 5512 5857 6226 
               
               
                 19 
                 2583 5506 5933 
               
               
                 20 
                 784 1801 4890 
               
               
                 21 
                 4734 4779 4875 
               
               
                 22 
                 938 5081 5377 
               
               
                 23 
                 127 4125 4704 
               
               
                 24 
                 1244 2178 3352 
               
               
                 25 
                 3659 6350 6465 
               
               
                 26 
                 1686 3464 4336 
               
               
                   
               
            
           
         
       
     
     In another example, when the length N ldpc  of the LDPC codeword is 16200, the code rate R is 10/15, and M is 360, the indexes of the rows where 1 is located in the 0 th  column of the i th  column group of the information word submatrix  210  are as shown in Table 11, 12 or 13 presented below: 
     
       
         
           
               
               
             
               
                 TABLE 11 
               
               
                   
               
               
                 i 
                 Index of row where 1 is located in the 0th column of the ith column group 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 0 
                 76 545 1005 1029 1390 1970 2525 2971 3448 3845  
               
               
                   
                 4088 4114 4163 4373 4640 4705 4970 5094 
               
               
                 1 
                 14 463 600 1676 2239 2319 2326 2815 2887 4278  
               
               
                   
                 4457 4493 4597 4918 4989 5038 5261 5384 
               
               
                 2 
                 451 632 829 1006 1530 1723 2205 2587 2801 3041  
               
               
                   
                 3849 4382 4595 4727 5006 5156 5224 5286 
               
               
                 3 
                 211 265 1293 1777 1926 2214 2909 2957 3178 3278  
               
               
                   
                 3771 4547 4563 4737 4879 5068 5232 5344 
               
               
                 4 
                 6 2901 3925 5384 
               
               
                 5 
                 2858 4152 5006 5202 
               
               
                 6 
                 9 1232 2063 2768 
               
               
                 7 
                 7 11 2781 3871 
               
               
                 8 
                 12 2161 2820 4078 
               
               
                 9 
                 3 3510 4668 5323 
               
               
                 10 
                 253 411 3215 5241 
               
               
                 11 
                 3919 4789 5040 5302 
               
               
                 12 
                 12 5113 5256 5352 
               
               
                 13 
                 9 1461 4004 5241 
               
               
                 14 
                 1688 3585 4480 5394 
               
               
                 15 
                 8 2127 3469 4360 
               
               
                 16 
                 2827 4049 5084 5379 
               
               
                 17 
                 1770 3331 5315 5386 
               
               
                 18 
                 1885 2817 4900 5088 
               
               
                 19 
                 2568 3854 4660 
               
               
                 20 
                 1604 3565 5373 
               
               
                 21 
                 2317 4636 5156 
               
               
                 22 
                 2480 2816 4094 
               
               
                 23 
                 14 4518 4826 
               
               
                 24 
                 127 1192 3872 
               
               
                 25 
                 93 2282 3663 
               
               
                 26 
                 2962 5085 5314 
               
               
                 27 
                 2078 4277 5089 
               
               
                 28 
                 9 5280 5292 
               
               
                 29 
                 50 2847 4742 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 12 
               
               
                   
               
               
                 i 
                 Index of row where 1 is located in the 0th column of the ith column group 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 0 
                 446 449 544 788 992 1389 1800 1933 2461 2975  
               
               
                   
                 3186 3442 3733 3773 4076 4308 4323 4605  
               
               
                   
                 4882 5034 5080 5135 5146 5269 5307 
               
               
                 1 
                 25 113 139 147 307 1066 1078 1572 1773 1957  
               
               
                   
                 2143 2609 2642 2901 3371 3414 3935 4141  
               
               
                   
                 4165 4271 4520 4754 4971 5160 5179 
               
               
                 2 
                 341 424 1373 1559 1953 2577 2721 3257 3706  
               
               
                   
                 4025 4273 4689 4995 5005 
               
               
                 3 
                 442 465 1892 2274 2292 2999 3156 3308 3883  
               
               
                   
                 4084 4316 4636 4743 5200 
               
               
                 4 
                 22 1809 2406 3332 3359 3430 3466 4610 4638  
               
               
                   
                 5224 5280 5288 5337 5381 
               
               
                 5 
                 29 1203 1444 1720 1836 2138 2902 3601 3642  
               
               
                   
                 4138 4269 4457 4965 5315 
               
               
                 6 
                 1138 2493 3852 4802 
               
               
                 7 
                 3050 5361 5396 
               
               
                 8 
                 278 399 4810 
               
               
                 9 
                 1200 3577 4904 
               
               
                 10 
                 1705 2811 3448 
               
               
                 11 
                 2180 4242 5336 
               
               
                 12 
                 4539 5069 5363 
               
               
                 13 
                 3318 3645 4427 
               
               
                 14 
                 2902 5134 5176 
               
               
                 15 
                 5123 5130 5229 
               
               
                 16 
                 47 4474 5356 
               
               
                 17 
                 2399 3981 5067 
               
               
                 18 
                 2377 2465 5080 
               
               
                 19 
                 2413 2471 5328 
               
               
                 20 
                 2502 4911 5329 
               
               
                 21 
                 4770 5139 5356 
               
               
                 22 
                 3263 4000 4022 
               
               
                 23 
                 648 2015 4867 
               
               
                 24 
                 311 2309 4063 
               
               
                 25 
                 1284 3246 3740 
               
               
                 26 
                 7 1080 3820 
               
               
                 27 
                 1261 2408 4608 
               
               
                 28 
                 3838 4076 4842 
               
               
                 29 
                 2294 4592 5254 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 13 
               
               
                   
               
               
                 i 
                 Index of row where 1 is located in the 0th column of the ith column group 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 0 
                 352 747 894 1437 1688 1807 1883 2119 2159  
               
               
                   
                 3321 3400 3543 3588 3770 3821 4384 4470  
               
               
                   
                 4884 5012 5036 5084 5101 5271 5281 5353 
               
               
                 1 
                 505 915 1156 1269 1518 1650 2153 2256 2344  
               
               
                   
                 2465 2509 2867 2875 3007 3254 3519 3687  
               
               
                   
                 4331 4439 4532 4940 5011 5076 5113 5367 
               
               
                 2 
                 268 346 650 919 1260 4389 4653 4721 4838 5054  
               
               
                   
                 5157 5162 5275 5362 
               
               
                 3 
                 220 236 828 1590 1792 3259 3647 4276 4281 4325  
               
               
                   
                 4963 4974 5003 5037 
               
               
                 4 
                 381 737 1099 1409 2364 2955 3228 3341 3473 3985  
               
               
                   
                 4257 4730 5173 5242 
               
               
                 5 
                 88 771 1640 1737 1803 2408 2575 2974 3167 3464  
               
               
                   
                 3780 4501 4901 5047 
               
               
                 6 
                 749 1502 2201 3189 
               
               
                 7 
                 2873 3245 3427 
               
               
                 8 
                 2158 2605 3165 
               
               
                 9 
                 1 3438 3606 
               
               
                 10 
                 10 3019 5221 
               
               
                 11 
                 371 2901 2923 
               
               
                 12 
                 9 3935 4683 
               
               
                 13 
                 1937 3502 3735 
               
               
                 14 
                 507 3128 4994 
               
               
                 15 
                 25 3854 4550 
               
               
                 16 
                 1178 4737 5366 
               
               
                 17 
                 2 223 5304 
               
               
                 18 
                 1146 5175 5197 
               
               
                 19 
                 1816 2313 3649 
               
               
                 20 
                 740 1951 3844 
               
               
                 21 
                 1320 3703 4791 
               
               
                 22 
                 1754 2905 4058 
               
               
                 23 
                 7 917 5277 
               
               
                 24 
                 3048 3954 5396 
               
               
                 25 
                 4804 4824 5105 
               
               
                 26 
                 2812 3895 5226 
               
               
                 27 
                 0 5318 5358 
               
               
                 28 
                 1483 2324 4826 
               
               
                 29 
                 2266 4752 5387 
               
               
                   
               
            
           
         
       
     
     In another example, when the length N ldpc  of the LDPC codeword is 16200, the code rate R is 11/15, and M is 360, the indexes of the rows where 1 is located in the 0 th  column of the i th  column group of the information word submatrix  210  are as shown in Table 14 presented below: 
     
       
         
           
               
               
             
               
                 TABLE 14 
               
               
                   
               
               
                 i 
                 Index of row where 1 is located in the 0th column of the ith column group 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 0 
                 108 297 703 742 1345 1443 1495 1628 1812 2341  
               
               
                   
                 2559 2669 2810 2877 3442 3690 3755 3904 4264 
               
               
                 1 
                 180 211 477 788 824 1090 1272 1578 1685 1948  
               
               
                   
                 2050 2195 2233 2546 2757 2946 3147 3299 3544 
               
               
                 2 
                 627 741 1135 1157 1226 1333 1378 1427 1454 1696  
               
               
                   
                 1757 1772 2099 2208 2592 3354 3580 4066 4242 
               
               
                 3 
                 9 795 959 989 1006 1032 1135 1209 1382 1484 1703  
               
               
                   
                 1855 1985 2043 2629 2845 3136 3450 3742 
               
               
                 4 
                 230 413 801 829 1108 1170 1291 1759 1793 1827  
               
               
                   
                 1976 2000 2423 2466 2917 3010 3600 3782 4143 
               
               
                 5 
                 56 142 236 381 1050 1141 1372 1627 1985 2247  
               
               
                   
                 2340 3023 3434 3519 3957 4013 4142 4164 4279 
               
               
                 6 
                 298 1211 2548 3643 
               
               
                 7 
                 73 1070 1614 1748 
               
               
                 8 
                 1439 2141 3614 
               
               
                 9 
                 284 1564 2629 
               
               
                 10 
                 607 660 855 
               
               
                 11 
                 1195 2037 2753 
               
               
                 12 
                 49 1198 2562 
               
               
                 13 
                 296 1145 3540 
               
               
                 14 
                 1516 2315 2382 
               
               
                 15 
                 154 722 4016 
               
               
                 16 
                 759 2375 3825 
               
               
                 17 
                 162 194 1749 
               
               
                 18 
                 2335 2422 2632 
               
               
                 19 
                 6 1172 2583 
               
               
                 20 
                 726 1325 1428 
               
               
                 21 
                 985 2708 2769 
               
               
                 22 
                 255 2801 3181 
               
               
                 23 
                 2979 3720 4090 
               
               
                 24 
                 208 1428 4094 
               
               
                 25 
                 199 3743 3757 
               
               
                 26 
                 1229 2059 4282 
               
               
                 27 
                 458 1100 1387 
               
               
                 28 
                 1199 2481 3284 
               
               
                 29 
                 1161 1467 4060 
               
               
                 30 
                 959 3014 4144 
               
               
                 31 
                 2666 3960 4125 
               
               
                 32 
                 2809 3834 4318 
               
               
                   
               
            
           
         
       
     
     In another example, when the length Nldpc of the LDPC codeword is 16200, the code rate R is 12/15, and M is 360, the indexes of the rows where 1 is located in the 0 th  column of the i th  column group of the information word submatrix  210  are as shown in Table 15 or 16 presented below: 
     
       
         
           
               
               
             
               
                 TABLE 15 
               
               
                   
               
               
                 i 
                 Index of row where 1 is located in the 0th column of the ith column group 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 0 
                 3 394 1014 1214 1361 1477 1534 1660 1856 2745  
               
               
                   
                 2987 2991 3124 3155 
               
               
                 1 
                 59 136 528 781 803 928 1293 1489 1944 2041 2200  
               
               
                   
                 2613 2690 2847 
               
               
                 2 
                 155 245 311 621 1114 1269 1281 1783 1995 2047  
               
               
                   
                 2672 2803 2885 3014 
               
               
                 3 
                 79 870 974 1326 1449 1531 2077 2317 2467 2627  
               
               
                   
                 2811 3083 3101 3132 
               
               
                 4 
                 4 582 660 902 1048 1482 1697 1744 1928 2628  
               
               
                   
                 2699 2728 3045 3104 
               
               
                 5 
                 175 395 429 1027 1061 1068 1154 1168 1175  
               
               
                   
                 2147 2359 2376 2613 2682 
               
               
                 6 
                 1388 2241 3118 3148 
               
               
                 7 
                 143 506 2067 3148 
               
               
                 8 
                 1594 2217 2705 
               
               
                 9 
                 398 988 2551 
               
               
                 10 
                 1149 2588 2654 
               
               
                 11 
                 678 2844 3115 
               
               
                 12 
                 1508 1547 1954 
               
               
                 13 
                 1199 1267 1710 
               
               
                 14 
                 2589 3163 3207 
               
               
                 15 
                 1 2583 2974 
               
               
                 16 
                 2766 2897 3166 
               
               
                 17 
                 929 1823 2742 
               
               
                 18 
                 1113 3007 3239 
               
               
                 19 
                 1753 2478 3127 
               
               
                 20 
                 0 509 1811 
               
               
                 21 
                 1672 2646 2984 
               
               
                 22 
                 965 1462 3230 
               
               
                 23 
                 3 1077 2917 
               
               
                 24 
                 1183 1316 1662 
               
               
                 25 
                 968 1593 3239 
               
               
                 26 
                 64 1996 2226 
               
               
                 27 
                 1442 2058 3181 
               
               
                 28 
                 513 973 1058 
               
               
                 29 
                 1263 3185 3229 
               
               
                 30 
                 681 1394 3017 
               
               
                 31 
                 419 2853 3217 
               
               
                 32 
                 3 2404 3175 
               
               
                 33 
                 2417 2792 2854 
               
               
                 34 
                 1879 2940 3235 
               
               
                 35 
                 647 1704 3060 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 16 
               
               
                   
               
               
                 i 
                 Index of row where 1 is located in the 0th column of the ith column group 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 0 
                 69 170 650 1107 1190 1250 1309 1486 1612 1625  
               
               
                   
                 2091 2416 2580 2673 2921 2995 3175 3234 
               
               
                 1 
                 299 652 680 732 1197 1394 1779 1848 1885 2206  
               
               
                   
                 2266 2286 2706 2795 3206 3229 
               
               
                 2 
                 107 133 351 640 805 1136 1175 1479 1817 2068  
               
               
                   
                 2139 2586 2809 2855 2862 2930 
               
               
                 3 
                 75 458 508 546 584 624 875 1948 2363 2471 2574  
               
               
                   
                 2715 3008 3052 3070 3166 
               
               
                 4 
                 0 7 897 1664 1981 2172 2268 2272 2364 2873 2902  
               
               
                   
                 3016 3020 3121 3203 3236 
               
               
                 5 
                 121 399 550 1157 1216 1326 1789 1838 1888 2160  
               
               
                   
                 2537 2745 2949 3001 3020 3152 
               
               
                 6 
                 1497 2022 2726 2871 
               
               
                 7 
                 872 2320 2504 3234 
               
               
                 8 
                 851 1684 3210 3217 
               
               
                 9 
                 1807 2918 3178 
               
               
                 10 
                 671 1203 2343 
               
               
                 11 
                 405 490 3212 
               
               
                 12 
                 1 1474 3235 
               
               
                 13 
                 527 1224 2139 
               
               
                 14 
                 3 1997 2072 
               
               
                 15 
                 833 2366 3183 
               
               
                 16 
                 385 1309 3196 
               
               
                 17 
                 1343 2691 3153 
               
               
                 18 
                 1815 2048 2394 
               
               
                 19 
                 812 2055 2926 
               
               
                 20 
                 166 826 2807 
               
               
                 21 
                 1 493 2961 
               
               
                 22 
                 2218 3032 3153 
               
               
                 23 
                 2099 2885 3228 
               
               
                 24 
                 1214 2677 3216 
               
               
                 25 
                 2292 2422 2835 
               
               
                 26 
                 574 2138 3053 
               
               
                 27 
                 576 1409 1912 
               
               
                 28 
                 354 1631 3142 
               
               
                 29 
                 3211 3228 3239 
               
               
                 30 
                 1335 2938 3184 
               
               
                 31 
                 729 995 1520 
               
               
                 32 
                 537 3115 3233 
               
               
                 33 
                 4 2631 3231 
               
               
                 34 
                 1130 2851 3030 
               
               
                 35 
                 1136 2728 3203 
               
               
                   
               
            
           
         
       
     
     In another example, when the length N ldpc  of the LDPC codeword is 16200, the code rate R is 13/15, and M is 360, the indexes of the rows where 1 is located in the 0 th  column of the i th  column group of the information word submatrix  210  are as shown in Table 17 presented below: 
     
       
         
           
               
               
             
               
                 TABLE 17 
               
               
                   
               
               
                 i 
                 Index of row where 1 is located in the 0th column of the ith column group 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 0 
                 37 144 161 199 220 496 510 589 731 808  
               
               
                   
                 834 965 1249 1264 1311 1377 1460 1520  
               
               
                   
                 1598 1707 1958 2055 2099 2154 
               
               
                 1 
                 20 27 165 462 546 583 742 796 1095 1110  
               
               
                   
                 1129 1145 1169 1190 1254 1363 1383 1463 
               
               
                   
                 1718 1835 1870 1879 2108 2128 
               
               
                 2 
                 288 362 463 505 638 691 745 861 1006 1083  
               
               
                   
                 1124 1175 1247 1275 1337 1353 1378 1506 
               
               
                   
                 1588 1632 1720 1868 1980 2135 
               
               
                 3 
                 405 464 478 511 566 574 641 766 785 802  
               
               
                   
                 836 996 1128 1239 1247 1449 1491 1537  
               
               
                   
                 1616 1643 1668 1950 1975 2149 
               
               
                 4 
                 86 192 245 357 363 374 700 713 852 903  
               
               
                   
                 992 1174 1245 1277 1342 1369 1381 1417  
               
               
                   
                 1463 1712 1900 1962 2053 2118 
               
               
                 5 
                 101 327 378 550 
               
               
                 6 
                 186 723 1318 1550 
               
               
                 7 
                 118 277 504 1835 
               
               
                 8 
                 199 407 1776 1965 
               
               
                 9 
                 387 1253 1328 1975 
               
               
                 10 
                 62 144 1163 2017 
               
               
                 11 
                 100 475 572 2136 
               
               
                 12 
                 431 865 1568 2055 
               
               
                 13 
                 283 640 981 1172 
               
               
                 14 
                 220 1038 1903 2147 
               
               
                 15 
                 483 1318 1358 2118 
               
               
                 16 
                 92 961 1709 1810 
               
               
                 17 
                 112 403 1485 2042 
               
               
                 18 
                 431 1110 1130 1365 
               
               
                 19 
                 587 1005 1206 1588 
               
               
                 20 
                 704 1113 1943 
               
               
                 21 
                 375 1487 2100 
               
               
                 22 
                 1507 1950 2110 
               
               
                 23 
                 962 1613 2038 
               
               
                 24 
                 554 1295 1501 
               
               
                 25 
                 488 784 1446 
               
               
                 26 
                 871 1935 1964 
               
               
                 27 
                 54 1475 1504 
               
               
                 28 
                 1579 1617 2074 
               
               
                 29 
                 1856 1967 2131 
               
               
                 30 
                 330 1582 2107 
               
               
                 31 
                 40 1056 1809 
               
               
                 32 
                 1310 1353 1410 
               
               
                 33 
                 232 554 1939 
               
               
                 34 
                 168 641 1099 
               
               
                 35 
                 333 437 1556 
               
               
                 36 
                 153 622 745 
               
               
                 37 
                 719 931 1188 
               
               
                 38 
                 237 638 1607 
               
               
                   
               
            
           
         
       
     
     In another example, when the length N ldpc  of the LDPC codeword is 64800, the code rate R is 5/15, and M is 360, the indexes of the rows where 1 is located in the 0 th  column of the i th  column group of the information word submatrix  210  are as shown in Table 18 presented below: 
     
       
         
           
               
               
             
               
                 TABLE 18 
               
               
                   
               
               
                 i 
                 Index of row where 1 is located in the 0th column of the ith column group 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 0 
                 2949 5639 7367 8468 8922 9552 11216 12483 12692  
               
               
                   
                 13305 14026 15331 16463 17169 17210 18200  
               
               
                   
                 18744 19729 21099 21976 22751 23405 25903  
               
               
                   
                 27283 27785 28232 30140 31378 31517 32596  
               
               
                   
                 33276 34715 37150 38321 39030 41119 41822 
               
               
                 1 
                 497 1675 2751 6204 6502 8092 9462 10174 11130  
               
               
                   
                 13320 15232 16384 19154 19161 19289 22598  
               
               
                   
                 23437 25056 27490 29258 29606 30519 30950  
               
               
                   
                 32033 33244 34263 34664 35613 36427 37214  
               
               
                   
                 39295 39721 40604 41339 42048 42956 42993 
               
               
                 2 
                 81 2015 3625 3922 5312 5478 10562 12344 15258  
               
               
                   
                 17199 18144 18734 20426 20680 20892 23405  
               
               
                   
                 23775 26987 27051 27928 30165 30931 31468  
               
               
                   
                 31734 32911 33246 34674 35490 36528 37198  
               
               
                   
                 40207 40753 40978 41099 42308 42368 43163 
               
               
                 3 
                 60 83 4850 12379 13152 15708 18322 18837 19306  
               
               
                   
                 19707 20498 20515 21581 25442 26973 28529  
               
               
                   
                 31811 33646 33932 34951 36620 38616 38999  
               
               
                   
                 39044 39113 40059 41349 41555 41862 42402  
               
               
                   
                 42498 42585 42675 42993 43024 43055 43096 
               
               
                 4 
                 0 4117 4725 7284 8569 9958 12270 13621 15234  
               
               
                   
                 16376 16601 19689 21366 23666 23974 24076  
               
               
                   
                 24394 27950 30679 31287 35577 36892 38152  
               
               
                   
                 38720 38876 39185 39252 39340 39775 40987  
               
               
                   
                 41909 41943 42437 42961 42973 43031 43097 
               
               
                 5 
                 967 2629 3433 4645 4982 6055 9235 9343 12533  
               
               
                   
                 16491 21527 24963 25960 28150 28991 29257  
               
               
                   
                 30381 31084 31236 31335 32838 34483 35276  
               
               
                   
                 36410 37071 37122 37300 37462 39998 40146  
               
               
                   
                 40154 41508 41728 42263 42446 42610 42800 
               
               
                 6 
                 20 183 4422 4776 8224 8345 9567 10020 12621  
               
               
                   
                 15894 16523 17333 20169 20579 23118 24244  
               
               
                   
                 27052 27722 29664 30390 35672 35676 36997  
               
               
                   
                 37033 37413 37601 38892 39128 39289 40096  
               
               
                   
                 40772 41443 42048 42224 42467 42745 43011 
               
               
                 7 
                 84 106 3077 11179 14909 18393 18487 19607  
               
               
                   
                 22021 22690 22803 25095 26576 27221 27921  
               
               
                   
                 28711 29634 29800 35182 35277 35908 36592  
               
               
                   
                 37177 37183 37282 38588 40818 40959 41614  
               
               
                   
                 41645 41731 41848 42076 42133 42686 42960 43081 
               
               
                 8 
                 11 69 118 1909 9297 9815 11631 13409 14586  
               
               
                   
                 15614 16965 23438 23714 25346 26766 27507  
               
               
                   
                 28079 30062 31032 31645 32897 34419 37279  
               
               
                   
                 37875 38926 39755 41098 41630 41738 41745  
               
               
                   
                 41950 42210 42263 42404 42787 43073 43114 
               
               
                 9 
                 847 4197 18971 21073 21632 21804 28372 29779 31957 
               
               
                 10 
                 887 2607 17001 22858 32823 42335 42766 42963 43068 
               
               
                 11 
                 10043 11204 16616 34509 38254 39794 40346 40904 41837 
               
               
                 12 
                 3140 6150 19328 27432 29211 30253 34818 35467 41835 
               
               
                 13 
                 43 7561 25050 27629 27970 36235 39071 41760 42680 
               
               
                 14 
                 4457 11073 22626 25705 26101 27653 37929 40444 43140 
               
               
                 15 
                 9356 22954 24346 26334 29985 38991 39405 39467 42161 
               
               
                 16 
                 5208 6811 9103 9459 9821 17992 20176 23613 25909 
               
               
                 17 
                 8028 8500 18269 26693 34977 39987 41007 41908 43134 
               
               
                 18 
                 9949 18141 19765 28691 35617 41501 42181 42613 42795 
               
               
                 19 
                 7088 18754 22437 24859 25006 25260 25986 40105 42107 
               
               
                 20 
                 1103 13160 38346 
               
               
                 21 
                 10019 14598 19503 
               
               
                 22 
                 9430 10336 25320 
               
               
                 23 
                 16076 21513 43031 
               
               
                 24 
                 16559 17352 42859 
               
               
                 25 
                 762 9254 27313 
               
               
                 26 
                 3248 31582 40864 
               
               
                 27 
                 39929 41844 42505 
               
               
                 28 
                 16862 37978 42989 
               
               
                 29 
                 1163 27452 40918 
               
               
                 30 
                 29919 41247 42965 
               
               
                 31 
                 5613 17649 33421 
               
               
                 32 
                 31620 37112 41081 
               
               
                 33 
                 2444 9823 40886 
               
               
                 34 
                 18347 24355 29735 
               
               
                 35 
                 17445 20377 23490 
               
               
                 36 
                 12214 30796 42127 
               
               
                 37 
                 2806 10061 31670 
               
               
                 38 
                 18024 36307 42997 
               
               
                 39 
                 1786 10898 40868 
               
               
                 40 
                 91 12816 34474 
               
               
                 41 
                 14181 32766 42963 
               
               
                 42 
                 14002 20589 43180 
               
               
                 43 
                 4615 35058 43192 
               
               
                 44 
                 109 10827 40754 
               
               
                 45 
                 1782 7637 41511 
               
               
                 46 
                 39185 42681 42708 
               
               
                 47 
                 2790 37933 43108 
               
               
                 48 
                 2024 25595 35385 
               
               
                 49 
                 3205 35128 36500 
               
               
                 50 
                 653 12319 21362 
               
               
                 51 
                 158 6617 34314 
               
               
                 52 
                 520 42957 43092 
               
               
                 53 
                 37614 41770 43179 
               
               
                 54 
                 16081 22755 40856 
               
               
                 55 
                 18163 19831 21768 
               
               
                 56 
                 3375 29411 43010 
               
               
                 57 
                 17033 22596 42767 
               
               
                 58 
                 11786 19137 31011 
               
               
                 59 
                 52 9964 19729 
               
               
                   
               
            
           
         
       
     
     In another example, when the length N ldpc  of the LDPC codeword is 64800, the code rate R is 6/15, and M is 360, the indexes of the rows where 1 is located in the 0 th  column of the i th  column group of the information word submatrix  210  are as shown in Table 19 presented below: 
     
       
         
           
               
               
             
               
                 TABLE 19 
               
               
                   
               
               
                 i 
                 Index of row where 1 is located in the 0th column of the ith column group 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 0 
                 1606 3402 4961 6751 7132 11516 12300 12482  
               
               
                   
                 12592 13342 13764 14123 21576 23946 24533  
               
               
                   
                 25376 25667 26836 31799 34173 35462 36153  
               
               
                   
                 36740 37085 37152 37468 37658 
               
               
                 1 
                 4621 5007 6910 8732 9757 11508 13099 15513  
               
               
                   
                 16335 18052 19512 21319 23663 25628 27208  
               
               
                   
                 31333 32219 33003 33239 33447 36200 36473  
               
               
                   
                 36938 37201 37283 37495 38642 
               
               
                 2 
                 16 1094 2020 3080 4194 5098 5631 6877 7889 8237 9804  
               
               
                   
                 10067 11017 11366 13136 13354 15379 18934 20199  
               
               
                   
                 24522 26172 28666 30386 32714 36390 37015 37162 
               
               
                 3 
                 700 897 1708 6017 6490 7372 7825 9546 10398 16605  
               
               
                   
                 18561 18745 21625 22137 23693 24340 24966 25015  
               
               
                   
                 26995 28586 28895 29687 33938 34520 34858 37056 38297 
               
               
                 4 
                 159 2010 2573 3617 4452 4958 5556 5832 6481 8227  
               
               
                   
                 9924 10836 14954 15594 16623 18065 19249 22394  
               
               
                   
                 22677 23408 23731 24076 24776 27007 28222 30343 38371 
               
               
                 5 
                 3118 3545 4768 4992 5227 6732 8170 9397 10522 11508  
               
               
                   
                 15536 20218 21921 28599 29445 29758 29968 31014  
               
               
                   
                 32027 33685 34378 35867 36323 36728 36870 38335 38623 
               
               
                 6 
                 1264 4254 6936 9165 9486 9950 10861 11653 13697 13961  
               
               
                   
                 15164 15665 18444 19470 20313 21189 24371 26431  
               
               
                   
                 26999 28086 28251 29261 31981 34015 35850 36129 37186 
               
               
                 7 
                 111 1307 1628 2041 2524 5358 7988 8191 10322 11905  
               
               
                   
                 12919 14127 15515 15711 17061 19024 21195 22902  
               
               
                   
                 23727 24401 24608 25111 25228 27338 35398 37794 38196 
               
               
                 8 
                 961 3035 7174 7948 13355 13607 14971 18189 18339  
               
               
                   
                 18665 18875 19142 20615 21136 21309 21758 23366  
               
               
                   
                 24745 25849 25982 27583 30006 31118 32106 36469  
               
               
                   
                 36583 37920 
               
               
                 9 
                 2990 3549 4273 4808 5707 6021 6509 7456 8240 10044  
               
               
                   
                 12262 12660 13085 14750 15680 16049 21587 23997  
               
               
                   
                 25803 28343 28693 34393 34860 35490 36021 37737 38296 
               
               
                 10 
                 955 4323 5145 6885 8123 9730 11840 12216 19194 20313  
               
               
                   
                 23056 24248 24830 25268 26617 26801 28557 29753  
               
               
                   
                 30745 31450 31973 32839 33025 33296 35710 37366 37509 
               
               
                 11 
                 264 605 4181 4483 5156 7238 8863 10939 11251  
               
               
                   
                 12964 16254 17511 20017 22395 22818 23261 23422 24064  
               
               
                   
                 26329 27723 28186 30434 31956 33971 34372 36764 38123 
               
               
                 12 
                 520 2562 2794 3528 3860 4402 5676 6963 8655 9018 9783  
               
               
                   
                 11933 16336 17193 17320 19035 20606 23579 23769  
               
               
                   
                 24123 24966 27866 32457 34011 34499 36620 37526 
               
               
                 13 
                 10106 10637 10906 34242 
               
               
                 14 
                 1856 15100 19378 21848 
               
               
                 15 
                 943 11191 27806 29411 
               
               
                 16 
                 4575 6359 13629 19383 
               
               
                 17 
                 4476 4953 18782 24313 
               
               
                 18 
                 5441 6381 21840 35943 
               
               
                 19 
                 9638 9763 12546 30120 
               
               
                 20 
                 9587 10626 11047 25700 
               
               
                 21 
                 4088 15298 28768 35047 
               
               
                 22 
                 2332 6363 8782 28863 
               
               
                 23 
                 4625 4933 28298 30289 
               
               
                 24 
                 3541 4918 18257 31746 
               
               
                 25 
                 1221 25233 26757 34892 
               
               
                 26 
                 8150 16677 27934 30021 
               
               
                 27 
                 8500 25016 33043 38070 
               
               
                 28 
                 7374 10207 16189 35811 
               
               
                 29 
                 611 18480 20064 38261 
               
               
                 30 
                 25416 27352 36089 38469 
               
               
                 31 
                 1667 17614 25839 32776 
               
               
                 32 
                 4118 12481 21912 37945 
               
               
                 33 
                 5573 13222 23619 31271 
               
               
                 34 
                 18271 26251 27182 30587 
               
               
                 35 
                 14690 26430 26799 34355 
               
               
                 36 
                 13688 16040 20716 34558 
               
               
                 37 
                 2740 14957 23436 32540 
               
               
                 38 
                 3491 14365 14681 36858 
               
               
                 39 
                 4796 6238 25203 27854 
               
               
                 40 
                 1731 12816 17344 26025 
               
               
                 41 
                 19182 21662 23742 27872 
               
               
                 42 
                 6502 13641 17509 34713 
               
               
                 43 
                 12246 12372 16746 27452 
               
               
                 44 
                 1589 21528 30621 34003 
               
               
                 45 
                 12328 20515 30651 31432 
               
               
                 46 
                 3415 22656 23427 36395 
               
               
                 47 
                 632 5209 25958 31085 
               
               
                 48 
                 619 3690 19648 37778 
               
               
                 49 
                 9528 13581 26965 36447 
               
               
                 50 
                 2147 26249 26968 28776 
               
               
                 51 
                 15698 18209 30683 
               
               
                 52 
                 1132 19888 34111 
               
               
                 53 
                 4608 25513 38874 
               
               
                 54 
                 475 1729 34100 
               
               
                 55 
                 7348 32277 38587 
               
               
                 56 
                 182 16473 33082 
               
               
                 57 
                 3865 9678 21265 
               
               
                 58 
                 4447 20151 27618 
               
               
                 59 
                 6335 14371 38711 
               
               
                 60 
                 704 9695 28858 
               
               
                 61 
                 4856 9757 30546 
               
               
                 62 
                 1993 19361 30732 
               
               
                 63 
                 756 28000 29138 
               
               
                 64 
                 3821 24076 31813 
               
               
                 65 
                 4611 12326 32291 
               
               
                 66 
                 7628 21515 34995 
               
               
                 67 
                 1246 13294 30068 
               
               
                 68 
                 6466 33233 35865 
               
               
                 69 
                 14484 23274 38150 
               
               
                 70 
                 21269 36411 37450 
               
               
                 71 
                 23129 26195 37653 
               
               
                   
               
            
           
         
       
     
     In another example, when the length N ldpc  of the LDPC codeword is 64800, the code rate R is 7/15, and M is 360, the indexes of the rows where 1 is located in the 0 th  column of the i th  column group of the information word submatrix  210  are as shown in Table 20 or 21 presented below: 
     
       
         
           
               
               
             
               
                 TABLE 20 
               
               
                   
               
               
                 i 
                 Index of row where 1 is located in the 0th column of the ith column group 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 0 
                 13 127 927 930 1606 2348 3361 3704 5194 6327 7843  
               
               
                   
                 8081 8615 12199 13947 15317 15774 16289 16687  
               
               
                   
                 17122 20468 21057 21853 22414 23829 23885 25452  
               
               
                   
                 28072 28699 28947 30289 31672 32470 
               
               
                 1 
                 36 53 60 86 93 407 3975 4478 5884 6578 7599 7613  
               
               
                   
                 7696 9573 11010 11183 11233 13750 17182 17860  
               
               
                   
                 20181 23974 24195 25089 25787 25892 26121 30880  
               
               
                   
                 32989 33383 33626 34153 34520 
               
               
                 2 
                 27 875 2693 3435 3682 6195 6227 6711 7629 8005  
               
               
                   
                 9081 11052 11190 11443 14832 17431 17756  
               
               
                   
                 17998 18254 18632 22234 22880 23562 23647 27092  
               
               
                   
                 29035 29620 30336 33492 33906 33960 34337 34474 
               
               
                 3 
                 10 722 1241 3558 5490 5508 6420 7128 12386 12847  
               
               
                   
                 12942 15305 15592 16799 18033 19134 20713  
               
               
                   
                 20870 21589 26380 27538 27577 27971 29744 32344  
               
               
                   
                 32347 32673 32892 33018 33674 33811 34253 34511 
               
               
                 4 
                 6 24 72 2552 3171 5179 11519 12484 13096 13282 15226  
               
               
                   
                 18193 19995 25166 25303 25693 26821 29193  
               
               
                   
                 30666 31952 33137 33187 33190 33319 33653 33950  
               
               
                   
                 34062 34255 34292 34365 34433 34443 34527 
               
               
                 5 
                 1 12 26 29 85 1532 3870 6763 7533 7630 8022 8857  
               
               
                   
                 11667 11919 14987 16133 20999 21830 23522  
               
               
                   
                 24160 27671 28451 30618 31556 31894 33436 33543  
               
               
                   
                 34146 34197 34313 34437 34480 34550 
               
               
                 6 
                 13 44 2482 5068 8153 13233 13728 14548 17278 20027  
               
               
                   
                 21273 22112 22376 24799 29175 
               
               
                 7 
                 26 50 8325 8891 12816 15672 15933 24049 30372 31245  
               
               
                   
                 333194 3238 33934 34093 34547 
               
               
                 8 
                 1412 6334 7945 8866 10886 14521 17224 23693 25160  
               
               
                   
                 29267 31337 31893 32346 33195 33687 
               
               
                 9 
                 27 47 14505 14786 18416 19963 23250 23475 27275 27921  
               
               
                   
                 28090 33985 34371 34374 34512 
               
               
                 10 
                 16 31 4924 7028 10240 12380 13479 16405 20197 27989  
               
               
                   
                 28084 32440 33996 34090 34435 
               
               
                 11 
                 17 57 95 6786 7427 7548 10452 13714 25632 30647 33054  
               
               
                   
                 34195 34237 34304 34447 
               
               
                 12 
                 4 62 331 10220 10518 10575 18401 19286 28718 30521  
               
               
                   
                 30968 31329 31848 32614 34343 
               
               
                 13 
                 42 79 4682 4747 7335 11487 17405 18089 19470 22457  
               
               
                   
                 33433 34373 34471 34519 34540 
               
               
                 14 
                 27 65 4911 10752 14803 24122 24531 25322 29130 30081  
               
               
                   
                 31280 32050 32693 34435 34508 
               
               
                 15 
                 24 29 2107 2152 5271 11032 14001 14902 21705 23126  
               
               
                   
                 31276 33946 34372 34380 34469 
               
               
                 16 
                 16 62 72 7470 14839 15299 15894 17716 18068 24959  
               
               
                   
                 25024 33343 34186 34398 34429 
               
               
                 17 
                 37 56 70 2089 10016 11316 14652 15665 17202 19804  
               
               
                   
                 19847 30498 33938 34126 34391 
               
               
                 18 
                 68 963 2099 9596 17606 19249 21839 27437 29901 30714  
               
               
                   
                 33060 33456 34347 34498 34527 
               
               
                 19 
                 6 69 1845 2504 7189 8603 10379 11421 13742 15757  
               
               
                   
                 16857 20642 28039 32833 34270 
               
               
                 20 
                 2235 15032 31823 
               
               
                 21 
                 4737 33978 34504 
               
               
                 22 
                 2 20263 30373 
               
               
                 23 
                 923 18929 25743 
               
               
                 24 
                 4587 22945 28380 
               
               
                 25 
                 22094 26147 34544 
               
               
                 26 
                 5177 20758 26476 
               
               
                 27 
                 8938 17291 27352 
               
               
                 28 
                 5286 24717 29331 
               
               
                 29 
                 71 16442 32683 
               
               
                 30 
                 81 22810 28015 
               
               
                 31 
                 14112 14419 29708 
               
               
                 32 
                 4156 7522 23358 
               
               
                 33 
                 12850 20777 28294 
               
               
                 34 
                 14692 31178 34238 
               
               
                 35 
                 3447 12356 21997 
               
               
                 36 
                 6098 15443 33447 
               
               
                 37 
                 5947 11648 21719 
               
               
                 38 
                 72 8695 18421 
               
               
                 39 
                 2173 18978 27232 
               
               
                 40 
                 13656 18222 19869 
               
               
                 41 
                 49 24684 33849 
               
               
                 42 
                 84 13870 18354 
               
               
                 43 
                 54 10089 10516 
               
               
                 44 
                 8035 18741 23775 
               
               
                 45 
                 7553 13539 25652 
               
               
                 46 
                 9116 26724 27525 
               
               
                 47 
                 22960 24382 26185 
               
               
                 48 
                 17384 24749 26726 
               
               
                 49 
                 12197 18965 32473 
               
               
                 50 
                 95 23126 26909 
               
               
                 51 
                 19327 31338 34320 
               
               
                 52 
                 9843 34130 34381 
               
               
                 53 
                 4031 9940 22329 
               
               
                 54 
                 58 31795 34468 
               
               
                 55 
                 103 17411 25220 
               
               
                 56 
                 26 4338 24625 
               
               
                 57 
                 9758 34395 34531 
               
               
                 58 
                 2186 17077 27646 
               
               
                 59 
                 9156 19462 34059 
               
               
                 60 
                 6 59 29352 
               
               
                 61 
                 16316 29453 34128 
               
               
                 62 
                 16244 32865 34517 
               
               
                 63 
                 918 22159 29265 
               
               
                 64 
                 13612 19465 20671 
               
               
                 65 
                 1 8261 8849 
               
               
                 66 
                 11214 28864 32696 
               
               
                 67 
                 11513 27595 34479 
               
               
                 68 
                 11895 21430 34524 
               
               
                 69 
                 82 5535 10552 
               
               
                 70 
                 66 15799 26966 
               
               
                 71 
                 20555 21816 32855 
               
               
                 72 
                 3772 27923 33492 
               
               
                 73 
                 12837 15856 21575 
               
               
                 74 
                 2 16865 34413 
               
               
                 75 
                 2682 2702 21630 
               
               
                 76 
                 10 22173 34016 
               
               
                 77 
                 9740 23216 33800 
               
               
                 78 
                 61 33792 33839 
               
               
                 79 
                 3961 29314 33446 
               
               
                 80 
                 11337 16620 20008 
               
               
                 81 
                 18461 25285 34267 
               
               
                 82 
                 46 117 8394 
               
               
                 83 
                 12291 25671 34505 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 21 
               
               
                   
               
               
                 i 
                 Index of row where 1 is located in the 0th column of the ith column group 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 0 
                 7 15 26 69 1439 3712 5756 5792 5911 8456 10579  
               
               
                   
                 19462 19782 21709 23214 25142 26040 30206  
               
               
                   
                 30475 31211 31427 32105 32989 33082 33502 34116  
               
               
                   
                 34241 34288 34292 34318 34373 34390 34465 
               
               
                 1 
                 83 1159 2271 6500 6807 7823 10344 10700 13367  
               
               
                   
                 14162 14242 14352 15015 17301 18952 20811  
               
               
                   
                 24974 25795 27868 28081 33077 33204 33262  
               
               
                   
                 33350 33516 33677 33680 33930 34090 34250 34290  
               
               
                   
                 34377 34398 
               
               
                 2 
                 25 2281 2995 3321 6006 7482 8428 11489 11601  
               
               
                   
                 14011 17409 26210 29945 30675 31101 31355  
               
               
                   
                 31421 31543 31697 32056 32216 33282 33453 33487  
               
               
                   
                 33696 34044 34107 34213 34247 34261  
               
               
                   
                 34276 34467 34495 
               
               
                 3 
                 043 87 2530 4485 4595 9951 11212 12270 12344  
               
               
                   
                 15566 21335 24699 26580 28518 28564 28812 29821  
               
               
                   
                 30418 31467 31871 32513 32597 33187 33402 33706  
               
               
                   
                 33838 33932 33977 34084 34283 34440 34473 
               
               
                 4 
                 81 3344 5540 7711 13308 15400 15885 18265 18632  
               
               
                   
                 22209 23657 27736 29158 29701 29845 30409  
               
               
                   
                 30654 30855 31420 31604 32519 32901 33267 33444  
               
               
                   
                 33525 33712 33878 34031 34172 34432  
               
               
                   
                 34496 34502 34541 
               
               
                 5 
                 42 50 66 2501 4706 6715 6970 8637 9999 14555  
               
               
                   
                 22776 26479 27442 27984 28534 29587 31309  
               
               
                   
                 31783 31907 31927 31934 32313 32369 32830 33364  
               
               
                   
                 33434 33553 33654 33725 33889 33962 34467 34482 
               
               
                 6 
                 6534 7122 8723 13137 13183 15818 18307 19324 20017  
               
               
                   
                 26389 29326 31464 32678 33668 34217 
               
               
                 7 
                 50 113 2119 5038 5581 6397 6550 10987 22308 25141  
               
               
                   
                 25943 29299 30186 33240 33399 
               
               
                 8 
                 7262 8787 9246 10032 10505 13090 14587 14790  
               
               
                   
                 16374 19946 21129 25726 31033 33660 33675 
               
               
                 9 
                 5004 5087 5291 7949 9477 11845 12698 14585  
               
               
                   
                 15239 17486 18100 18259 21409 21789 24280 
               
               
                 10 
                 28 82 3939 5007 6682 10312 12485 14384 21570  
               
               
                   
                 25512 26612 26854 30371 31114 32689 
               
               
                 11 
                 437 3055 9100 9517 12369 19030 19950 21328  
               
               
                   
                 24196 24236 25928 28458 30013 32181 33560 
               
               
                 12 
                 18 3590 4832 7053 8919 21149 24256 26543 27266  
               
               
                   
                 30747 31839 32671 33089 33571 34296 
               
               
                 13 
                 2678 4569 4667 6551 7639 10057 24276 24563 25818  
               
               
                   
                 26592 27879 28028 29444 29873 34017 
               
               
                 14 
                 72 77 2874 9092 10041 13669 20676 20778 25566 28470  
               
               
                   
                 28888 30338 31772 32143 33939 
               
               
                 15 
                 296 2196 7309 11901 14025 15733 16768 23587  
               
               
                   
                 25489 30936 31533 33749 34331 34431 34507 
               
               
                 16 
                 6 8144 12490 13275 14140 18706 20251 20644 21441  
               
               
                   
                 21938 23703 34190 34444 34463 34495 
               
               
                 17 
                 5108 14499 15734 19222 24695 25667 28359 28432  
               
               
                   
                 30411 30720 34161 34386 34465 34511 34522 
               
               
                 18 
                 61 89 3042 5524 12128 22505 22700 22919 24454  
               
               
                   
                 30526 33437 34114 34188 34490 34502 
               
               
                 19 
                 11 83 4668 4856 6361 11633 15342 16393 16958  
               
               
                   
                 26613 29136 30917 32559 34346 34504 
               
               
                 20 
                 3185 9728 25062 
               
               
                 21 
                 1643 5531 21573 
               
               
                 22 
                 2285 6088 24083 
               
               
                 23 
                 78 14678 19119 
               
               
                 24 
                 49 13705 33535 
               
               
                 25 
                 21192 32280 32781 
               
               
                 26 
                 10753 21469 22084 
               
               
                 27 
                 10082 11950 13889 
               
               
                 28 
                 7861 25107 29167 
               
               
                 29 
                 14051 34171 34430 
               
               
                 30 
                 706 894 8316 
               
               
                 31 
                 29693 30445 32281 
               
               
                 32 
                 10202 30964 34448 
               
               
                 33 
                 15815 32453 34463 
               
               
                 34 
                 4102 21608 24740 
               
               
                 35 
                 4472 29399 31435 
               
               
                 36 
                 1162 7118 23226 
               
               
                 37 
                 4791 33548 34096 
               
               
                 38 
                 1084 34099 34418 
               
               
                 39 
                 1765 20745 33714 
               
               
                 40 
                 1302 21300 33655 
               
               
                 41 
                 33 8736 16646 
               
               
                 42 
                 53 18671 19089 
               
               
                 43 
                 21 572 2028 
               
               
                 44 
                 3339 11506 16745 
               
               
                 45 
                 285 6111 12643 
               
               
                 46 
                 27 10336 11586 
               
               
                 47 
                 21046 32728 34538 
               
               
                 48 
                 22215 24195 34026 
               
               
                 49 
                 19975 26938 29374 
               
               
                 50 
                 16473 26777 34212 
               
               
                 51 
                 20 29260 32784 
               
               
                 52 
                 35 31645 32837 
               
               
                 53 
                 26132 34410 34495 
               
               
                 54 
                 12446 20649 26851 
               
               
                 55 
                 6796 10992 31061 
               
               
                 56 
                 0 46 8420 
               
               
                 57 
                 10 636 22885 
               
               
                 58 
                 7183 16342 18305 
               
               
                 59 
                 1 5604 28258 
               
               
                 60 
                 6071 18675 34489 
               
               
                 61 
                 16786 25023 33323 
               
               
                 62 
                 3573 5081 10925 
               
               
                 63 
                 5067 31761 34415 
               
               
                 64 
                 3735 33534 34522 
               
               
                 65 
                 85 32829 34518 
               
               
                 66 
                 6555 23368 34559 
               
               
                 67 
                 22083 29335 29390 
               
               
                 68 
                 6738 21110 34316 
               
               
                 69 
                 120 4192 11123 
               
               
                 70 
                 3313 4144 20824 
               
               
                 71 
                 27783 28550 31034 
               
               
                 72 
                 6597 8164 34427 
               
               
                 73 
                 18009 23474 32460 
               
               
                 74 
                 94 6342 12656 
               
               
                 75 
                 17 31962 34535 
               
               
                 76 
                 15091 24955 28545 
               
               
                 77 
                 15 3213 28298 
               
               
                 78 
                 26562 30236 34537 
               
               
                 79 
                 16832 20334 24628 
               
               
                 80 
                 4841 20669 26509 
               
               
                 81 
                 18055 23700 34534 
               
               
                 82 
                 23576 31496 34492 
               
               
                 83 
                 10699 13826 34440 
               
               
                   
               
            
           
         
       
     
     In another example, when the length N ldpc  of the LDPC codeword is 64800, the code rate R is 8/15, and M is 360, the indexes of the rows where 1 is located in the 0 th  column of the i th  column group of the information word submatrix  210  are as shown in Table 22 presented below: 
     
       
         
           
               
               
             
               
                 TABLE 22 
               
               
                   
               
               
                 i 
                 Index of row where 1 is located in the 0th column of the ith column group 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 0 
                 2768 3039 4059 5856 6245 7013 8157 9341 9802 10470 11521 12083 16610 18361 
               
               
                   
                 20321 24601 27420 28206 29788 
               
               
                 1 
                 2739 8244 8891 9157 12624 12973 15534 16622 16919 18402 18780 19854 20220 
               
               
                   
                 20543 22306 25540 27478 27678 28053 
               
               
                 2 
                 1727 2268 6246 7815 9010 9556 10134 10472 11389 14599 15719 16204 17342 17666 
               
               
                   
                 18850 22058 25579 25860 29207 
               
               
                 3 
                 28 1346 3721 5565 7019 9240 12355 13109 14800 16040 16839 17369 17631 19357 
               
               
                   
                 19473 19891 20381 23911 29683 
               
               
                 4 
                 869 2450 4386 5316 6160 7107 10362 11132 11271 13149 16397 16532 17113 19894 
               
               
                   
                 22043 22784 27383 28615 28804 
               
               
                 5 
                 508 4292 5831 8559 10044 10412 11283 14810 15888 17243 17538 19903 20528 
               
               
                   
                 22090 22652 27235 27384 28208 28485 
               
               
                 6 
                 389 2248 5840 6043 7000 9054 11075 11760 12217 12565 13587 15403 19422 19528 
               
               
                   
                 21493 25142 27777 28566 28702 
               
               
                 7 
                 1015 2002 5764 6777 9346 9629 11039 11153 12690 13068 13990 16841 17702 20021 
               
               
                   
                 24106 26300 29332 30081 30196 
               
               
                 8 
                 1480 3084 3467 4401 4798 5187 7851 11368 12323 14325 14546 16360 17158 18010 
               
               
                   
                 21333 25612 26556 26906 27005 
               
               
                 9 
                 6925 8876 12392 14529 15253 15437 19226 19950 20321 23021 23651 24393 24653 
               
               
                   
                 26668 27205 28269 28529 29041 29292 
               
               
                 10 
                 2547 3404 3538 4666 5126 5468 7695 8799 14732 15072 15881 17410 18971 19609 
               
               
                   
                 19717 22150 24941 27908 29018 
               
               
                 11 
                 888 1581 2311 5511 7218 9107 10454 12252 13662 15714 15894 17025 18671 24304 
               
               
                   
                 25316 25556 28489 28977 29212 
               
               
                 12 
                 1047 1494 1718 4645 5030 6811 7868 8146 10611 15767 17682 18391 22614 23021 
               
               
                   
                 23763 25478 26491 29088 29757 
               
               
                 13 
                 59 1781 1900 3814 4121 8044 8906 9175 11156 14841 15789 16033 16755 17292 
               
               
                   
                 18550 19310 22505 29567 29850 
               
               
                 14 
                 1952 3057 4399 9476 10171 10769 11335 11569 15002 19501 20621 22642 23452 
               
               
                   
                 24360 25109 25290 25828 28505 29122 
               
               
                 15 
                 2895 3070 3437 4764 4905 6670 9244 11845 13352 13573 13975 14600 15871 17996 
               
               
                   
                 19672 20079 20579 25327 27958 
               
               
                 16 
                 612 1528 2004 4244 4599 4926 5843 7684 10122 10443 12267 14368 18413 19058 
               
               
                   
                 22985 24257 26202 26596 27899 
               
               
                 17 
                 1361 2195 4146 6708 7158 7538 9138 9998 14862 15359 16076 18925 21401 21573 
               
               
                   
                 22503 24146 24247 27778 29312 
               
               
                 18 
                 5229 6235 7134 7655 9139 13527 15408 16058 16705 18320 19909 20901 22238 
               
               
                   
                 22437 23654 25131 27550 28247 29903 
               
               
                 19 
                 697 2035 4887 5275 6909 9166 11805 15338 16381 18403 20425 20688 21547 24590 
               
               
                   
                 25171 26726 28848 29224 29412 
               
               
                 20 
                 5379 17329 22659 23062 
               
               
                 21 
                 11814 14759 22329 22936 
               
               
                 22 
                 2423 2811 10296 12727 
               
               
                 23 
                 8460 15260 16769 17290 
               
               
                 24 
                 14191 14608 29536 30187 
               
               
                 25 
                 7103 10069 20111 22850 
               
               
                 26 
                 4285 15413 26448 29069 
               
               
                 27 
                 548 2137 9189 10928 
               
               
                 28 
                 4581 7077 23382 23949 
               
               
                 29 
                 3942 17248 19486 27922 
               
               
                 30 
                 8668 10230 16922 26678 
               
               
                 31 
                 6158 9980 13788 28198 
               
               
                 32 
                 12422 16076 24206 29887 
               
               
                 33 
                 8778 10649 18747 22111 
               
               
                 34 
                 21029 22677 27150 28980 
               
               
                 35 
                 7918 15423 27672 27803 
               
               
                 36 
                 5927 18086 23525 
               
               
                 37 
                 3397 15058 30224 
               
               
                 38 
                 24016 25880 26268 
               
               
                 39 
                 1096 4775 7912 
               
               
                 40 
                 3259 17301 20802 
               
               
                 41 
                 129 8396 15132 
               
               
                 42 
                 17825 28119 28676 
               
               
                 43 
                 2343 8382 28840 
               
               
                 44 
                 3907 18374 20939 
               
               
                 45 
                 1132 1290 8786 
               
               
                 46 
                 1481 4710 28846 
               
               
                 47 
                 2185 3705 26834 
               
               
                 48 
                 5496 15681 21854 
               
               
                 49 
                 12697 13407 22178 
               
               
                 50 
                 12788 21227 22894 
               
               
                 51 
                 629 2854 6232 
               
               
                 52 
                 2289 18227 27458 
               
               
                 53 
                 7593 21935 23001 
               
               
                 54 
                 3836 7081 12282 
               
               
                 55 
                 7925 18440 23135 
               
               
                 56 
                 497 6342 9717 
               
               
                 57 
                 11199 22046 30067 
               
               
                 58 
                 12572 28045 28990 
               
               
                 59 
                 1240 2023 10933 
               
               
                 60 
                 19566 20629 25186 
               
               
                 61 
                 6442 13303 28813 
               
               
                 62 
                 4765 10572 16180 
               
               
                 63 
                 552 19301 24286 
               
               
                 64 
                 6782 18480 21383 
               
               
                 65 
                 11267 12288 15758 
               
               
                 66 
                 771 5652 15531 
               
               
                 67 
                 16131 20047 25649 
               
               
                 68 
                 13227 23035 24450 
               
               
                 69 
                 4839 13467 27488 
               
               
                 70 
                 2852 4677 22993 
               
               
                 71 
                 2504 28116 29524 
               
               
                 72 
                 12518 17374 24267 
               
               
                 73 
                 1222 11859 27922 
               
               
                 74 
                 9660 17286 18261 
               
               
                 75 
                 232 11296 29978 
               
               
                 76 
                 9750 11165 16295 
               
               
                 77 
                 4894 9505 23622 
               
               
                 78 
                 10861 11980 14110 
               
               
                 79 
                 2128 15883 22836 
               
               
                 80 
                 6274 17243 21989 
               
               
                 81 
                 10866 13202 22517 
               
               
                 82 
                 11159 16111 21608 
               
               
                 83 
                 3719 18787 22100 
               
               
                 84 
                 1756 2020 23901 
               
               
                 85 
                 20913 29473 30103 
               
               
                 86 
                 2729 15091 26976 
               
               
                 87 
                 4410 8217 12963 
               
               
                 88 
                 5395 24564 28235 
               
               
                 89 
                 3859 17909 23051 
               
               
                 90 
                 5733 26005 29797 
               
               
                 91 
                 1935 3492 29773 
               
               
                 92 
                 11903 21380 29914 
               
               
                 93 
                 6091 10469 29997 
               
               
                 94 
                 2895 8930 15594 
               
               
                 95 
                 1827 10028 20070 
               
               
                   
               
            
           
         
       
     
     In another example, when the length N ldpc  of the LDPC codeword is 64800, the code rate R is 9/15, and M is 360, the indexes of the rows where 1 is located in the 0 th  column of the i th  column group of the information word submatrix  210  are as shown in Table 23 presented below: 
     
       
         
           
               
               
             
               
                 TABLE 23 
               
               
                   
               
               
                 i 
                 Index of row where 1 is located in the 0th column of the ith column group 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 0 
                 113 1557 3316 5680 6241 10407 13404 13947 14040 14353 15522 15698 16079  
               
               
                   
                 17363 19374 19543 20530 22833 24339 
               
               
                 1 
                 271 1361 6236 7006 7307 7333 12768 15441 15568 17923 18341 20321 21502  
               
               
                   
                 22023 23938 25351 25590 25876 25910 
               
               
                 2 
                 73 605 872 4008 6279 7653 10346 10799 12482 12935 13604 15909 16526 19782 
               
               
                   
                 20506 22804 23629 24859 25600 
               
               
                 3 
                 1445 1690 4304 4851 8919 9176 9252 13783 16076 16675 17274 18806 18882  
               
               
                   
                 20819 21958 22451 23869 23999 24177 
               
               
                 4 
                 1290 2337 5661 6371 8996 10102 10941 11360 12242 14918 16808 20571 23374 
               
               
                   
                 24046 25045 25060 25662 25783 25913 
               
               
                 5 
                 28 42 1926 3421 3503 8558 9453 10168 15820 17473 19571 19685 22790 23336  
               
               
                   
                 23367 23890 24061 25657 25680 
               
               
                 6 
                 0 1709 4041 4932 5968 7123 8430 9564 10596 11026 14761 19484 20762 20858  
               
               
                   
                 23803 24016 24795 25853 25863 
               
               
                 7 
                 29 1625 6500 6609 16831 18517 18568 18738 19387 20159 20544 21603 21941  
               
               
                   
                 24137 24269 24416 24803 25154 25395 
               
               
                 8 
                 55 66 871 3700 11426 13221 15001 16367 17601 18380 22796 23488 23938 25476 
               
               
                   
                 25635 25678 25807 25857 25872 
               
               
                 9 
                 1 19 5958 8548 8860 11489 16845 18450 18469 19496 20190 23173 25262 25566 
               
               
                   
                 25668 25679 25858 25888 25915 
               
               
                 10 
                 7520 7690 8855 9183 14654 16695 17121 17854 18083 18428 19633 20470 20736 
               
               
                   
                 21720 22335 23273 25083 25293 25403 
               
               
                 11 
                 48 58 410 1299 3786 10668 18523 18963 20864 22106 22308 23033 23107 23128 
               
               
                   
                 23990 24286 24409 24595 25802 
               
               
                 12 
                 12 51 3894 6539 8276 10885 11644 12777 13427 14039 15954 17078 19053 20537 
               
               
                   
                 22863 24521 25087 25463 25838 
               
               
                 13 
                 3509 8748 9581 11509 15884 16230 17583 19264 20900 21001 21310 22547 22756 
               
               
                   
                 22959 24768 24814 25594 25626 25880 
               
               
                 14 
                 21 29 69 1448 2386 4601 6626 6667 10242 13141 13852 14137 18640 19951 22449 
               
               
                   
                 23454 24431 25512 25814 
               
               
                 15 
                 18 53 7890 9934 10063 16728 19040 19809 20825 21522 21800 23582 24556 25031 
               
               
                   
                 25547 25562 25733 25789 25906 
               
               
                 16 
                 4096 4582 5766 5894 6517 10027 12182 13247 15207 17041 18958 20133 20503 
               
               
                   
                 22228 24332 24613 25689 25855 25883 
               
               
                 17 
                 0 25 819 5539 7076 7536 7695 9532 13668 15051 17683 19665 20253 21996 24136 
               
               
                   
                 24890 25758 25784 25807 
               
               
                 18 
                 34 40 44 4215 6076 7427 7965 8777 11017 15593 19542 22202 22973 23397 23423 
               
               
                   
                 24418 24873 25107 25644 
               
               
                 19 
                 1595 6216 22850 25439 
               
               
                 20 
                 1562 15172 19517 22362 
               
               
                 21 
                 7508 12879 24324 24496 
               
               
                 22 
                 6298 15819 16757 18721 
               
               
                 23 
                 11173 15175 19966 21195 
               
               
                 24 
                 59 13505 16941 23793 
               
               
                 25 
                 2267 4830 12023 20587 
               
               
                 26 
                 8827 9278 13072 16664 
               
               
                 27 
                 14419 17463 23398 25348 
               
               
                 28 
                 6112 16534 20423 22698 
               
               
                 29 
                 493 8914 21103 24799 
               
               
                 30 
                 6896 12761 13206 25873 
               
               
                 31 
                 2 1380 12322 21701 
               
               
                 32 
                 11600 21306 25753 25790 
               
               
                 33 
                 8421 13076 14271 15401 
               
               
                 34 
                 9630 14112 19017 20955 
               
               
                 35 
                 212 13932 21781 25824 
               
               
                 36 
                 5961 9110 16654 19636 
               
               
                 37 
                 58 5434 9936 12770 
               
               
                 38 
                 6575 11433 19798 
               
               
                 39 
                 2731 7338 20926 
               
               
                 40 
                 14253 18463 25404 
               
               
                 41 
                 21791 24805 25869 
               
               
                 42 
                 2 11646 15850 
               
               
                 43 
                 6075 8586 23819 
               
               
                 44 
                 18435 22093 24852 
               
               
                 45 
                 2103 2368 11704 
               
               
                 46 
                 10925 17402 18232 
               
               
                 47 
                 9062 25061 25674 
               
               
                 48 
                 18497 20853 23404 
               
               
                 49 
                 18606 19364 19551 
               
               
                 50 
                 7 1022 25543 
               
               
                 51 
                 6744 15481 25868 
               
               
                 52 
                 9081 17305 25164 
               
               
                 53 
                 8 23701 25883 
               
               
                 54 
                 9680 19955 22848 
               
               
                 55 
                 56 4564 19121 
               
               
                 56 
                 5595 15086 25892 
               
               
                 57 
                 3174 17127 23183 
               
               
                 58 
                 19397 19817 20275 
               
               
                 59 
                 12561 24571 25825 
               
               
                 60 
                 7111 9889 25865 
               
               
                 61 
                 19104 20189 21851 
               
               
                 62 
                 549 9686 25548 
               
               
                 63 
                 6586 20325 25906 
               
               
                 64 
                 3224 20710 21637 
               
               
                 65 
                 641 15215 25754 
               
               
                 66 
                 13484 23729 25818 
               
               
                 67 
                 2043 7493 24246 
               
               
                 68 
                 16860 25230 25768 
               
               
                 69 
                 22047 24200 24902 
               
               
                 70 
                 9391 18040 19499 
               
               
                 71 
                 7855 24336 25069 
               
               
                 72 
                 23834 25570 25852 
               
               
                 73 
                 1977 8800 25756 
               
               
                 74 
                 6671 21772 25859 
               
               
                 75 
                 3279 6710 24444 
               
               
                 76 
                 24099 25117 25820 
               
               
                 77 
                 5553 12306 25915 
               
               
                 78 
                 48 11107 23907 
               
               
                 79 
                 10832 11974 25773 
               
               
                 80 
                 2223 17905 25484 
               
               
                 81 
                 16782 17135 20446 
               
               
                 82 
                 475 2861 3457 
               
               
                 83 
                 16218 22449 24362 
               
               
                 84 
                 11716 22200 25897 
               
               
                 85 
                 8315 15009 22633 
               
               
                 86 
                 13 20480 25852 
               
               
                 87 
                 12352 18658 25687 
               
               
                 88 
                 3681 14794 23703 
               
               
                 89 
                 30 24531 25846 
               
               
                 90 
                 4103 22077 24107 
               
               
                 91 
                 23837 25622 25812 
               
               
                 92 
                 3627 13387 25839 
               
               
                 93 
                 908 5367 19388 
               
               
                 94 
                 0 6894 25795 
               
               
                 95 
                 20322 23546 25181 
               
               
                 96 
                 8178 25260 25437 
               
               
                 97 
                 2449 13244 22565 
               
               
                 98 
                 31 18928 22741 
               
               
                 99 
                 1312 5134 14838 
               
               
                 100 
                 6085 13937 24220 
               
               
                 101 
                 66 14633 25670 
               
               
                 102 
                 47 22512 25472 
               
               
                 103 
                 8867 24704 25279 
               
               
                 104 
                 6742 21623 22745 
               
               
                 105 
                 147 9948 24178 
               
               
                 106 
                 8522 24261 24307 
               
               
                 107 
                 19202 22406 24609 
               
               
                   
               
            
           
         
       
     
     In another example, when the length N ldpc  of the LDPC codeword is 64800, the code rate R is 10/15, and M is 360, the indexes of the rows where 1 is located in the 0 th  column of the i th  column group of the information word submatrix  210  are as shown in Table 24 or 25 presented below. 
     
       
         
           
               
               
             
               
                 TABLE 24 
               
               
                   
               
               
                 i 
                 Index of row where 1 is located in the 0th column of the ith column group 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 0 
                 979 1423 4166 4609 6341 8258 10334 10548 14098 14514 17051 17333  
               
               
                   
                 17653 17830 17990 
               
               
                 1 
                 2559 4025 6344 6510 9167 9728 11312 14856 17104 17721 18600 18791  
               
               
                   
                 19079 19697 19840 
               
               
                 2 
                 3243 6894 7950 10539 12042 13233 13938 14752 16449 16727 17025 18297 
               
               
                   
                 18796 19400 21577 
               
               
                 3 
                 3272 3574 6341 6722 9191 10807 10957 12531 14036 15580 16651 17007 
               
               
                   
                 17309 19415 19845 
               
               
                 4 
                 155 4598 10201 10975 11086 11296 12713 15364 15978 16395 17542 18164 
               
               
                   
                 18451 18612 20617 
               
               
                 5 
                 1128 1999 3926 4069 5558 6085 6337 8386 10693 12450 15438 16223 16370 
               
               
                   
                 17308 18634 
               
               
                 6 
                 2408 2929 3630 4357 5852 7329 8536 8695 10603 11003 14304 14937 15767 
               
               
                   
                 18402 21502 
               
               
                 7 
                 199 3066 6446 6849 8973 9536 10452 12857 13675 15913 16717 17654  
               
               
                   
                 19802 20115 21579 
               
               
                 8 
                 312 870 2095 2586 5517 6196 6757 7311 7368 13046 15384 18576 20349  
               
               
                   
                 21424 21587 
               
               
                 9 
                 985 1591 3248 3509 3706 3847 6174 6276 7864 9033 13618 15675 16446  
               
               
                   
                 18355 18843 
               
               
                 10 
                 975 3774 4083 5825 6166 7218 7633 9657 10103 13052 14240 17320 18126 
               
               
                   
                 19544 20208 
               
               
                 11 
                 1795 2005 2544 3418 6148 8051 9066 9725 10676 10752 11512 15171  
               
               
                   
                 17523 20481 21059 
               
               
                 12 
                 167 315 1824 2325 2640 2868 6070 6597 7016 8109 9815 11608 16142  
               
               
                   
                 17912 19625 
               
               
                 13 
                 1298 1896 3039 4303 4690 8787 12241 13600 14478 15492 16602 17115  
               
               
                   
                 17913 19466 20597 
               
               
                 14 
                 568 3695 6045 6624 8131 8404 8590 9059 9246 11570 14336 18657 18941 
               
               
                   
                 19218 21506 
               
               
                 15 
                 228 1889 1967 2299 3011 5074 7044 7596 7689 9534 10244 10697 11691  
               
               
                   
                 17902 21410 
               
               
                 16 
                 1330 1579 1739 2234 3701 3865 5713 6677 7263 11172 12143 12765 17121 
               
               
                   
                 20011 21436 
               
               
                 17 
                 303 1668 2501 4925 5778 5985 9635 10140 10820 11779 11849 12058  
               
               
                   
                 15650 20426 20527 
               
               
                 18 
                 698 2484 3071 3219 4054 4125 5663 5939 6928 7086 8054 12173 16280  
               
               
                   
                 17945 19302 
               
               
                 19 
                 232 1619 3040 4901 7438 8135 9117 9233 10131 13321 17347 17436 18193 
               
               
                   
                 18586 19929 
               
               
                 20 
                 12 3721 6254 6609 7880 8139 10437 12262 13928 14065 14149 15032 15694 
               
               
                   
                 16264 18883 
               
               
                 21 
                 482 915 1548 1637 6687 9338 10163 11768 11970 15524 15695 17386 18787 
               
               
                   
                 19210 19340 
               
               
                 22 
                 1291 2500 4109 4511 5099 5194 10014 13165 13256 13972 15409 16113  
               
               
                   
                 16214 18584 20998 
               
               
                 23 
                 1761 4778 7444 7740 8129 8341 8931 9136 9207 10003 10678 13959 17673 
               
               
                   
                 18194 20990 
               
               
                 24 
                 3060 3522 5361 5692 6833 8342 8792 11023 11211 11548 11914 13987  
               
               
                   
                 15442 15541 19707 
               
               
                 25 
                 1322 2348 2970 5632 6349 7577 8782 9113 9267 9376 12042 12943 16680 
               
               
                   
                 16970 21321 
               
               
                 26 
                 6785 11960 21455 
               
               
                 27 
                 1223 15672 19550 
               
               
                 28 
                 5976 11335 20385 
               
               
                 29 
                 2818 9387 15317 
               
               
                 30 
                 2763 3554 18102 
               
               
                 31 
                 5230 11489 18997 
               
               
                 32 
                 5809 15779 20674 
               
               
                 33 
                 2620 17838 18533 
               
               
                 34 
                 3025 9342 9931 
               
               
                 35 
                 3728 5337 12142 
               
               
                 36 
                 2520 6666 9164 
               
               
                 37 
                 12892 15307 20912 
               
               
                 38 
                 10736 12393 16539 
               
               
                 39 
                 1075 2407 12853 
               
               
                 40 
                 4921 5411 18206 
               
               
                 41 
                 5955 15647 16838 
               
               
                 42 
                 6384 10336 19266 
               
               
                 43 
                 429 10421 17266 
               
               
                 44 
                 4880 10431 12208 
               
               
                 45 
                 2910 11895 12442 
               
               
                 46 
                 7366 18362 18772 
               
               
                 47 
                 4341 7903 14994 
               
               
                 48 
                 4564 6714 7378 
               
               
                 49 
                 4639 8652 18871 
               
               
                 50 
                 15787 18048 20246 
               
               
                 51 
                 3241 11079 13640 
               
               
                 52 
                 1559 2936 15881 
               
               
                 53 
                 2737 6349 10881 
               
               
                 54 
                 10394 16107 17073 
               
               
                 55 
                 8207 9043 12874 
               
               
                 56 
                 7805 16058 17905 
               
               
                 57 
                 11189 15767 17764 
               
               
                 58 
                 5823 12923 14316 
               
               
                 59 
                 11080 20390 20924 
               
               
                 60 
                 568 8263 17411 
               
               
                 61 
                 1845 3557 6562 
               
               
                 62 
                 2890 10936 14756 
               
               
                 63 
                 9031 14220 21517 
               
               
                 64 
                 3529 12955 15902 
               
               
                 65 
                 413 6750 8735 
               
               
                 66 
                 6784 12092 16421 
               
               
                 67 
                 12019 13794 15308 
               
               
                 68 
                 12588 15378 17676 
               
               
                 69 
                 8067 14589 19304 
               
               
                 70 
                 1244 5877 6085 
               
               
                 71 
                 15897 19349 19993 
               
               
                 72 
                 1426 2394 12264 
               
               
                 73 
                 3456 8931 12075 
               
               
                 74 
                 13342 15273 20351 
               
               
                 75 
                 9138 13352 20798 
               
               
                 76 
                 7031 7626 14081 
               
               
                 77 
                 4280 4507 15617 
               
               
                 78 
                 4170 10569 14335 
               
               
                 79 
                 3839 7514 16578 
               
               
                 80 
                 4688 12815 18782 
               
               
                 81 
                 4861 7858 9435 
               
               
                 82 
                 605 5445 12912 
               
               
                 83 
                 2280 4734 7311 
               
               
                 84 
                 6668 8128 12638 
               
               
                 85 
                 3733 10621 19534 
               
               
                 86 
                 13933 18316 19341 
               
               
                 87 
                 1786 3037 21566 
               
               
                 88 
                 2202 13239 16432 
               
               
                 89 
                 4882 5808 9300 
               
               
                 90 
                 4580 8484 16754 
               
               
                 91 
                 14630 17502 18269 
               
               
                 92 
                 6889 11119 12447 
               
               
                 93 
                 8162 9078 16330 
               
               
                 94 
                 6538 17851 18100 
               
               
                 95 
                 17763 19793 20816 
               
               
                 96 
                 2183 11907 17567 
               
               
                 97 
                 6640 14428 15175 
               
               
                 98 
                 877 12035 14081 
               
               
                 99 
                 1336 6468 12328 
               
               
                 100 
                 5948 9146 12003 
               
               
                 101 
                 3782 5699 12445 
               
               
                 102 
                 1770 7946 8244 
               
               
                 103 
                 7384 12639 14989 
               
               
                 104 
                 1469 11586 20959 
               
               
                 105 
                 7943 10450 15907 
               
               
                 106 
                 5005 8153 10035 
               
               
                 107 
                 17750 18826 21513 
               
               
                 108 
                 4725 8041 10112 
               
               
                 109 
                 3837 16266 17376 
               
               
                 110 
                 11340 17361 17512 
               
               
                 111 
                 1269 4611 4774 
               
               
                 112 
                 2322 10813 16157 
               
               
                 113 
                 16752 16843 18959 
               
               
                 114 
                 70 4325 18753 
               
               
                 115 
                 3165 8153 15384 
               
               
                 116 
                 160 8045 16823 
               
               
                 117 
                 14112 16724 16792 
               
               
                 118 
                 4291 7667 18176 
               
               
                 119 
                 5943 19879 20721 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 25 
               
               
                   
               
               
                 i 
                 Index of row where 1 is located in the 0th column of the ith column group 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 0 
                 316 1271 3692 9495 12147 12849 14928 16671 16938 17864 19108 
               
               
                   
                 20502 21097 21115 
               
               
                 1 
                 2341 2559 2643 2816 2865 5137 5331 7000 7523 8023 10439 10797 
               
               
                   
                 13208 15041 
               
               
                 2 
                 5556 6858 7677 10162 10207 11349 12321 12398 14787 15743 15859 
               
               
                   
                 15952 19313 20879 
               
               
                 3 
                 349 573 910 2702 3654 6214 9246 9353 10638 11772 14447 14953  
               
               
                   
                 16620 19888 
               
               
                 4  
                 204 1390 2887 3835 6230 6533 7443 7876 9299 10291 10896 13960 
               
               
                   
                 18287 20086 
               
               
                 5 
                 541 2429 2838 7144 8523 8637 10490 10585 11074 12074 15762 
               
               
                   
                 16812 17900 18548 
               
               
                 6 
                 733 1659 3838 5323 5805 7882 9429 10682 13697 16909 18846 19587 
               
               
                   
                 19592 20904 
               
               
                 7  
                 1134 2136 4631 4653 4718 5197 10410 11666 14996 15305 16048 
               
               
                   
                 17417 18960 20303 
               
               
                 8 
                 734 1001 1283 4959 10016 10176 10973 11578 12051 15550 15915 
               
               
                   
                 19022 19430 20121 
               
               
                 9 
                 745 4057 5855 9885 10594 10989 13156 13219 13351 13631 13685 
               
               
                   
                 14577 17713 20386 
               
               
                 10 
                 968 1446 2130 2502 3092 3787 5323 8104 8418 9998 11681 13972  
               
               
                   
                 17747 17929 
               
               
                 11 
                 3020 3857 5275 5786 6319 8608 11943 14062 17144 17752 18001 
               
               
                   
                 18453 19311 21414 
               
               
                 12 
                 709 747 1038 2181 5320 8292 10584 10859 13964 15009 15277 16953 
               
               
                   
                 20675 21509 
               
               
                 13 
                 1663 3247 5003 5760 7186 7360 10346 14211 14717 14792 15155 16128  
               
               
                   
                 17355 17970 
               
               
                 14 
                 516 578 1914 6147 9419 11148 11434 13289 13325 13332 19106 19257 
               
               
                   
                 20962 21556 
               
               
                 15  
                 5009 5632 6531 9430 9886 10621 11765 13969 16178 16413 18110  
               
               
                   
                 18249 20616 20759 
               
               
                 16 
                 457 2686 3318 4608 5620 5858 6480 7430 9602 12691 14664  
               
               
                   
                 18777 20152 20848 
               
               
                 17 
                 33 2877 5334 6851 7907 8654 10688 15401 16123 17942 17969 
               
               
                   
                 18747 18931 20224 
               
               
                 18 
                 87 897 7636 8663 11425 1228 12672 14199 16435 17615 17950 18953  
               
               
                   
                 19667 20281  
               
               
                 19 
                 1042 1832 2545 2719 2947 3672 3700 6249 6398 6833 11114 14283  
               
               
                   
                 17694 20477 
               
               
                 20  
                 326 488 2662 2880 3009 5357 6587 8882 11604 14374 18781 19051  
               
               
                   
                 19057 20508 
               
               
                 21 
                 854 1294 2436 2852 4903 6466 7761 9072 9564 10321 13638  
               
               
                   
                 15658 16946 19119 
               
               
                 22 
                 194 899 1711 2408 2786 5391 7108 8079 8716 11453 17303 19484  
               
               
                   
                 20989 21389 
               
               
                 23 
                 1631 3121 3994 5005 7810 8850 10315 10589 13407 17162 18624 
               
               
                   
                 18758 19311 20301 
               
               
                 24 
                 736 2424 4792 5600 6370 10061 16053 16775 18600 
               
               
                 25 
                 1254 8163 8876 9157 12141 14587 16545 17175 18191 
               
               
                 26 
                 388 6641 8974 10607 10716 14477 16825 17191 18400 
               
               
                 27 
                 5578 6082 6824 7360 7745 8655 11402 11665 12428 
               
               
                 28 
                 3603 8729 13463 14698 15210 19112 19550 20727 21052 
               
               
                 29 
                 48 1732 3805 5158 15442 16909 19854 21071 21579 
               
               
                 30 
                 11707 14014 21531 
               
               
                 31 
                 1542 4133 4925 
               
               
                 32 
                 10083 13505 21198 
               
               
                 33 
                 14300 15765 16752 
               
               
                 34 
                 778 1237 11215 
               
               
                 35 
                 1325 3199 14534 
               
               
                 36  
                 2007 14510 20599 
               
               
                 37 
                 1996 5881 16429 
               
               
                 38 
                 5111 15018 15980 
               
               
                 39 
                 4989 10681 12810 
               
               
                 40 
                 3763 10715 16515 
               
               
                 41 
                 2259 10080 15642 
               
               
                 42 
                 9032 11319 21305 
               
               
                 43 
                 3915 15213 20884 
               
               
                 44 
                 11150 15022 20201 
               
               
                 45 
                 1147 6749 19625 
               
               
                 46 
                 12139 12939 18870 
               
               
                 47 
                 3840 4634 10244 
               
               
                 48 
                 1018 10231 17720 
               
               
                 49 
                 2708 13056 13393 
               
               
                 50 
                 5781 11588 18888 
               
               
                 51 
                 1345 2036 5252 
               
               
                 52 
                 5908 8143 15141 
               
               
                 53 
                 1804 13693 18640 
               
               
                 54 
                 10433 13965 16950 
               
               
                 55 
                 9568 10122 15945 
               
               
                 56 
                 547 6722 14015 
               
               
                 57 
                 321 12844 14095 
               
               
                 58 
                 2632 10513 14936 
               
               
                 59 
                 6369 11995 20321 
               
               
                 60 
                 9920 19136 21529 
               
               
                 61 
                 1990 2726 10183 
               
               
                 62 
                 5763 12118 15467 
               
               
                 63 
                 503 10006 19564 
               
               
                 64 
                 9839 11942 19472 
               
               
                 65 
                 11205 13552 15389 
               
               
                 66 
                 8841 13797 19697 
               
               
                 67 
                 124 6053 18224 
               
               
                 68 
                 6477 14406 21146 
               
               
                 69 
                 1224 8027 16011 
               
               
                 70 
                 3046 4422 17717 
               
               
                 71 
                 739 12308 17760 
               
               
                 72 
                 4014 4130 7835 
               
               
                 73 
                 2266 5652 11981 
               
               
                 74 
                 2711 7970 18317 
               
               
                 75 
                 2196 15229 17217 
               
               
                 76 
                 8636 13302 16764 
               
               
                 77 
                 5612 15010 16657 
               
               
                 78 
                 615 1249 4639 
               
               
                 79 
                 3821 12073 18506 
               
               
                 80 
                 1066 16522 21536 
               
               
                 81 
                 11307 18363 19740 
               
               
                 82 
                 3240 8560 10391 
               
               
                 83 
                 3124 11424 20779 
               
               
                 84 
                 1604 8861 17394 
               
               
                 85 
                 2083 7400 8093 
               
               
                 86 
                 3218 7454 9155 
               
               
                 87 
                 9855 15998 20533 
               
               
                 88 
                 316 2850 20652 
               
               
                 89 
                 5583 9768 10333 
               
               
                 90 
                 7147 7713 18339 
               
               
                 91 
                 12607 17428 21418 
               
               
                 92 
                 14216 16954 18164 
               
               
                 93 
                 8477 15970 18488 
               
               
                 94 
                 1632 8032 9751 
               
               
                 95 
                 4573 9080 13507 
               
               
                 96 
                 11747 12441 13876 
               
               
                 97 
                 1183 15605 16675 
               
               
                 98 
                 4408 10264 17109 
               
               
                 99 
                 5495 7882 12150 
               
               
                 100 
                 1010 3763 5065 
               
               
                 101 
                 9828 18054 21599 
               
               
                 102 
                 6342 7353 15358 
               
               
                 103 
                 6362 9462 19999 
               
               
                 104 
                 7184 13693 17622 
               
               
                 105 
                 4343 4654 10995 
               
               
                 106 
                 7099 8466 18520 
               
               
                 107 
                 11505 14395 15138 
               
               
                 108 
                 6779 16691 18726 
               
               
                 109 
                 7146 12644 20196 
               
               
                 110 
                 5865 16728 19634 
               
               
                 111 
                 4657 8714 21246 
               
               
                 112 
                 4580 5279 18750 
               
               
                 113 
                 3767 6620 18905 
               
               
                 114 
                 9209 13093 17575 
               
               
                 115 
                 12486 15875 19791 
               
               
                 116 
                 8046 14636 17491 
               
               
                 117 
                 2120 4643 13206 
               
               
                 118 
                 6186 9675 12601 
               
               
                 119 
                 784 5770 21585 
               
               
                   
               
            
           
         
       
     
     In another example, when the length N ldpc  of the LDPC codeword is 64800, the code rate R is 12/15, and M is 360, the indexes of the rows where 1 is located in the 0 th  column of the i th  column group of the information word submatrix  210  are as shown in Table 26 presented below: 
     
       
         
           
               
               
             
               
                 TABLE 26 
               
               
                   
               
               
                 i 
                 Index of row where 1 is located in the 0th column of the ith column group 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 0 
                 584 1472 1621 1867 3338 3568 3723 4185 5126 5889 7737 8632 8940 9725 
               
               
                 1 
                 221 445 590 3779 3835 6939 7743 8280 8448 8491 9367 10042 11242 12917 
               
               
                 2 
                 4662 4837 4900 5029 6449 6687 6751 8684 9936 11681 11811 11886 12089 12909 
               
               
                 3 
                 2418 3018 3647 4210 4473 7447 7502 9490 10067 11092 11139 11256 12201 12383 
               
               
                 4 
                 2591 2947 3349 3406 4417 4519 5176 6672 8498 8863 9201 11294 11376 12184 
               
               
                 5 
                 27 101 197 290 871 1727 3911 5411 6676 8701 9350 10310 10798 12439 
               
               
                 6 
                 1765 1897 2923 3584 3901 4048 6963 7054 7132 9165 10184 10824 11278 12669 
               
               
                 7 
                 2183 3740 4808 5217 5660 6375 6787 8219 8466 9037 10353 10583 11118 12762 
               
               
                 8 
                 73 1594 2146 2715 3501 3572 3639 3725 6959 7187 8406 10120 10507 10691 
               
               
                 9 
                 240 732 1215 2185 2788 2830 3499 3881 4197 4991 6425 7061 9756 10491 
               
               
                 10 
                 831 1568 1828 3424 4319 4516 4639 6018 9702 10203 10417 11240 11518 12458 
               
               
                 11 
                 2024 2970 3048 3638 3676 4152 5284 5779 5926 9426 9945 10873 11787 11837 
               
               
                 12 
                 1049 1218 1651 2328 3493 4363 5750 6483 7613 8782 9738 9803 11744 11937 
               
               
                 13 
                 1193 2060 2289 2964 3478 4592 4756 6709 7162 8231 8326 11140 11908 12243 
               
               
                 14 
                 978 2120 2439 3338 3850 4589 6567 8745 9656 9708 10161 10542 10711 12639 
               
               
                 15 
                 2403 2938 3117 3247 3711 5593 5844 5932 7801 10152 10226 11498 12162 12941 
               
               
                 16 
                 1781 2229 2276 2533 3582 3951 5279 5774 7930 9824 10920 11038 12340 12440 
               
               
                 17 
                 289 384 1980 2230 3464 3873 5958 8656 8942 9006 10175 11425 11745 12530 
               
               
                 18 
                 155 354 1090 1330 2002 2236 3559 3705 4922 5958 6576 8564 9972 12760 
               
               
                 19 
                 303 876 2059 2142 5244 5330 6644 7576 8614 9598 10410 10718 11033 12957 
               
               
                 20 
                 3449 3617 4408 4602 4727 6182 8835 8928 9372 9644 10237 10747 11655 12747 
               
               
                 21 
                 811 2565 2820 8677 8974 9632 11069 11548 11839 12107 12411 12695 12812 12890 
               
               
                 22 
                 972 4123 4943 6385 6449 7339 7477 8379 9177 9359 10074 11709 12552 12831 
               
               
                 23 
                 842 973 1541 2262 2905 5276 6758 7099 7894 8128 8325 8663 8875 10050 
               
               
                 24 
                 474 791 968 3902 4924 4965 5085 5908 6109 6329 7931 9038 9401 10568 
               
               
                 25 
                 1397 4461 4658 5911 6037 7127 7318 8678 8924 9000 9473 9602 10446 12692 
               
               
                 26 
                 1334 7571 12881 
               
               
                 27 
                 1393 1447 7972 
               
               
                 28 
                 633 1257 10597 
               
               
                 29 
                 4843 5102 11056 
               
               
                 30 
                 3294 8015 10513 
               
               
                 31 
                 1108 10374 10546 
               
               
                 32 
                 5353 7824 10111 
               
               
                 33 
                 3398 7674 8569 
               
               
                 34 
                 7719 9478 10503 
               
               
                 35 
                 2997 9418 9581 
               
               
                 36 
                 5777 6519 11229 
               
               
                 37 
                 1966 5214 9899 
               
               
                 38 
                 6 4088 5827 
               
               
                 39 
                 836 9248 9612 
               
               
                 40 
                 483 7229 7548 
               
               
                 41 
                 7865 8289 9804 
               
               
                 42 
                 2915 11098 11900 
               
               
                 43 
                 6180 7096 9481 
               
               
                 44 
                 1431 6786 8924 
               
               
                 45 
                 748 6757 8625 
               
               
                 46 
                 3312 4475 7204 
               
               
                 47 
                 1852 8958 11020 
               
               
                 48 
                 1915 2903 4006 
               
               
                 49 
                 6776 10886 12531 
               
               
                 50 
                 2594 9998 12742 
               
               
                 51 
                 159 2002 12079 
               
               
                 52 
                 853 3281 3762 
               
               
                 53 
                 5201 5798 6413 
               
               
                 54 
                 3882 6062 12047 
               
               
                 55 
                 4133 6775 9657 
               
               
                 56 
                 228 6874 11183 
               
               
                 57 
                 7433 10728 10864 
               
               
                 58 
                 7735 8073 12734 
               
               
                 59 
                 2844 4621 11779 
               
               
                 60 
                 3909 7103 12804 
               
               
                 61 
                 6002 9704 11060 
               
               
                 62 
                 5864 6856 7681 
               
               
                 63 
                 3652 5869 7605 
               
               
                 64 
                 2546 2657 4461 
               
               
                 65 
                 2423 4203 9111 
               
               
                 66 
                 244 1855 4691 
               
               
                 67 
                 1106 2178 6371 
               
               
                 68 
                 391 1617 10126 
               
               
                 69 
                 250 9259 10603 
               
               
                 70 
                 3435 4614 6924 
               
               
                 71 
                 1742 8045 9529 
               
               
                 72 
                 7667 8875 11451 
               
               
                 73 
                 4023 6108 6911 
               
               
                 74 
                 8621 10184 11650 
               
               
                 75 
                 6726 10861 12348 
               
               
                 76 
                 3228 6302 7388 
               
               
                 77 
                 1 1137 5358 
               
               
                 78 
                 381 2424 8537 
               
               
                 79 
                 3256 7508 10044 
               
               
                 80 
                 1980 2219 4569 
               
               
                 81 
                 2468 5699 10319 
               
               
                 82 
                 2803 3314 12808 
               
               
                 83 
                 8578 9642 11533 
               
               
                 84 
                 829 4585 7923 
               
               
                 85 
                 59 329 5575 
               
               
                 86 
                 1067 5709 6867 
               
               
                 87 
                 1175 4744 12219 
               
               
                 88 
                 109 2518 6756 
               
               
                 89 
                 2105 10626 11153 
               
               
                 90 
                 5192 10696 10749 
               
               
                 91 
                 6260 7641 8233 
               
               
                 92 
                 2998 3094 11214 
               
               
                 93 
                 3398 6466 11494 
               
               
                 94 
                 6574 10448 12160 
               
               
                 95 
                 2734 10755 12780 
               
               
                 96 
                 1028 7958 10825 
               
               
                 97 
                 8545 8602 10793 
               
               
                 98 
                 392 3398 11417 
               
               
                 99 
                 6639 9291 12571 
               
               
                 100 
                 1067 7919 8934 
               
               
                 101 
                 1064 2848 12753 
               
               
                 102 
                 6076 8656 12690 
               
               
                 103 
                 5504 6193 10171 
               
               
                 104 
                 1951 7156 7356 
               
               
                 105 
                 4389 4780 7889 
               
               
                 106 
                 526 4804 9141 
               
               
                 107 
                 1238 3648 10464 
               
               
                 108 
                 2587 5624 12557 
               
               
                 109 
                 5560 5903 11963 
               
               
                 110 
                 1134 2570 3297 
               
               
                 111 
                 10041 11583 12157 
               
               
                 112 
                 1263 9585 12912 
               
               
                 113 
                 3744 7898 10646 
               
               
                 114 
                 45 9074 10315 
               
               
                 115 
                 1051 6188 10038 
               
               
                 116 
                 2242 8394 12712 
               
               
                 117 
                 3598 9025 12651 
               
               
                 118 
                 2295 3540 5610 
               
               
                 119 
                 1914 4378 12423 
               
               
                 120 
                 1766 3635 12759 
               
               
                 121 
                 5177 9586 11143 
               
               
                 122 
                 943 3590 11649 
               
               
                 123 
                 4864 6905 10454 
               
               
                 124 
                 5852 6042 10421 
               
               
                 125 
                 6095 8285 12349 
               
               
                 126 
                 2070 7171 8563 
               
               
                 127 
                 718 12234 12716 
               
               
                 128 
                 512 10667 11353 
               
               
                 129 
                 3629 6485 7040 
               
               
                 130 
                 2880 8865 11466 
               
               
                 131 
                 4490 10220 11796 
               
               
                 132 
                 5440 8819 9103 
               
               
                 133 
                 5262 7543 12411 
               
               
                 134 
                 516 7779 10940 
               
               
                 135 
                 2515 5843 9202 
               
               
                 136 
                 4684 5994 10586 
               
               
                 137 
                 573 2270 3324 
               
               
                 138 
                 7870 8317 10322 
               
               
                 139 
                 6856 7638 12909 
               
               
                 140 
                 1583 7669 10781 
               
               
                 141 
                 8141 9085 12555 
               
               
                 142 
                 3903 5485 9992 
               
               
                 143 
                 4467 11998 12904 
               
               
                   
               
            
           
         
       
     
     According to an exemplary embodiment, even when the order of numbers, i.e., indexes, in a sequence corresponding to the i th  column group of the parity check matrix  200  as shown in the above-described Tables 4 to 26 is changed, the changed parity check matrix is a parity check matrix used for the same LDPC code. Therefore, a case in which the order of numbers in the sequence corresponding to the i th  column group in Tables 4 to 26 is changed is covered by the inventive concept. 
     According to an exemplary embodiment, even when one sequence corresponding to one column group is changed and another sequence corresponding to another column group are changed to each other in Tables 4 to 26, cycle characteristics on a graph of the LDPC code and algebraic characteristics such as degree distribution are not changed. Therefore, a case in which the arrangement order of the sequences shown in Tables 4 to 26 is changed is also covered by the inventive concept. 
     In addition, even when a multiple of Q ldpc  is equally added to all numbers, i.e., indexes, corresponding to a certain column group in Tables 4 to 26, the cycle characteristics on the graph of the LDPC code or the algebraic characteristics such as degree distribution are not changed. Therefore, a result of equally adding a multiple of Q ldpc  to the sequences shown in Tables 4 to 26 is also covered by the inventive concept. However, it should be noted that, when the resulting value obtained by adding a multiple of Q ldpc  to a given sequence is greater than or equal to (N ldpc -K ldpc ), a value obtained by applying a modulo operation for (N ldpc -K ldpc ) to the resulting value should be applied instead. 
     Once positions of the rows where 1 exists in the 0 th  column of the i th  column group of the information word submatrix  210  are defined as shown in Tables 4 to 26, positions of rows where 1 exists in another column of each column group may be defined since the positions of the rows where 1 exists in the 0 th  column are cyclic-shifted by Q ldpc  in the next column. 
     For example, in the case of Table 4, in the 0 th  column of the 0 th  column group of the information word submatrix  210 , 1 exists in the 245 th  row 449th row 491″ row, . . . . 
     In this case, since Q ldpc =(N ldpc -K ldpc )/M=(16200-5400)/360=30, the indexes of the rows where 1 is located in the 1 st  column of the 0 th  column group may be 275(=245+30), 479(=449+30), 521(=491+30), . . . , and the indexes of the rows where 1 is located in the 2 nd  column of the 0 th  column group may be 305(=275+30), 509(=479+30), 551(=521+30). 
     The parity submatrix  220  of the parity check matrix  200  shown in  FIG.  2    may be defined as follows: 
     The parity submatrix  220  includes N ldpc -K ldpc  number of columns (that is, K ldpc   th  column to (N ldpc -1) th  column), and has a dual diagonal configuration. Accordingly, the degree of columns except the last column (that is, (N ldpc -1) th  column) from among the columns included in the parity submatrix  220  is 2, and the degree of the last column is 1. 
     As a result, the information word submatrix  210  of the parity check matrix  200  may be defined by Tables 4 to 26, and the parity submatrix  220  may have a dual diagonal configuration. 
     When the columns and rows of the parity check matrix  200  shown in  FIG.  2    are permutated based on Equation 4 and Equation 5, the parity check matrix shown in  FIG.  2    may be changed to a parity check matrix  300  shown in  FIG.  3   . 
         Q   ldpc   ·i+j⇒M·j+i  (0 ≤i&lt;M, 0 ≤j&lt;Q   ldpc )   (4)
 
         K   ldpc   +Q   ldpc   ·k+l⇒K   ldpc   +M·l+k  (0 ≤k&lt;M, 0 ≤l&lt;Q   ldpc )   (5)
 
     The method for permutating based on Equation 4 and Equation 5 will be explained below. Since row permutation and column permutation apply the same principle , the row permutation will be explained by the way of an example. 
     In the case of the row permutation, regarding the X th  row, i and j satisfying X=Q ldpc ×i+j are calculated and the X th  row is permutated by assigning the calculated i and j to M×j+i. For example, regarding the 7 th  row, i andj satisfying 7=2×i+j are 3 and 1, respectively. Therefore, the 7 th  row is permutated to the 13 th  row (10×1+3=13). 
     When the row permutation and the column permutation are performed in the above-described method, the parity check matrix of  FIG.  2    may be converted into the parity check matrix of  FIG.  3   . 
     Referring to  FIG.  3   , the parity check matrix  300  is divided into a plurality of partial blocks, and a quasi-cyclic matrix of M×M corresponds to each partial block. 
     Accordingly, the parity check matrix  300  having the configuration of  FIG.  3    is formed of matrix units of M×M. That is, the submatrices of M×M are arranged in the plurality of partial blocks, constituting the parity check matrix  300 . 
     Since the parity check matrix  300  is formed of the quasi-cyclic matrices of M×M, M number of columns may be referred to as a column block and M number of rows may be referred to as a row block. Accordingly, the parity check matrix  300  having the configuration of  FIG.  3    is formed of N qc_column =N ldpc /M number of column blocks and N qc_row =N parity /M number of row blocks. 
     Hereinafter, the submatrix of M×M will be explained. 
     First, the (N qc_column -1) th  column block of the 0 th  row block has a form shown in Equation 6 presented below: 
     
       
         
           
             
               
                 
                   A 
                   = 
                   
                     [ 
                     
                       
                         
                           0 
                         
                         
                           0 
                         
                         
                           … 
                         
                         
                           0 
                         
                         
                           0 
                         
                       
                       
                         
                           1 
                         
                         
                           0 
                         
                         
                           … 
                         
                         
                           0 
                         
                         
                           0 
                         
                       
                       
                         
                           0 
                         
                         
                           1 
                         
                         
                           … 
                         
                         
                           0 
                         
                         
                           0 
                         
                       
                       
                         
                           ⋮ 
                         
                         
                           ⋮ 
                         
                         
                           ⋮ 
                         
                         
                           ⋮ 
                         
                         
                           ⋮ 
                         
                       
                       
                         
                           0 
                         
                         
                           0 
                         
                         
                           … 
                         
                         
                           1 
                         
                         
                           0 
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     As described above, A  330  is an M×M matrix, values of the 0 th  row and the (M-1) th  column are all “0”, and, regarding 0≤i≤(M-2), the (i+1) th  row of the i th  column is “1” and the other values are “0”. 
     Second, regarding 0≤i≤(N ldpc -K ldpc )/M-1 in the parity submatrix  320 , the i th  row block of the (K ldpc /M+i) th  column block is configured by a unit matrix I M×M    340 . In addition, regarding 0&lt;i&lt;(N ldpc -K ldpc )/M-2, the (i+1) th  row block of the (K ldpc /M+i) th  column block is configured by a unit matrix I M×M    340 . 
     Third, a block  350  constituting the information word submatrix  310  may have a cyclic-shifted format of a cyclic matrix P, P aij  , or an added format of the cyclic-shifted matrix P aij  of the cyclic matrix P (or an overlapping format). 
     For example, a format in which the cyclic matrix P is cyclic-shifted to the right by 1 may be expressed by Equation 7 presented below: 
     
       
         
           
             
               
                 
                   P 
                   = 
                   
                     [ 
                     
                       
                         
                           0 
                         
                         
                           1 
                         
                         
                           0 
                         
                         
                             
                         
                         
                           0 
                         
                       
                       
                         
                           0 
                         
                         
                           0 
                         
                         
                           1 
                         
                         
                           … 
                         
                         
                           0 
                         
                       
                       
                         
                           ⋮ 
                         
                         
                           ⋮ 
                         
                         
                           ⋮ 
                         
                         
                              
                         
                         
                           ⋮ 
                         
                       
                       
                         
                           0 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           … 
                         
                         
                           1 
                         
                       
                       
                         
                           1 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                             
                         
                         
                           0 
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     The cyclic matrix P is a square matrix having an M×M size and is a matrix in which a weight of each of M number of rows is 1 and a weight of each of M number of columns is 1. When a ij  is 0, the cyclic matrix P, that is, P 0  indicates a unit matrix I M×M , and when a ij  is ∞, P ∞  is a zero matrix. 
     A submatrix existing where the i th  row block and the j  th  column block intersect in the parity check matrix  300  of  FIG.  3    may be P aij . Accordingly, i and j indicate the number of row blocks and the number of column blocks in the partial blocks corresponding to the information word. Accordingly, in the parity check matrix 300, the total number of columns is N ldpc =M×N qc_column , and the total number of rows is N parity =M×N gc_row . That is, the parity check matrix  300  is formed of N qc_column  number of column blocks and N gc_row  number of row blocks. 
     Referring back to  FIG.  1   , the encoder  110  may perform the LDPC encoding by using various code rates such as 5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12/15, 13/15, etc. In addition, the encoder  110  may generate an LDPC codeword having various lengths such as 16200, 64800, etc., based on the length of the information word bits and the code rate. 
     In this case, the encoder  110  may perform the LDPC encoding by using the parity check matrix in which the information word submatrix is defined by Tables 4 to 26, and the parity submatrix has the dual diagonal configuration (that is, the parity check matrix shown in  FIG.  2   ), or may perform the LDPC encoding by using the parity check matrix in which rows and columns are permutated from the parity check matrix of  FIG.  2    based on Equations 4 and 5 (that is, the configuration of  FIG.  3   ). 
     In addition, the encoder  110  may perform Bose, Chaudhuri, Hocquenghem (BCH) encoding as well as LDPC encoding. To achieve this, the encoder  110  may further include a BCH encoder (not shown) to perform BCH encoding. 
     In this case, the encoder  110  may perform encoding in an order of BCH encoding and LDPC encoding. Specifically, the encoder  110  may add BCH parity bits to input bits by performing BCH encoding and LDPC-encodes the bits to which the BCH parity bits are added into information word bits, thereby generating the LDPC codeword. 
     The interleaver  120  interleaves the LDPC codeword. That is, the interleaver  120  receives the LDPC codeword from the encoder  110 , and interleaves the LDPC codeword based on various interleaving rules. 
     In particular, the interleaver  120  may interleave the LDPC codeword such that a bit included in a predetermined group from among a plurality of groups constituting the LDPC codeword (that is, a plurality of bit groups or a plurality of blocks) is mapped onto a predetermined bit of a modulation symbol. 
     Hereinafter, an interleaving rules used in the interleaver  120  will be explained in detail according to exemplary embodiments. 
     Exemplary Embodiment 1: Use of Block Interleaver 
     According to a first exemplary embodiment, the interleaver  120  may interleave the LDPC codeword in a method described below such that a bit included in a predetermined group from among a plurality of groups constituting the interleaved LDPC codeword is mapped onto a predetermined bit in a modulation symbol. A detailed description thereof is provided with reference to  FIG.  4   . 
       FIG.  4    is a block diagram to illustrate a configuration of an interleaver according to exemplary embodiment. Referring to  FIG.  4   , the interleaver  120  includes a parity interleaver  121 , a group interleaver (or a group-wise interleaver  122 ), a group twist interleaver  123  and a block interleaver  124 . 
     The parity interleaver  121  interleaves parity bits constituting the LDPC codeword. 
     Specifically, when the LDPC codeword is generated based on the parity check matrix  200  having the configuration of  FIG.  2   , the parity interleaver  121  may interleave only the parity bits of the LDPC codeword by using Equations 8 presented below: 
         u   i   =c   i  for 0 ≤i&lt;K   ldpc , and 
         u   K     ldpc     +M·t+s   =c   K     ldpc     +Q     ldpc     ·s+t  for 0 ≤s&lt;M,  0 ≤t&lt;Q   ldpc    (8),
 
     where M is an interval at which a pattern of a column group, which includes a plurality of columns, is repeated in the information word submatrix  210 , that is, the number of columns included in a column group (for example, M=360), and Q ldpc  is a size by which each column is cyclic-shifted in the information word submatrix  210 . That is, the parity interleaver  121  performs parity interleaving with respect to the LDPC codeword c=(c 0 , c 1 , . . . c N     ldpc     -1 ), and outputs U=(u 0 , u 1 , . . . , u N     ldpc     -1 ). 
     When the LDPC codeword encoded based on the parity check matrix  200  of  FIG.  2    is parity-interleaved based on Equations 8, the parity-interleaved LDPC codeword is the same as the LDPC codeword encoded by the parity check matrix  300  of  FIG.  3   . Accordingly, when the LDPC codeword is generated based on the parity check matrix  300  of  FIG.  3   , the parity interleaver  121  may be omitted. 
     The LDPC codeword parity-interleaved after having been encoded based on the parity check matrix  200  of  FIG.  2   , or the LDPC codeword encoded based on the parity check matrix having the format of  FIG.  3    may be characterized in that a predetermined number of continuous bits of the LDPC codeword have similar decoding characteristics (cycle distribution, a degree of a column, etc.). 
     For example, the LDPC codeword may have the same characteristics on the basis of M number of continuous bits. Herein, M is an interval at which a pattern of a column group is repeated in the information word submatrix and, for example, may be 360. 
     Specifically, a product of the LDPC codeword bits and the parity check matrix should be “0”. This means that a sum of products of the i th  LDPC codeword bit, c i (i=0, 1, . . . , N ldpc -1) and the i th  column of the parity check matrix should be a “0” vector. Accordingly, the i th  LDPC codeword bit may be regarded as corresponding to the i th  column of the parity check matrix. 
     In a parity check matrix according to an exemplary embodiment, M number of columns belonging to the same group have the same degree, and have a substantially great cycle characteristic. Accordingly, since M number of continuous bits in an LDPC codeword correspond to the same column group of the parity check matrix and the cycle between M number of continuous bits is substantially great, these bits have a low decoding correlation. 
     Specifically, in the case of the parity check matrix of  FIG.  2   , since the information word submatrix  210  has the same characteristics on the basis of a column group of M number of columns (e.g., the columns of the same column group have the same degree distribution), the information word bits of the LDPC codeword encoded based on the parity check matrix  200  are formed of a plurality of bit groups each of which has M number of continuous bits of the same codeword characteristics. When the parity bits of the LDPC codeword are interleaved by the parity interleaver  121 , the parity bits of the LDPC codeword may be formed of a plurality of bit groups each of which has M number of continuous bits having the same codeword characteristics. 
     In addition, in the case of the parity check matrix of  FIG.  3   , since the information word submatrix  310  and the parity submatrix  320  of the parity check matrix  300  have the same characteristics on the basis of a column group including M number of columns due to the row and column permutation, the information word bits and the parity bits of the LDPC codeword encoded based on the parity check matrix  300  are formed of a plurality of bit groups each of which has M number of continuous bits of the same codeword characteristics. 
     Herein, the row permutation does not influence the cycle characteristic or algebraic characteristic of the LDPC codeword such as a degree distribution, a minimum distance, etc. since the row permutation is just to rearrange the order of rows in the parity check matrix. In addition, since the column permutation is performed for the parity submatrix  320  to correspond to parity interleaving performed in the parity interleaver  121 , the parity bits of the LDPC codeword encoded by the parity check matrix  300  of  FIG.  3    are formed of a plurality of bit groups each of which has M number of continuous bits like the parity bits of the LDPC codeword encoded by the parity check matrix  200  of  FIG.  2   . 
     Accordingly, the bits constituting an LDPC codeword may have the same characteristics on the basis of M number of continuous bits, according to the present exemplary embodiment. 
     The group interleaver  122  may divide the parity-interleaved LDPC codeword into a plurality of groups and rearrange the order of the plurality of groups. That is, the group interleaver  122  interleaves the plurality of groups in group units. 
     To achieve this, the group interleaver  122  divides the parity-interleaved LDPC codeword into a plurality of groups by using Equation 9 or Equation 10 presented below. 
     
       
         
           
             
               
                 
                   
                     X 
                     j 
                   
                   = 
                   
                     
                       
                         { 
                         
                           
                             
                               
                                 u 
                                 k 
                               
                               | 
                               j 
                             
                             = 
                             
                               ⌊ 
                               
                                 k 
                                 
                                   3 
                                   ⁢ 
                                   6 
                                   ⁢ 
                                   0 
                                 
                               
                               ⌋ 
                             
                           
                           , 
                           
                             0 
                             ≤ 
                             k 
                             &lt; 
                             
                               N 
                               ldpc 
                             
                           
                         
                         } 
                       
                       ⁢ 
                          
                       for 
                       ⁢ 
                       
                            
                            
                       
                       ⁢ 
                       0 
                     
                     ≤ 
                     j 
                     &lt; 
                     
                       N 
                       group 
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     X 
                     j 
                   
                   = 
                   
                     
                       
                         { 
                         
                           
                             
                               u 
                               k 
                             
                             | 
                             
                               360 
                               ⨯ 
                               j 
                             
                           
                           ≤ 
                           k 
                           &lt; 
                           
                             
                               360 
                               ⨯ 
                               
                                 ( 
                                 
                                   j 
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                             , 
                             0 
                           
                           ≤ 
                           k 
                           &lt; 
                           
                             N 
                             ldpc 
                           
                         
                         } 
                       
                       ⁢ 
                          
                       for 
                       ⁢ 
                           
                       0 
                     
                     ≤ 
                     j 
                     &lt; 
                     
                       N 
                       group 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     where N group  is the total number of groups, X j  is the j th  group, and uk is the k th  LDPC codeword bit input to the group interleaver  122 . In addition, 
     
       
         
           
             ⌊ 
             
               k 
               
                 3 
                 ⁢ 
                 6 
                 ⁢ 
                 0 
               
             
             ⌋ 
           
         
       
     
     is the largest integer below k/360. 
     Since  360  in these equations indicates an example of the interval M at which the pattern of a column group is repeated in the information word submatrix,  360  in these equations can be changed to M. 
     The LDPC codeword which is divided into the plurality of groups may be as shown in  FIG.  5   . 
     Referring to  FIG.  5   , the LDPC codeword is divided into the plurality of groups and each group is formed of M number of continuous bits. 
     Specifically, since the LDPC codeword is divided by M number of continuous bits, K ldpc  number of information word bits are divided into (K ldpc /M) number of groups and N ldpc -K ldpc , number of parity bits are divided into (N ldpc -K ldpc )/M number of groups. Accordingly, the LDPC codeword may be divided into (N ldpc /M) number of groups in total. 
     For example, when M=360 and the length N ldpc  of the LDPC codeword is 64800, the number of groups N groups  is 180, and, when the length N ldpc  of the LDPC codeword is 16200, the number of groups N group  is 45. 
     As described above, the group interleaver  122  divides the LDPC codeword such that M number of continuous bits are included in a same group since the LDPC codeword has the same codeword characteristics on the basis of M number of continuous bits. Accordingly, when the LDPC codeword is grouped by M number of continuous bits, the bits having the same codeword characteristics belong to the same group. 
     Meanwhile, in the above exemplary embodiment, M number of bits forms each group, but this is only an example. The number of bits forming each group may vary. 
     For example, the number of bits forming each group may be a divisor of M. In other words, the number of bits forming each group may be a divisor of the number of columns constitituing a column group of an information word submatrix of a parity check matrix. In this case, each group may consist of the number of bits which is a divisor of M. For example, if the number of columns forming a column group of an information word submatrix is 360, that is, M=360, the group interleaver  122  may divide a LDPC codeword into a plurality of groups so that the number of bits consitituing each group becomes one of divisors of 360. 
     However, in this specification, only a case where the number of bits forming a group is M will be described for convenience of explanation, 
     Thereafter, the group interleaver  122  interleaves the LDPC codeword in group units. That is, the group interleaver  122  changes positions of the plurality of groups constituting the LDPC codeword and rearranges the order of the plurality of groups constituting the LDPC codeword. 
     In this case, the group interleaver  122  may rearrange the order of the plurality of groups by using Equation 11 presented below: 
         Y   j   =X   π(j) (0 ≤j&lt;N   group )   (11),
 
     where X j  is the j th  group before group interleaving, and Y j  is the j th  group after group interleaving. 
     In addition, π(j) is a parameter indicating an interleaving order and is determined by at least one of a length of an LDPC codeword, a code rate and a modulation method. 
     According to an exemplary embodiment, an example of π(j) may be defined as in Tables 27 to 41 presented below. 
     For example, when the length N ldpc  of the LDPC codeword is 16200, the code rate is 10/15, 11/15, 12/15 and 13/15, and the modulation method is 16-QAM, π(j) may be defined as in Table 27 or 28 presented below: 
     
       
         
           
               
               
             
               
                 TABLE 27 
               
               
                   
               
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                   
               
               
                 10/15, 11/15, 
                 7 
                 17 
                 33 
                 31 
                 26 
                 10 
                 32 
                 41 
                 28 
                 8 
                 24 
                 42 
                 20 
                 9 
                 35 
                 43 
                 22 
                 12 
                 38 
                 3 
                 5 
                 14 
                 37 
               
               
                 12/15, 13/15  
                 40 
                 19 
                 16 
                 27 
                 39 
                 25 
                 4 
                 21 
                 1 
                 23 
                 18 
                 36 
                 0 
                 6 
                 11 
                 34 
                 2 
                 29 
                 15 
                 30 
                 13 
                 44 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 28 
               
               
                   
               
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                   
               
               
                 10/15, 11/15, 
                 6 
                 34 
                 11 
                 21 
                 12 
                 8 
                 9 
                 23 
                 22 
                 2 
                 10 
                 15 
                 7 
                 14 
                 30 
                 13 
                 32 
                 17 
                 18 
                 3 
                 19 
                 16 
                 25 
               
               
                 12/15, 13/15  
                 24 
                 46 
                 40 
                 38 
                 36 
                 37 
                 39 
                 44 
                 41 
                 42 
                 4 
                 0 
                 20 
                 31 
                 5 
                 33 
                 35 
                 1 
                 28 
                 26 
                 27 
                 29 
               
               
                   
               
            
           
         
       
     
     In the case of Table 27, Equation 11 may be expressed as Y 0 =X π(0) =X 7 , Y 1 =X π(1) =X 17 , Y 2 =X π(2) =X 33 , . . . , Y 43 =X π(43) =X 13 , and Y 44 =X π(44) =X 44 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups by changing the 7 th  group to the 0 th  group, the 17 th  group to the 1 st  group, the 33 rd  group to the 2 nd  group, . . . , the 13 th  group to the 43- rd  group, and the 44 th  group to the 44 th  group. 
     In the case of Table 28, Equation 11 may be expressed as Y 0 =X π(0) =X 6 , Y 1 =X π(1) =X 34 , Y 2 =X π(2) =X 11 , . . . , Y 43 =X π(43) =X 27 , and Y 44 =X π(44) =X 29 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups by changing the 6 th  group to the 0 th  group, the 34 th  group to the 1 st  group, the 11 th  group to the 2 nd  group, . . . , the 27 th  group to the 43 rd  group, and the 29 th  group to the 44 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 16200, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 16-QAM, π(j) may be defined as in Table 29 or 30 presented below: 
     
       
         
           
               
               
             
               
                 TABLE 29 
               
               
                   
               
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                   
               
               
                 6/15, 7/15, 
                 32 
                 4 
                 23 
                 27 
                 35 
                 24 
                 16 
                 39 
                 5 
                 22 
                 33 
                 40 
                 18 
                 13 
                 8 
                 6 
                 37 
                 34 
                 0 
                 15 
                 21 
                 38 
                 30 
               
               
                 8/15, 9/15  
                 26 
                 14 
                 17 
                 10 
                 31 
                 25 
                 28 
                 12 
                 1 
                 29 
                 9 
                 41 
                 3 
                 20 
                 19 
                 36 
                 11 
                 7 
                 2 
                 42 
                 43 
                 44 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 30 
               
               
                   
               
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                   
               
               
                 6/15, 7/15, 
                 32 
                 16 
                 18 
                 0 
                 14 
                 12 
                 20 
                 4 
                 39 
                 13 
                 15 
                 17 
                 1 
                 19 
                 23 
                 5 
                 8 
                 21 
                 10 
                 29 
                 36 
                 27 
                 22 
               
               
                 8/15, 9/15  
                 6 
                 38 
                 31 
                 9 
                 11 
                 35 
                 33 
                 37 
                 30 
                 25 
                 41 
                 7 
                 24 
                 40 
                 34 
                 26 
                 28 
                 3 
                 2 
                 42 
                 43 
                 44 
               
               
                   
               
            
           
         
       
     
     In the case of Table 29, Equation 11 may be expressed as Y 0 =X π(0) =X 32 , Y 1 =X π(1) −X 4 , Y 2 =X π(2) =X 23 , . . . , Y 43 =X π(43) =X 43 , and Y 44 =X π(44) =X 44 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups by changing the 32 nd  group to the 0 th  group, the 4 th  group to the 1 st  group, the 23 rd  group to the 2 nd  group, . . . , the 43 rd  group to the 43 rd  group, and the 44 th  group to the 44 th  group. 
     In the case of Table 30, Equation 11 may be expressed as Y 0 =X π(0) =X 32 , Y 1 =X π(1) =X 16 , Y 2 =X π(2) =X 18 , . . . , Y 43 =X π(43) =X 43 , and Y 44 =X π(44) =X 44 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups by changing the 32 nd  group to the 0 th  group, the 16 th  group to the 1 st  group, the 18 th  group to the 2 nd  group, . . . , the 43 rd  group to the 43 rd  group, and the 44 th  group to the 44  th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 16200, the code rate is 10/15, 11/15, 12/15 and 13/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 31 or 32 presented below: 
     
       
         
           
               
               
             
               
                 TABLE 31 
               
               
                   
               
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                   
               
               
                 10/15, 11/15, 
                 28 
                 6 
                 15 
                 8 
                 0 
                 22 
                 37 
                 35 
                 21 
                 26 
                 7 
                 12 
                 27 
                 1 
                 32 
                 33 
                 13 
                 11 
                 10 
                 18 
                 34 
                 9 
                 39 
               
               
                 12/15, 13/15  
                 38 
                 24 
                 17 
                 29 
                 25 
                 5 
                 16 
                 30 
                 2 
                 4 
                 19 
                 23 
                 14 
                 20 
                 3 
                 31 
                 36 
                 40 
                 41 
                 42 
                 43 
                 44 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 32 
               
               
                   
               
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                   
               
               
                 10/15, 11/15, 
                 21 
                 8 
                 30 
                 0 
                 20 
                 9 
                 1 
                 22 
                 23 
                 24 
                 13 
                 11 
                 12 
                 14 
                 10 
                 17 
                 16 
                 6 
                 15 
                 2 
                 33 
                 18 
                 31 
               
               
                 12/15, 13/15  
                 7 
                 34 
                 38 
                 37 
                 5 
                 19 
                 36 
                 44 
                 39 
                 41 
                 43 
                 40 
                 42 
                 3 
                 35 
                 32 
                 4 
                 25 
                 26 
                 27 
                 28 
                 29 
               
               
                   
               
            
           
         
       
     
     In the case of Table 31, Equation 11 may be expressed as Y 0 =X π(0) =X 28 , Y 1 =X π(1) =X 6 , Y 2 =X π(2) =X 15 , . . . , Y 43 =X π(43) =X 43 , and Y 44 =X π(44) =X 44 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups by changing the 28 th  group to the 0 th  group, the 6 th  group to the 1 st  group, the 15 th  group to the 2 nd  group, . . . , the 43 rd  group to the 43 rd  group, and the 44 th  group to the 44  th  group. 
     In the case of Table 32, Equation 11 may be expressed as Y 0 =X π(0) =X 21 , Y 1 =X π(1) =X 8 , Y 2 =X π(2) =X 30 , . . . , Y 43 =X π(43) =X 28 , and Y 44 =X π(44) =X 29 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups by changing the 21 st  group to the 0 th  group, the 8 th  group to the 1 st  group, the 30 th  group to the 2 nd  group, . . . , the 28 th  group to the 43 rd  group, and the 29 th  group to the 44 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 16200, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 1024-QAM, π(j) may be defined as in Table 33 or 34 presented below: 
     
       
         
           
               
               
             
               
                 TABLE 33 
               
               
                   
               
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                   
               
               
                 6/15, 7/15, 
                 16 
                 13 
                 1 
                 25 
                 24 
                 33 
                 4 
                 29 
                 32 
                 30 
                 0 
                 17 
                 22 
                 18 
                 8 
                 9 
                 27 
                 11 
                 37 
                 35 
                 12 
                 15 
                 10 
               
               
                 8/15, 9/15  
                 20 
                 5 
                 6 
                 36 
                 38 
                 2 
                 26 
                 14 
                 7 
                 19 
                 3 
                 21 
                 23 
                 31 
                 34 
                 28 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 34 
               
               
                   
               
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                   
               
               
                 6/15, 7/15, 
                 16 
                 12 
                 14 
                 19 
                 34 
                 13 
                 15 
                 17 
                 8 
                 11 
                 4 
                 6 
                 7 
                 44 
                 9 
                 5 
                 1 
                 21 
                 18 
                 31 
                 40 
                 10 
                 28 
               
               
                 8/15, 9/15  
                 20 
                 24 
                 27 
                 41 
                 32 
                 30 
                 42 
                 26 
                 36 
                 0 
                 23 
                 35 
                 29 
                 33 
                 25 
                 22 
                 43 
                 2 
                 3 
                 37 
                 38 
                 39 
               
               
                   
               
            
           
         
       
     
     In the case of Table 33, Equation 11 may be expressed as Y 0 =X π(0) =X 16 , Y 1 =X π(1) =X 13 , Y 2 =X π(2) =X 1 , . . . , Y 43 =X π(43) =X 43 , and Y 44 =X π(44) =X 44 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups by changing the 16 th  group to the 0 th  group, the 13 th  group to the 1 st  group, the 1 st  group to the 2 nd  group, . . . , the 43 rd  group to the 43 rd  group, and the 44 th  group to the 44 th  group. 
     In the case of Table 34, Equation 11 may be expressed as Y 0 =X π(0) =X 16 , Y 1 =X π(1) =X 12 , Y 2 =X π(2) =X 14 , . . . , Y 43 =X π(43) =X 38 , and Y 44 =X π(44) =X 39 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups by changing the 16 th  group to the 0 th  group, the 12 th  group to the 1 st  group, the 14 th  group to the 2 nd  group, . . . , the 38 th  group to the 43 rd  group, and the 39 th  group to the 44 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 64800, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 35 or 36 presented below: 
     
       
         
           
               
               
             
               
                 TABLE 35 
               
               
                   
               
             
            
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
               
               
                   
                 46 
                 47 
                 48 
                 49 
                 50 
                 51 
                 52 
                 53 
                 54 
                 55 
                 56 
                 57 
               
               
                   
                 69 
                 70 
                 71 
                 72 
                 73 
                 74 
                 75 
                 76 
                 77 
                 78 
                 79 
                 80 
               
               
                   
                 92 
                 93 
                 94 
                 95 
                 96 
                 97 
                 98 
                 99 
                 100 
                 101 
                 102 
                 103 
               
               
                   
                 115 
                 116 
                 117 
                 118 
                 119 
                 120 
                 121 
                 122 
                 123 
                 124 
                 125 
                 126 
               
               
                   
                 138 
                 139 
                 140 
                 141 
                 142 
                 143 
                 144 
                 145 
                 146 
                 147 
                 148 
                 149 
               
               
                   
                 161 
                 162 
                 163 
                 164 
                 165 
                 166 
                 167 
                 168 
                 169 
                 170 
                 171 
                 172 
               
               
                 6/15, 7/15, 
                 48 
                 4 
                 15 
                 97 
                 108 
                 76 
                 1 
                 174 
                 61 
                 0 
                 59 
                 71 
               
               
                 8/15, 9/15  
                 138 
                 35 
                 62 
                 43 
                 86 
                 153 
                 73 
                 173 
                 165 
                 23 
                 49 
                 91 
               
               
                   
                 110 
                 80 
                 58 
                 42 
                 40 
                 103 
                 159 
                 83 
                 127 
                 111 
                 63 
                 89 
               
               
                   
                 123 
                 79 
                 141 
                 51 
                 21 
                 17 
                 45 
                 126 
                 150 
                 3 
                 168 
                 41 
               
               
                   
                 14 
                 131 
                 82 
                 134 
                 55 
                 33 
                 50 
                 84 
                 28 
                 105 
                 6 
                 145 
               
               
                   
                 30 
                 151 
                 18 
                 148 
                 129 
                 53 
                 100 
                 22 
                 107 
                 16 
                 170 
                 143 
               
               
                   
                 37 
                 24 
                 130 
                 136 
                 161 
                 75 
                 29 
                 9 
                 47 
                 60 
                 162 
                 146 
               
               
                   
                 13 
                 85 
                 88 
                 135 
                 116 
                 12 
                 163 
                 20 
                 46 
                 87 
                 94 
                 139 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 Code Rate 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                   
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                 45 
               
               
                   
                   
                 58 
                 59 
                 60 
                 61 
                 62 
                 63 
                 64 
                 65 
                 66 
                 67 
                 68 
               
               
                   
                   
                 81 
                 82 
                 83 
                 84 
                 85 
                 86 
                 87 
                 88 
                 89 
                 90 
                 91 
               
               
                   
                   
                 104 
                 105 
                 106 
                 107 
                 108 
                 109 
                 110 
                 111 
                 112 
                 113 
                 114 
               
               
                   
                   
                 127 
                 128 
                 129 
                 130 
                 131 
                 132 
                 133 
                 134 
                 135 
                 136 
                 137 
               
               
                   
                   
                 150 
                 151 
                 152 
                 153 
                 154 
                 155 
                 156 
                 157 
                 158 
                 159 
                 160 
               
               
                   
                   
                 173 
                 174 
                 175 
                 176 
                 177 
                 178 
                 179 
                   
                   
                   
                   
               
               
                   
                 6/15, 7/15, 
                 120 
                 175 
                 167 
                 114 
                 65 
                 98 
                 101 
                 19 
                 112 
                 109 
                 152 
               
               
                   
                 8/15, 9/15  
                 5 
                 169 
                 99 
                 77 
                 149 
                 26 
                 36 
                 25 
                 56 
                 156 
                 155 
               
               
                   
                   
                 11 
                 52 
                 144 
                 142 
                 133 
                 154 
                 44 
                 96 
                 93 
                 66 
                 122 
               
               
                   
                   
                 106 
                 124 
                 64 
                 147 
                 78 
                 8 
                 118 
                 113 
                 39 
                 69 
                 140 
               
               
                   
                   
                 7 
                 27 
                 132 
                 92 
                 115 
                 164 
                 74 
                 10 
                 68 
                 102 
                 67 
               
               
                   
                   
                 121 
                 38 
                 57 
                 95 
                 90 
                 172 
                 81 
                 158 
                 171 
                 32 
                 119 
               
               
                   
                   
                 137 
                 157 
                 70 
                 104 
                 31 
                 34 
                 166 
                 128 
                 117 
                 125 
                 2 
               
               
                   
                   
                 54 
                 72 
                 160 
                 176 
                 177 
                 178 
                 179 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 36 
               
               
                   
               
             
            
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
               
               
                   
                 46 
                 47 
                 48 
                 49 
                 50 
                 51 
                 52 
                 53 
                 54 
                 55 
                 56 
                 57 
               
               
                   
                 69 
                 70 
                 71 
                 72 
                 73 
                 74 
                 75 
                 76 
                 77 
                 78 
                 79 
                 80 
               
               
                   
                 92 
                 93 
                 94 
                 95 
                 96 
                 97 
                 98 
                 99 
                 100 
                 101 
                 102 
                 103 
               
               
                   
                 115 
                 116 
                 117 
                 118 
                 119 
                 120 
                 121 
                 122 
                 123 
                 124 
                 125 
                 126 
               
               
                   
                 138 
                 139 
                 140 
                 141 
                 142 
                 143 
                 144 
                 145 
                 146 
                 147 
                 148 
                 149 
               
               
                   
                 161 
                 162 
                 163 
                 164 
                 165 
                 166 
                 167 
                 168 
                 169 
                 170 
                 171 
                 172 
               
               
                 6/15, 7/15, 
                 48 
                 61 
                 65 
                 35 
                 23 
                 26 
                 58 
                 63 
                 44 
                 51 
                 41 
                 113 
               
               
                 8/15, 9/15  
                 0 
                 98 
                 62 
                 49 
                 36 
                 42 
                 89 
                 96 
                 21 
                 106 
                 39 
                 33 
               
               
                   
                 101 
                 43 
                 91 
                 25 
                 40 
                 11 
                 93 
                 17 
                 124 
                 69 
                 50 
                 132 
               
               
                   
                 86 
                 5 
                 56 
                 103 
                 52 
                 66 
                 45 
                 64 
                 140 
                 84 
                 92 
                 30 
               
               
                   
                 169 
                 156 
                 59 
                 144 
                 122 
                 126 
                 147 
                 14 
                 28 
                 115 
                 151 
                 16 
               
               
                   
                 155 
                 83 
                 142 
                 123 
                 150 
                 78 
                 131 
                 105 
                 164 
                 18 
                 170 
                 81 
               
               
                   
                 127 
                 133 
                 79 
                 3 
                 8 
                 82 
                 6 
                 74 
                 148 
                 143 
                 158 
                 161 
               
               
                   
                 154 
                 141 
                 168 
                 118 
                 134 
                 145 
                 10 
                 129 
                 121 
                 171 
                 75 
                 157 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 Code Rate 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                   
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                 45 
               
               
                   
                   
                 58 
                 59 
                 60 
                 61 
                 62 
                 63 
                 64 
                 65 
                 66 
                 67 
                 68 
               
               
                   
                   
                 81 
                 82 
                 83 
                 84 
                 85 
                 86 
                 87 
                 88 
                 89 
                 90 
                 91 
               
               
                   
                   
                 104 
                 105 
                 106 
                 107 
                 108 
                 109 
                 110 
                 111 
                 112 
                 113 
                 114 
               
               
                   
                   
                 127 
                 128 
                 129 
                 130 
                 131 
                 132 
                 133 
                 134 
                 135 
                 136 
                 137 
               
               
                   
                   
                 150 
                 151 
                 152 
                 153 
                 154 
                 155 
                 156 
                 157 
                 158 
                 159 
                 160 
               
               
                   
                   
                 173 
                 174 
                 175 
                 176 
                 177 
                 178 
                 179 
                   
                   
                   
                   
               
               
                   
                 6/15, 7/15, 
                 55 
                 7 
                 68 
                 53 
                 38 
                 32 
                 29 
                 70 
                 2 
                 20 
                 4 
               
               
                   
                 8/15, 9/15  
                 27 
                 102 
                 100 
                 57 
                 119 
                 9 
                 104 
                 13 
                 46 
                 15 
                 59 
               
               
                   
                   
                 67 
                 22 
                 95 
                 37 
                 47 
                 31 
                 85 
                 87 
                 97 
                 71 
                 19 
               
               
                   
                   
                 107 
                 90 
                 24 
                 60 
                 34 
                 88 
                 94 
                 108 
                 120 
                 112 
                 153 
               
               
                   
                   
                 172 
                 130 
                 162 
                 166 
                 135 
                 139 
                 76 
                 175 
                 109 
                 73 
                 99 
               
               
                   
                   
                 136 
                 146 
                 128 
                 116 
                 54 
                 1 
                 167 
                 152 
                 173 
                 77 
                 110 
               
               
                   
                   
                 137 
                 117 
                 12 
                 72 
                 174 
                 114 
                 138 
                 165 
                 149 
                 80 
                 111 
               
               
                   
                   
                 125 
                 163 
                 160 
                 176 
                 177 
                 178 
                 179 
               
               
                   
               
            
           
         
       
     
     In the case of Table 35, Equation 11 may be expressed as Y 0 =X π(0) =X 48 , Y 1 =X π(1) =X 4 , Y 2 =X π(2) =X 15 , . . . , Y 178 =X π(178) =X 178 , and Y 179 =X π(179) =X 179 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups by changing the 48 th  group to the 0 th  group, the 4 th  group to the 1 st  group, the 15 th  group to the 2 nd  group, . . . , the 178 th  group to the 178 th  group, and the 179 th  group to the 179 th  group. 
     In the case of Table 36, Equation 11 may be expressed as Y 0 =X π(0) =X 48 , Y 1 =X π(1) =X 61 , Y 2 =X π(2) =X 65 , . . . , Y 178 =X π(178) =X 178 , and Y 179 =X π(179) =X 179 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups by changing the 48 th  group to the 0 th  group, the 61 st  group to the 1 st  group, the 65 th  group to the 2 nd  group, . . . , the 178 th  group to the 178 th  group, and the 179 th  group to the 179 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 64800, the code rate is 6/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 37 presented below: 
     
       
         
           
               
               
             
               
                 TABLE 37 
               
               
                   
               
             
            
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
               
               
                   
                 46 
                 47 
                 48 
                 49 
                 50 
                 51 
                 52 
                 53 
                 54 
                 55 
                 56 
                 57 
               
               
                   
                 69 
                 70 
                 71 
                 72 
                 73 
                 74 
                 75 
                 76 
                 77 
                 78 
                 79 
                 80 
               
               
                   
                 92 
                 93 
                 94 
                 95 
                 96 
                 97 
                 98 
                 99 
                 100 
                 101 
                 102 
                 103 
               
               
                   
                 115 
                 116 
                 117 
                 118 
                 119 
                 120 
                 121 
                 122 
                 123 
                 124 
                 125 
                 126 
               
               
                   
                 138 
                 139 
                 140 
                 141 
                 142 
                 143 
                 144 
                 145 
                 146 
                 147 
                 148 
                 149 
               
               
                   
                 161 
                 162 
                 163 
                 164 
                 165 
                 166 
                 167 
                 168 
                 169 
                 170 
                 171 
                 172 
               
               
                 6/15, 
                 53 
                 3 
                 28 
                 46 
                 68 
                 15 
                 43 
                 29 
                 49 
                 0 
                 58 
                 42 
               
               
                   
                 63 
                 51 
                 57 
                 67 
                 54 
                 48 
                 60 
                 61 
                 59 
                 70 
                 45 
                 55 
               
               
                   
                 151 
                 178 
                 119 
                 50 
                 105 
                 84 
                 27 
                 10 
                 25 
                 165 
                 174 
                 44 
               
               
                   
                 170 
                 89 
                 141 
                 139 
                 89 
                 107 
                 12 
                 73 
                 79 
                 118 
                 167 
                 166 
               
               
                   
                 157 
                 163 
                 117 
                 74 
                 90 
                 158 
                 153 
                 81 
                 6 
                 104 
                 88 
                 123 
               
               
                   
                 38 
                 75 
                 100 
                 76 
                 136 
                 20 
                 134 
                 94 
                 35 
                 132 
                 152 
                 156 
               
               
                   
                 85 
                 155 
                 131 
                 176 
                 150 
                 130 
                 124 
                 113 
                 173 
                 91 
                 95 
                 110 
               
               
                   
                 148 
                 116 
                 161 
                 80 
                 177 
                 83 
                 4 
                 133 
                 122 
                 160 
                 121 
                 128 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 Code Rate 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                   
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                 45 
               
               
                   
                   
                 58 
                 59 
                 60 
                 61 
                 62 
                 63 
                 64 
                 65 
                 66 
                 67 
                 68 
               
               
                   
                   
                 81 
                 82 
                 83 
                 84 
                 85 
                 86 
                 87 
                 88 
                 89 
                 90 
                 91 
               
               
                   
                   
                 104 
                 105 
                 106 
                 107 
                 108 
                 109 
                 110 
                 111 
                 112 
                 113 
                 114 
               
               
                   
                   
                 127 
                 128 
                 129 
                 130 
                 131 
                 132 
                 133 
                 134 
                 135 
                 136 
                 137 
               
               
                   
                   
                 150 
                 151 
                 152 
                 153 
                 154 
                 155 
                 156 
                 157 
                 158 
                 159 
                 160 
               
               
                   
                   
                 173 
                 174 
                 175 
                 176 
                 177 
                 178 
                 179 
                   
                   
                   
                   
               
               
                   
                 6/15, 
                 23 
                 1 
                 47 
                 32 
                 7 
                 36 
                 34 
                 14 
                 37 
                 18 
                 71 
               
               
                   
                   
                 56 
                 66 
                 64 
                 17 
                 40 
                 69 
                 52 
                 62 
                 65 
                 135 
                 106 
               
               
                   
                   
                 21 
                 19 
                 145 
                 112 
                 30 
                 140 
                 16 
                 13 
                 172 
                 154 
                 115 
               
               
                   
                   
                 72 
                 171 
                 82 
                 96 
                 127 
                 142 
                 162 
                 164 
                 159 
                 179 
                 5 
               
               
                   
                   
                 99 
                 101 
                 144 
                 97 
                 168 
                 137 
                 8 
                 98 
                 11 
                 39 
                 87 
               
               
                   
                   
                 146 
                 103 
                 77 
                 2 
                 41 
                 114 
                 143 
                 108 
                 109 
                 175 
                 125 
               
               
                   
                   
                 93 
                 92 
                 149 
                 138 
                 126 
                 120 
                 147 
                 129 
                 102 
                 33 
                 9 
               
               
                   
                   
                 78 
                 111 
                 169 
                 22 
                 24 
                 26 
                 31 
               
               
                   
               
            
           
         
       
     
     In the case of Table 37, Equation 11 may be expressed as Y 0 =X π(0) =X53, Y 1 =X π(1) =X 3 , Y 2 =X π(2) =X 28 , . . . , Y 178 =X π(178) =X 26 , and Y 179 =X π(179) =X 31 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups by changing the 53 rd  group to the 0 th  group, the 3 rd  group to the 1 st  group, the 28 th  group to the 2 nd  group, . . . , the 26 th  group to the 178 th  group, and the 31st group to the 179 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 64800, the code rate is 8/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 37 presented below: 
     
       
         
           
               
               
             
               
                 TABLE 38 
               
               
                   
               
             
            
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
               
               
                   
                 46 
                 47 
                 48 
                 49 
                 50 
                 51 
                 52 
                 53 
                 54 
                 55 
                 56 
                 57 
               
               
                   
                 69 
                 70 
                 71 
                 72 
                 73 
                 74 
                 75 
                 76 
                 77 
                 78 
                 79 
                 80 
               
               
                   
                 92 
                 93 
                 94 
                 95 
                 96 
                 97 
                 98 
                 99 
                 100 
                 101 
                 102 
                 103 
               
               
                   
                 115 
                 116 
                 117 
                 118 
                 119 
                 120 
                 121 
                 122 
                 123 
                 124 
                 125 
                 126 
               
               
                   
                 138 
                 139 
                 140 
                 141 
                 142 
                 143 
                 144 
                 145 
                 146 
                 147 
                 148 
                 149 
               
               
                   
                 161 
                 162 
                 163 
                 164 
                 165 
                 166 
                 167 
                 168 
                 169 
                 170 
                 171 
                 172 
               
               
                 8/15, 
                 71 
                 104 
                 84 
                 69 
                 94 
                 93 
                 74 
                 89 
                 57 
                 58 
                 56 
                 59 
               
               
                   
                 87 
                 62 
                 10 
                 75 
                 12 
                 85 
                 17 
                 47 
                 80 
                 7 
                 60 
                 68 
               
               
                   
                 76 
                 67 
                 66 
                 98 
                 52 
                 79 
                 164 
                 46 
                 90 
                 120 
                 51 
                 82 
               
               
                   
                 49 
                 28 
                 23 
                 31 
                 50 
                 14 
                 25 
                 65 
                 40 
                 30 
                 19 
                 24 
               
               
                   
                 138 
                 108 
                 166 
                 149 
                 144 
                 123 
                 169 
                 148 
                 112 
                 156 
                 167 
                 100 
               
               
                   
                 111 
                 27 
                 137 
                 26 
                 160 
                 21 
                 20 
                 163 
                 162 
                 32 
                 134 
                 22 
               
               
                   
                 159 
                 109 
                 101 
                 135 
                 153 
                 116 
                 106 
                 124 
                 102 
                 146 
                 168 
                 130 
               
               
                   
                 174 
                 170 
                 9 
                 131 
                 125 
                 3 
                 118 
                 161 
                 81 
                 126 
                 0 
                 150 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 Code Rate 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                   
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                 45 
               
               
                   
                   
                 58 
                 59 
                 60 
                 61 
                 62 
                 63 
                 64 
                 65 
                 66 
                 67 
                 68 
               
               
                   
                   
                 81 
                 82 
                 83 
                 84 
                 85 
                 86 
                 87 
                 88 
                 89 
                 90 
                 91 
               
               
                   
                   
                 104 
                 105 
                 106 
                 107 
                 108 
                 109 
                 110 
                 111 
                 112 
                 113 
                 114 
               
               
                   
                   
                 127 
                 128 
                 129 
                 130 
                 131 
                 132 
                 133 
                 134 
                 135 
                 136 
                 137 
               
               
                   
                   
                 150 
                 151 
                 152 
                 153 
                 154 
                 155 
                 156 
                 157 
                 158 
                 159 
                 160 
               
               
                   
                   
                 173 
                 174 
                 175 
                 176 
                 177 
                 178 
                 179 
                   
                   
                   
                   
               
               
                   
                 8/15, 
                 173 
                 86 
                 132 
                 83 
                 77 
                 55 
                 64 
                 45 
                 54 
                 41 
                 36 
               
               
                   
                   
                 6 
                 92 
                 43 
                 13 
                 70 
                 91 
                 48 
                 61 
                 1 
                 38 
                 110 
               
               
                   
                   
                 133 
                 44 
                 39 
                 115 
                 165 
                 37 
                 119 
                 155 
                 78 
                 63 
                 53 
               
               
                   
                   
                 88 
                 29 
                 95 
                 73 
                 2 
                 8 
                 72 
                 140 
                 176 
                 142 
                 158 
               
               
                   
                   
                 114 
                 177 
                 179 
                 147 
                 105 
                 178 
                 35 
                 34 
                 33 
                 97 
                 172 
               
               
                   
                   
                 151 
                 136 
                 15 
                 42 
                 121 
                 175 
                 145 
                 127 
                 96 
                 143 
                 141 
               
               
                   
                   
                 152 
                 139 
                 99 
                 113 
                 171 
                 154 
                 122 
                 128 
                 107 
                 157 
                 103 
               
               
                   
                   
                 129 
                 117 
                 11 
                 4 
                 5 
                 16 
                 18 
               
               
                   
               
            
           
         
       
     
     In the case of Table 38, Equation 11 may be expressed as Y 0 =X π(0) =X 71 , Y 1 =X π(1) =X 104 , Y 2 =X π(2) =X 84 , . . . , Y 178 =X π(178) =X 16 , and Y 179 =X π(179) =X 18 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups by changing the 71 st  group to the 0 th  group, the 104 th  group to the 1 st  group, the 84 th  group to the 2 nd  group, . . . , the 16 th  group to the 178 th  group, and the 18 th  group to the 179 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 39 presented below. In particular, when the encoder  110  performs the LDPC encoding based on the parity check matrix defined by Table 24, the group interleaver  122  may perform group interleaving by using π(j) defined as in Table 39: 
     
       
         
           
               
               
             
               
                 TABLE 39 
               
               
                   
               
             
            
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
               
               
                   
                 46 
                 47 
                 48 
                 49 
                 50 
                 51 
                 52 
                 53 
                 54 
                 55 
                 56 
                 57 
               
               
                   
                 69 
                 70 
                 71 
                 72 
                 73 
                 74 
                 75 
                 76 
                 77 
                 78 
                 79 
                 80 
               
               
                   
                 92 
                 93 
                 94 
                 95 
                 96 
                 97 
                 98 
                 99 
                 100 
                 101 
                 102 
                 103 
               
               
                   
                 115 
                 116 
                 117 
                 118 
                 119 
                 120 
                 121 
                 122 
                 123 
                 124 
                 125 
                 126 
               
               
                   
                 138 
                 139 
                 140 
                 141 
                 142 
                 143 
                 144 
                 145 
                 146 
                 147 
                 148 
                 149 
               
               
                   
                 161 
                 162 
                 163 
                 164 
                 165 
                 166 
                 167 
                 168 
                 169 
                 170 
                 171 
                 172 
               
               
                 10/15, 
                 111 
                 65 
                 78 
                 49 
                 68 
                 44 
                 119 
                 96 
                 97 
                 108 
                 69 
                 114 
               
               
                   
                 101 
                 105 
                 45 
                 55 
                 98 
                 93 
                 41 
                 109 
                 42 
                 110 
                 87 
                 36 
               
               
                   
                 94 
                 60 
                 104 
                 19 
                 117 
                 46 
                 102 
                 75 
                 91 
                 76 
                 50 
                 5 
               
               
                   
                 81 
                 84 
                 0 
                 2 
                 21 
                 80 
                 26 
                 33 
                 70 
                 74 
                 57 
                 88 
               
               
                   
                 47 
                 113 
                 151 
                 52 
                 86 
                 154 
                 6 
                 40 
                 11 
                 107 
                 31 
                 177 
               
               
                   
                 161 
                 162 
                 22 
                 133 
                 174 
                 82 
                 124 
                 160 
                 18 
                 158 
                 176 
                 168 
               
               
                   
                 163 
                 146 
                 138 
                 139 
                 17 
                 143 
                 159 
                 25 
                 10 
                 152 
                 145 
                 59 
               
               
                   
                 126 
                 121 
                 147 
                 135 
                 140 
                 137 
                 144 
                 175 
                 157 
                 127 
                 9 
                 171 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 Code Rate 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                   
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                 45 
               
               
                   
                   
                 58 
                 59 
                 60 
                 61 
                 62 
                 63 
                 64 
                 65 
                 66 
                 67 
                 68 
               
               
                   
                   
                 81 
                 82 
                 83 
                 84 
                 85 
                 86 
                 87 
                 88 
                 89 
                 90 
                 91 
               
               
                   
                   
                 104 
                 105 
                 106 
                 107 
                 108 
                 109 
                 110 
                 111 
                 112 
                 113 
                 114 
               
               
                   
                   
                 127 
                 128 
                 129 
                 130 
                 131 
                 132 
                 133 
                 134 
                 135 
                 136 
                 137 
               
               
                   
                   
                 150 
                 151 
                 152 
                 153 
                 154 
                 155 
                 156 
                 157 
                 158 
                 159 
                 160 
               
               
                   
                   
                 173 
                 174 
                 175 
                 176 
                 177 
                 178 
                 179 
                   
                   
                   
                   
               
               
                   
                 10/15, 
                 51 
                 66 
                 29 
                 62 
                 73 
                 106 
                 54 
                 103 
                 43 
                 89 
                 39 
               
               
                   
                   
                 90 
                 32 
                 116 
                 4 
                 20 
                 23 
                 38 
                 71 
                 8 
                 34 
                 115 
               
               
                   
                   
                 79 
                 92 
                 35 
                 95 
                 99 
                 53 
                 37 
                 72 
                 100 
                 58 
                 56 
               
               
                   
                   
                 13 
                 27 
                 14 
                 77 
                 7 
                 30 
                 61 
                 48 
                 63 
                 67 
                 112 
               
               
                   
                   
                 132 
                 64 
                 136 
                 131 
                 150 
                 16 
                 155 
                 148 
                 1 
                 125 
                 24 
               
               
                   
                   
                 149 
                 134 
                 178 
                 169 
                 128 
                 173 
                 3 
                 130 
                 12 
                 15 
                 172 
               
               
                   
                   
                 153 
                 179 
                 166 
                 129 
                 120 
                 142 
                 141 
                 165 
                 167 
                 170 
                 164 
               
               
                   
                   
                 122 
                 123 
                 156 
                 28 
                 83 
                 85 
                 118 
               
               
                   
               
            
           
         
       
     
     In the case of Table 39, Equation 11 may be expressed as Y 0 =X π(0) =X 111 , Y 1 =X π(2) =X 65 , Y 2 =X π(2) =X 78 , . . . , Y 178 =X π(178) =X 85 , and Y 179 =X π(179) =X 118 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups by changing the 111 th  group to the 0 th  group, the 65 th  group to the 1 st  group, the 78 th  group to the 2 nd  group, . . . , the 85 th  group to the 178 th  group, and the 118 th  group to the 179 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 40 presented below. In particular, when the encoder  110  performs the LDPC encoding based on the parity check matrix defined by Table 25, the group interleaver  122  may perform group interleaving by using π(j) defined as in Table 40: 
     
       
         
           
               
               
             
               
                 TABLE 40 
               
               
                   
               
             
            
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
               
               
                   
                 46 
                 47 
                 48 
                 49 
                 50 
                 51 
                 52 
                 53 
                 54 
                 55 
                 56 
                 57 
               
               
                   
                 69 
                 70 
                 71 
                 72 
                 73 
                 74 
                 75 
                 76 
                 77 
                 78 
                 79 
                 80 
               
               
                   
                 92 
                 93 
                 94 
                 95 
                 96 
                 97 
                 98 
                 99 
                 100 
                 101 
                 102 
                 103 
               
               
                   
                 115 
                 116 
                 117 
                 118 
                 119 
                 120 
                 121 
                 122 
                 123 
                 124 
                 125 
                 126 
               
               
                   
                 138 
                 139 
                 140 
                 141 
                 142 
                 143 
                 144 
                 145 
                 146 
                 147 
                 148 
                 149 
               
               
                   
                 161 
                 162 
                 163 
                 164 
                 165 
                 166 
                 167 
                 168 
                 169 
                 170 
                 171 
                 172 
               
               
                 10/15, 
                 89 
                 64 
                 50 
                 28 
                 32 
                 26 
                 52 
                 98 
                 66 
                 31 
                 90 
                 59 
               
               
                   
                 118 
                 84 
                 95 
                 81 
                 7 
                 96 
                 36 
                 18 
                 3 
                 65 
                 1 
                 116 
               
               
                   
                 35 
                 82 
                 67 
                 33 
                 44 
                 48 
                 91 
                 112 
                 49 
                 78 
                 55 
                 106 
               
               
                   
                 2 
                 23 
                 86 
                 105 
                 53 
                 38 
                 62 
                 110 
                 4 
                 83 
                 15 
                 87 
               
               
                   
                 103 
                 158 
                 93 
                 58 
                 101 
                 34 
                 77 
                 61 
                 164 
                 173 
                 132 
                 39 
               
               
                   
                 159 
                 14 
                 143 
                 139 
                 146 
                 161 
                 130 
                 129 
                 171 
                 179 
                 157 
                 148 
               
               
                   
                 168 
                 136 
                 160 
                 170 
                 5 
                 150 
                 124 
                 144 
                 156 
                 167 
                 123 
                 149 
               
               
                   
                 131 
                 122 
                 10 
                 155 
                 154 
                 174 
                 162 
                 80 
                 133 
                 16 
                 22 
                 128 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 Code Rate 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                   
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                 45 
               
               
                   
                   
                 58 
                 59 
                 60 
                 61 
                 62 
                 63 
                 64 
                 65 
                 66 
                 67 
                 68 
               
               
                   
                   
                 81 
                 82 
                 83 
                 84 
                 85 
                 86 
                 87 
                 88 
                 89 
                 90 
                 91 
               
               
                   
                   
                 104 
                 105 
                 106 
                 107 
                 108 
                 109 
                 110 
                 111 
                 112 
                 113 
                 114 
               
               
                   
                   
                 127 
                 128 
                 129 
                 130 
                 131 
                 132 
                 133 
                 134 
                 135 
                 136 
                 137 
               
               
                   
                   
                 150 
                 151 
                 152 
                 153 
                 154 
                 155 
                 156 
                 157 
                 158 
                 159 
                 160 
               
               
                   
                   
                 173 
                 174 
                 175 
                 176 
                 177 
                 178 
                 179 
                   
                   
                   
                   
               
               
                   
                 10/15, 
                 70 
                 17 
                 76 
                 117 
                 54 
                 68 
                 11 
                 43 
                 57 
                 92 
                 20 
               
               
                   
                   
                 97 
                 119 
                 94 
                 100 
                 107 
                 75 
                 69 
                 63 
                 30 
                 72 
                 109 
               
               
                   
                   
                 46 
                 108 
                 51 
                 113 
                 102 
                 71 
                 40 
                 111 
                 104 
                 74 
                 21 
               
               
                   
                   
                 73 
                 79 
                 115 
                 6 
                 56 
                 42 
                 47 
                 85 
                 99 
                 145 
                 114 
               
               
                   
                   
                 151 
                 88 
                 60 
                 41 
                 37 
                 45 
                 172 
                 166 
                 152 
                 127 
                 169 
               
               
                   
                   
                 9 
                 138 
                 147 
                 0 
                 135 
                 13 
                 177 
                 178 
                 19 
                 137 
                 12 
               
               
                   
                   
                 134 
                 142 
                 121 
                 141 
                 165 
                 126 
                 125 
                 140 
                 153 
                 175 
                 176 
               
               
                   
                   
                 163 
                 120 
                 8 
                 24 
                 25 
                 27 
                 29 
               
               
                   
               
            
           
         
       
     
     In the case of Table 40, Equation 11 may be expressed as Y 0 =X π(0) =X 89 , Y 1 =X π(1) =X 64 , Y 2 =X π(2) =X 50 , . . . , Y 178 =X π(178) =X 27 , and Y 179 =X π(179) =X 29 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups by changing the 89 th  group to the 0 th  group, the 64 th  group to the 1 st  group, the 50 th  group to the 2 nd  group, . . . , the 27 th  group to the 178 th  group, and the 29 th  group to the 179 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 64800, the code rate is 12/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 41 presented below: 
     
       
         
           
               
               
             
               
                 TABLE 41 
               
               
                   
               
             
            
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
               
               
                   
                 46 
                 47 
                 48 
                 49 
                 50 
                 51 
                 52 
                 53 
                 54 
                 55 
                 56 
                 57 
               
               
                   
                 69 
                 70 
                 71 
                 72 
                 73 
                 74 
                 75 
                 76 
                 77 
                 78 
                 79 
                 80 
               
               
                   
                 92 
                 93 
                 94 
                 95 
                 96 
                 97 
                 98 
                 99 
                 100 
                 101 
                 102 
                 103 
               
               
                   
                 115 
                 116 
                 117 
                 118 
                 119 
                 120 
                 121 
                 122 
                 123 
                 124 
                 125 
                 126 
               
               
                   
                 138 
                 139 
                 140 
                 141 
                 142 
                 143 
                 144 
                 145 
                 146 
                 147 
                 148 
                 149 
               
               
                   
                 161 
                 162 
                 163 
                 164 
                 165 
                 166 
                 167 
                 168 
                 169 
                 170 
                 171 
                 172 
               
               
                 12/15, 
                 51 
                 122 
                 91 
                 111 
                 95 
                 100 
                 119 
                 130 
                 78 
                 57 
                 65 
                 26 
               
               
                   
                 14 
                 3 
                 21 
                 71 
                 134 
                 2 
                 0 
                 140 
                 106 
                 7 
                 118 
                 23 
               
               
                   
                 129 
                 107 
                 30 
                 45 
                 137 
                 114 
                 37 
                 87 
                 53 
                 85 
                 101 
                 141 
               
               
                   
                 97 
                 38 
                 124 
                 86 
                 33 
                 74 
                 32 
                 29 
                 128 
                 67 
                 104 
                 80 
               
               
                   
                 54 
                 40 
                 81 
                 103 
                 121 
                 76 
                 44 
                 84 
                 96 
                 123 
                 154 
                 98 
               
               
                   
                 36 
                 59 
                 90 
                 79 
                 52 
                 133 
                 60 
                 92 
                 139 
                 110 
                 27 
                 73 
               
               
                   
                 164 
                 158 
                 157 
                 160 
                 150 
                 171 
                 167 
                 145 
                 151 
                 153 
                 9 
                 155 
               
               
                   
                 148 
                 172 
                 178 
                 24 
                 22 
                 179 
                 4 
                 163 
                 174 
                 173 
                 19 
                 10 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 Code Rate 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                   
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                 45 
               
               
                   
                   
                 58 
                 59 
                 60 
                 61 
                 62 
                 63 
                 64 
                 65 
                 66 
                 67 
                 68 
               
               
                   
                   
                 81 
                 82 
                 83 
                 84 
                 85 
                 86 
                 87 
                 88 
                 89 
                 90 
                 91 
               
               
                   
                   
                 104 
                 105 
                 106 
                 107 
                 108 
                 109 
                 110 
                 111 
                 112 
                 113 
                 114 
               
               
                   
                   
                 127 
                 128 
                 129 
                 130 
                 131 
                 132 
                 133 
                 134 
                 135 
                 136 
                 137 
               
               
                   
                   
                 150 
                 151 
                 152 
                 153 
                 154 
                 155 
                 156 
                 157 
                 158 
                 159 
                 160 
               
               
                   
                   
                 173 
                 174 
                 175 
                 176 
                 177 
                 178 
                 179 
                   
                   
                   
                   
               
               
                   
                 12/15, 
                 61 
                 126 
                 105 
                 143 
                 70 
                 132 
                 39 
                 102 
                 115 
                 116 
                 6 
               
               
                   
                   
                 35 
                 20 
                 17 
                 50 
                 48 
                 112 
                 13 
                 66 
                 5 
                 75 
                 42 
               
               
                   
                   
                 120 
                 99 
                 88 
                 117 
                 64 
                 28 
                 135 
                 138 
                 108 
                 113 
                 58 
               
               
                   
                   
                 127 
                 56 
                 34 
                 89 
                 94 
                 49 
                 55 
                 93 
                 136 
                 68 
                 62 
               
               
                   
                   
                 82 
                 142 
                 46 
                 169 
                 131 
                 72 
                 47 
                 69 
                 125 
                 31 
                 83 
               
               
                   
                   
                 43 
                 77 
                 109 
                 63 
                 41 
                 168 
                 147 
                 161 
                 165 
                 175 
                 162 
               
               
                   
                   
                 170 
                 146 
                 166 
                 149 
                 15 
                 159 
                 11 
                 176 
                 152 
                 156 
                 144 
               
               
                   
                   
                 177 
                 12 
                 16 
                 1 
                 8 
                 18 
                 25 
               
               
                   
               
            
           
         
       
     
     In the case of Table 41, Equation 11 may be expressed as Y 0 =X π(0) =X 51 , Y 1 =X π(1) =X 122 , Y 2 =X π(2) =X 91 , . . . , Y 178 =X π(178) =X 18 , and Y 179 =X π(179) =X 25 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups by changing the 51 st  group to the 0 th  group, the 122 nd  group to the 1 st  group, the 91 st  group to the 2 nd  group, . . . , the 18 th  group to the 178 th  group, and the 25 th  group to the 179 th  group. 
     As described above, it is possible to rearrange the order of column groups in the parity check matrix having the shape of  FIGS.  2  and  3   , and a column group corresponds to a bit group. Accordingly, if the order of column groups is changed in the partiy check matrix, the order of bit groups may also be changed accordingly. 
     As described above, the group interleaver  122  may rearrange the order of the plurality of groups by using Equation 11 and Tables 27 to 41. 
     On the other hand, since the order of the groups constituting the LDPC codeword is rearranged by the group interleaver  122 , and then the groups are block-interleaved by the block interleaver  124 , which will be described below, “Order of bits groups to be block interleaved” is set forth in Tables 27 to 41 in relation to π(j). 
     In addition, the group interleaver  122  may interleave the LDPC codeword in group units by using Equation 12 presented below: 
       Y π(j) =X j (0≤j&lt;N group )   (12),
 
     where X j  is the j th  group before group interleaving, and Y j  is the j th  group after group interleaving. 
     In addition, π(j) is a parameter indicating an interleaving order and is determined by at least one of a length of an LDPC codeword, a code rate and a modulation method. 
     According to an exemplary embodiment, an example of π(j) may be defined as in Tables 42 to 51 presented below. 
     For example, when the length N ldpc  of the LDPC codeword is 16200, the code rate is 10/15, 11/15, 12/15 and 13/15, and the modulation method is 16-QAM, π(j) may be defined as in Table 42 or 43 presented below: 
     
       
         
           
               
               
             
               
                 TABLE 42 
               
               
                   
               
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                   
               
               
                 10/15, 11/15, 
                 35 
                 31 
                 39 
                 19 
                 29 
                 20 
                 36 
                 0 
                 9 
                 13 
                 5 
                 37 
                 17 
                 43 
                 21 
                 41 
                 25 
                 1 
                 33 
                 24 
                 12 
                 30 
                 16 
               
               
                 12/15, 13/15  
                 32 
                 10 
                 28 
                 4 
                 26 
                 8 
                 40 
                 42 
                 3 
                 6 
                 2 
                 38 
                 14 
                 34 
                 22 
                 18 
                 27 
                 23 
                 7 
                 11 
                 15 
                 44 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 43 
               
               
                   
               
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                   
               
               
                 10/15, 11/15, 
                 34 
                 40 
                 9 
                 19 
                 33 
                 37 
                 0 
                 12 
                 5 
                 6 
                 10 
                 2 
                 4 
                 15 
                 13 
                 11 
                 21 
                 17 
                 18 
                 20 
                 35 
                 3 
                 8 
               
               
                 12/15, 13/15  
                 7 
                 23 
                 22 
                 42 
                 43 
                 41 
                 44 
                 14 
                 36 
                 16 
                 38 
                 1 
                 39 
                 27 
                 28 
                 26 
                 29 
                 25 
                 31 
                 32 
                 24 
                 30 
               
               
                   
               
            
           
         
       
     
     In the case of Table 42, Equation 12 may be expressed as X 0 =Y π(0) =Y 35 , X 1 =Y π(1) =Y 31 , X 2 =Y π(2) =Y 39 , . . . , X 43 =Y π(43) =Y 15 , and X 44 =Y π(44) =Y 44 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups by changing the 0 th  group to the 35 th  group, the 1 st  group to the 31 st  group, the 2 nd  group to the 39 th  group, . . . , the 43 rd  group to the 15 th  group, and the 44 th  group to the 44 th  group. 
     In the case of Table 43, Equation 12 may be expressed as X 0 =Y π(0) =Y 34 , X 1 =Y π(1) =Y 40 , X 2 =Y π(2) =Y 9 , . . . , X 43 =Y π(43) =Y 24 , and X 44 =Y π(44) =Y 30 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups by changing the 0 th  group to the 34 th  group, the 1 st  group to the 40 th  group, the 2 nd  group to the 9 th  group, . . . , the 43 rd  group to the 24 th  group, and the 44 th  group to the 30 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 16200, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 64-QAM, π(j) may be defined as in Table 44 or 45 presented below: 
     
       
         
           
               
               
             
               
                 TABLE 44 
               
               
                   
               
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                   
               
               
                 6/15, 7/15, 
                 18 
                 31 
                 41 
                 35 
                 1 
                 8 
                 15 
                 40 
                 14 
                 33 
                 26 
                 39 
                 30 
                 13 
                 24 
                 19 
                 6 
                 25 
                 12 
                 37 
                 36 
                 20 
                 9 
               
               
                 8/15, 9/15  
                 2 
                 5 
                 28 
                 23 
                 3 
                 29 
                 32 
                 22 
                 27 
                 0 
                 10 
                 17 
                 4 
                 38 
                 16 
                 21 
                 7 
                 11 
                 34 
                 42 
                 43 
                 44 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 45 
               
               
                   
               
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                   
               
               
                 6/15, 7/15, 
                 3 
                 12 
                 41 
                 40 
                 7 
                 15 
                 23 
                 34 
                 16 
                 26 
                 18 
                 27 
                 5 
                 9 
                 4 
                 10 
                 1 
                 11 
                 2 
                 13 
                 6 
                 17 
                 22 
               
               
                 8/15, 9/15  
                 14 
                 35 
                 32 
                 38 
                 21 
                 39 
                 19 
                 31 
                 25 
                 0 
                 29 
                 37 
                 28 
                 20 
                 30 
                 24 
                 8 
                 36 
                 33 
                 42 
                 43 
                 44 
               
               
                   
               
            
           
         
       
     
     In the case of Table 44, Equation 12 may be expressed as X 0 =Y π(0) =Y 18 , X 1 =Y π(1) =Y 31 , X 2 =Y π(2) =Y 41 , . . . , X 43 =Y π(43) =Y 43 , and X 44 =Y π(44) =Y 44 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups by changing the 0 th  group to the 18 th  group, the 1 st  group to the 31 st  group, the 2nd group to the 41 th  group, . . . , the 43 rd  group to the 43 rd  group, and the 44 th  group to the 44 th  group. 
     In the case of Table 45, Equation 12 may be expressed as X 0 =Y π(0) =Y 3 , X 1 =Y π(1) =Y 12 , X 2 =Y π(2) =Y 41 , . . . , X 43 =Y π(43) =Y 43 , and X 44 =Y π(44) =Y 44 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups by changing the 0 th  group to the 3 rd  group, the 1 st  group to the 12 th  group, the 2 nd  group to the 41 st  group, . . . , the 43 rd  group to the 43 rd  group, and the 44 th  group to the 44 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 16200, the code rate is 10/15, 11/15, 12/15 and 13/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 46 or 47 presented below: 
     
       
         
           
               
               
             
               
                 TABLE 46 
               
               
                   
               
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                   
               
               
                 10/15, 11/15, 
                 4 
                 13 
                 31 
                 37 
                 32 
                 28 
                 1 
                 10 
                 3 
                 21 
                 18 
                 17 
                 11 
                 16 
                 35 
                 2 
                 29 
                 25 
                 19 
                 33 
                 36 
                 8 
                 5 
               
               
                 12/15, 13/15  
                 34 
                 24 
                 27 
                 9 
                 12 
                 0 
                 26 
                 30 
                 38 
                 14 
                 15 
                 20 
                 7 
                 39 
                 6 
                 23 
                 22 
                 40 
                 41 
                 42 
                 43 
                 44 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 47 
               
               
                   
               
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                   
               
               
                 10/15, 11/15, 
                 3 
                 6 
                 19 
                 36 
                 39 
                 27 
                 17 
                 23 
                 1 
                 5 
                 14 
                 11 
                 12 
                 10 
                 13 
                 18 
                 16 
                 15 
                 21 
                 28 
                 4 
                 0 
                 7 
               
               
                 12/15, 13/15  
                 8 
                 9 
                 40 
                 41 
                 42 
                 43 
                 44 
                 2 
                 22 
                 38 
                 20 
                 24 
                 37 
                 29 
                 26 
                 25 
                 31 
                 34 
                 32 
                 35 
                 33 
                 30 
               
               
                   
               
            
           
         
       
     
     In the case of Table 46, Equation 12 may be expressed as X 0 =Y π(0) =Y 4 , X 1 =Y π(1) =Y 13 , X 2 =Y π(2) =Y 31 , . . . , X 43 =Y π(43) =Y 43 , and X 44 =Y π(44) =Y 44 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups by changing the 0 th  group to the 4 th  group, the 1 st  group to the 13 th  group, the 2 nd  group to the 31′ group, . . . , the 43 rd  group to the 43 rd  group, and the 44 th  group to the 44 th  group. 
     In the case of Table 47, Equation 12 may be expressed as X 0 =Y π(0) =Y 3 , X 1 =Y π(1) =Y 6 , X 2 =Y π(2) =Y 19 , . . . , X 43 =Y π(43) =Y 33 , and X 44 =Y π(44) =Y 30 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups by changing the 0 th  group to the 3 rd  group, the 1 st  group to the 6 th  group, the 2 nd  group to the 19 th  group, . . . , the 43 rd  group to the 33 rd  group, and the 44 th  group to the 30 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 16200, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 1024-QAM, π(j) may be defined as in Table 48 or 49 presented below: 
     
       
         
           
               
             
               
                 TABLE 48 
               
               
                   
               
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                   
               
               
                 6/15, 7/15, 
                 10 
                 2 
                 28 
                 33 
                 6 
                 24 
                 25 
                 31 
                 14 
                 15 
                 22 
                 17 
                 20 
                 1 
                 30 
                 21 
                 0 
                 11 
                 13 
                 32 
                 23 
                 34 
                 12 
               
               
                 8/15, 9/15  
                 35 
                 4 
                 3 
                 29 
                 16 
                 38 
                 7 
                 9 
                 36 
                 8 
                 5 
                 37 
                 19 
                 26 
                 18 
                 27 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 49 
               
               
                   
               
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                   
               
               
                 6/15, 7/15, 
                 32 
                 16 
                 40 
                 41 
                 10 
                 15 
                 11 
                 12 
                 8 
                 14 
                 21 
                 9 
                 1 
                 5 
                 2 
                 6 
                 0 
                 7 
                 18 
                 3 
                 23 
                 17 
                 38 
               
               
                 8/15, 9/15  
                 33 
                 24 
                 37 
                 30 
                 25 
                 22 
                 35 
                 28 
                 19 
                 27 
                 36 
                 4 
                 34 
                 31 
                 42 
                 43 
                 44 
                 20 
                 26 
                 29 
                 39 
                 13 
               
               
                   
               
            
           
         
       
     
     In the case of Table 48, Equation 12 may be expressed as X 0 =Y π(0) =Y 10 , X 1 =Y π(0) =Y 2 , X 2 =Y π(2) =Y 28 , . . . , X 43 =Y π(43) =Y 43 , and X 44 =Y π(44) =Y 44 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups by changing the 0 th  group to the 10 th  group, the 1 st  group to the 2 nd  group, the 2 nd  group to the 28 th  group, . . . , the 43 rd  group to the 43 rd  group, and the 44 th  group to the 44 th  group. 
     In the case of Table 49, Equation 12 may be expressed as X 0 =Y π(0) =Y 32 , X 1 =Y π(1) =Y 16 , X 2 =Y π(2) =Y 40 , . . . , X 43 =Y π(43) =Y 39 , and X 44 =Y π(44) =Y 13 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups by changing the 0 th  group to the 32 nd  group, the 1 st  group to the 16 th  group, the 2 nd  group to the 40 th  group, . . . , the 43 rd  group to the 39 th  group, and the 44 th  group to the 13 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 64800, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 50 or 51 presented below: 
     
       
         
           
               
               
             
               
                 TABLE 50 
               
               
                   
               
             
            
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
               
               
                   
                 46 
                 47 
                 48 
                 49 
                 50 
                 51 
                 52 
                 53 
                 54 
                 55 
                 56 
                 57 
               
               
                   
                 69 
                 70 
                 71 
                 72 
                 73 
                 74 
                 75 
                 76 
                 77 
                 78 
                 79 
                 80 
               
               
                   
                 92 
                 93 
                 94 
                 95 
                 96 
                 97 
                 98 
                 99 
                 100 
                 101 
                 102 
                 103 
               
               
                   
                 115 
                 116 
                 117 
                 118 
                 119 
                 120 
                 121 
                 122 
                 123 
                 124 
                 125 
                 126 
               
               
                   
                 138 
                 139 
                 140 
                 141 
                 142 
                 143 
                 144 
                 145 
                 146 
                 147 
                 148 
                 149 
               
               
                   
                 161 
                 162 
                 163 
                 164 
                 165 
                 166 
                 167 
                 168 
                 169 
                 170 
                 171 
                 172 
               
               
                 6/15, 7/15, 
                 9 
                 6 
                 160 
                 78 
                 1 
                 35 
                 102 
                 104 
                 86 
                 145 
                 111 
                 58 
               
               
                 8/15, 9/15  
                 32 
                 139 
                 42 
                 40 
                 105 
                 100 
                 144 
                 115 
                 154 
                 136 
                 97 
                 155 
               
               
                   
                 169 
                 146 
                 0 
                 33 
                 98 
                 72 
                 59 
                 120 
                 173 
                 96 
                 43 
                 129 
               
               
                   
                 90 
                 152 
                 11 
                 174 
                 29 
                 110 
                 143 
                 5 
                 38 
                 85 
                 70 
                 47 
               
               
                   
                 107 
                 66 
                 171 
                 130 
                 65 
                 3 
                 17 
                 37 
                 121 
                 18 
                 113 
                 51 
               
               
                   
                 108 
                 165 
                 158 
                 87 
                 137 
                 12 
                 127 
                 68 
                 69 
                 82 
                 159 
                 76 
               
               
                   
                 23 
                 172 
                 91 
                 71 
                 61 
                 126 
                 60 
                 103 
                 149 
                 84 
                 118 
                 39 
               
               
                   
                 142 
                 148 
                 167 
                 109 
                 31 
                 156 
                 14 
                 79 
                 36 
                 125 
                 135 
                 132 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 Code Rate 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                   
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                 45 
               
               
                   
                   
                 58 
                 59 
                 60 
                 61 
                 62 
                 63 
                 64 
                 65 
                 66 
                 67 
                 68 
               
               
                   
                   
                 81 
                 82 
                 83 
                 84 
                 85 
                 86 
                 87 
                 88 
                 89 
                 90 
                 91 
               
               
                   
                   
                 104 
                 105 
                 106 
                 107 
                 108 
                 109 
                 110 
                 111 
                 112 
                 113 
                 114 
               
               
                   
                   
                 127 
                 128 
                 129 
                 130 
                 131 
                 132 
                 133 
                 134 
                 135 
                 136 
                 137 
               
               
                   
                   
                 150 
                 151 
                 152 
                 153 
                 154 
                 155 
                 156 
                 157 
                 158 
                 159 
                 160 
               
               
                   
                   
                 173 
                 174 
                 175 
                 176 
                 177 
                 178 
                 179 
                   
                   
                   
                   
               
               
                   
                 6/15, 7/15, 
                 166 
                 161 
                 92 
                 2 
                 124 
                 74 
                 117 
                 19 
                 168 
                 73 
                 122 
               
               
                   
                 8/15, 9/15  
                 24 
                 41 
                 138 
                 128 
                 89 
                 50 
                 80 
                 49 
                 26 
                 64 
                 75 
               
               
                   
                   
                 48 
                 10 
                 147 
                 8 
                 25 
                 56 
                 83 
                 16 
                 67 
                 114 
                 112 
               
               
                   
                   
                 133 
                 94 
                 53 
                 99 
                 162 
                 27 
                 170 
                 163 
                 57 
                 131 
                 34 
               
               
                   
                   
                 153 
                 101 
                 81 
                 123 
                 4 
                 21 
                 46 
                 55 
                 20 
                 88 
                 15 
               
               
                   
                   
                 54 
                 157 
                 119 
                 140 
                 93 
                 106 
                 62 
                 95 
                 164 
                 141 
                 150 
               
               
                   
                   
                 72 
                 116 
                 22 
                 28 
                 63 
                 45 
                 44 
                 151 
                 134 
                 52 
                 175 
               
               
                   
                   
                 30 
                 7 
                 13 
                 179 
                 178 
                 177 
                 176 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 51 
               
               
                   
               
             
            
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
               
               
                   
                 46 
                 47 
                 48 
                 49 
                 50 
                 51 
                 52 
                 53 
                 54 
                 55 
                 56 
                 57 
               
               
                   
                 69 
                 70 
                 71 
                 72 
                 73 
                 74 
                 75 
                 76 
                 77 
                 78 
                 79 
                 80 
               
               
                   
                 92 
                 93 
                 94 
                 95 
                 96 
                 97 
                 98 
                 99 
                 100 
                 101 
                 102 
                 103 
               
               
                   
                 115 
                 116 
                 117 
                 118 
                 119 
                 120 
                 121 
                 122 
                 123 
                 124 
                 125 
                 126 
               
               
                   
                 138 
                 139 
                 140 
                 141 
                 142 
                 143 
                 144 
                 145 
                 146 
                 147 
                 148 
                 149 
               
               
                   
                 161 
                 162 
                 163 
                 164 
                 165 
                 166 
                 167 
                 168 
                 169 
                 170 
                 171 
                 172 
               
               
                 6/15, 7/15, 
                 23 
                 132 
                 20 
                 141 
                 22 
                 70 
                 144 
                 13 
                 142 
                 40 
                 167 
                 51 
               
               
                 8/15, 9/15  
                 4 
                 83 
                 49 
                 5 
                 35 
                 100 
                 18 
                 80 
                 63 
                 17 
                 34 
                 85 
               
               
                   
                 43 
                 62 
                 0 
                 26 
                 56 
                 9 
                 73 
                 15 
                 131 
                 12 
                 71 
                 38 
               
               
                   
                 55 
                 19 
                 67 
                 153 
                 113 
                 145 
                 171 
                 110 
                 136 
                 120 
                 140 
                 159 
               
               
                   
                 79 
                 52 
                 87 
                 60 
                 30 
                 66 
                 24 
                 114 
                 37 
                 46 
                 36 
                 72 
               
               
                   
                 101 
                 130 
                 151 
                 164 
                 39 
                 89 
                 169 
                 96 
                 118 
                 54 
                 173 
                 97 
               
               
                   
                 156 
                 109 
                 77 
                 162 
                 117 
                 147 
                 95 
                 166 
                 128 
                 98 
                 145 
                 158 
               
               
                   
                 149 
                 106 
                 174 
                 123 
                 157 
                 107 
                 133 
                 163 
                 92 
                 125 
                 170 
                 104 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 Code Rate 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                   
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                 45 
               
               
                   
                   
                 58 
                 59 
                 60 
                 61 
                 62 
                 63 
                 64 
                 65 
                 66 
                 67 
                 68 
               
               
                   
                   
                 81 
                 82 
                 83 
                 84 
                 85 
                 86 
                 87 
                 88 
                 89 
                 90 
                 91 
               
               
                   
                   
                 104 
                 105 
                 106 
                 107 
                 108 
                 109 
                 110 
                 111 
                 112 
                 113 
                 114 
               
               
                   
                   
                 127 
                 128 
                 129 
                 130 
                 131 
                 132 
                 133 
                 134 
                 135 
                 136 
                 137 
               
               
                   
                   
                 150 
                 151 
                 152 
                 153 
                 154 
                 155 
                 156 
                 157 
                 158 
                 159 
                 160 
               
               
                   
                   
                 173 
                 174 
                 175 
                 176 
                 177 
                 178 
                 179 
                   
                   
                   
                   
               
               
                   
                 6/15, 7/15, 
                 152 
                 42 
                 99 
                 44 
                 103 
                 53 
                 124 
                 68 
                 21 
                 31 
                 59 
               
               
                   
                 8/15, 9/15  
                 3 
                 27 
                 61 
                 16 
                 33 
                 50 
                 10 
                 28 
                 47 
                 8 
                 75 
               
               
                   
                   
                 6 
                 45 
                 84 
                 1 
                 25 
                 7 
                 76 
                 2 
                 74 
                 58 
                 14 
               
               
                   
                   
                 126 
                 143 
                 116 
                 78 
                 64 
                 69 
                 65 
                 86 
                 29 
                 82 
                 48 
               
               
                   
                   
                 41 
                 122 
                 32 
                 81 
                 88 
                 112 
                 137 
                 160 
                 90 
                 11 
                 155 
               
               
                   
                   
                 138 
                 129 
                 168 
                 105 
                 121 
                 57 
                 139 
                 165 
                 108 
                 127 
                 150 
               
               
                   
                   
                 119 
                 102 
                 134 
                 91 
                 161 
                 115 
                 93 
                 172 
                 148 
                 94 
                 175 
               
               
                   
                   
                 135 
                 154 
                 111 
                 176 
                 177 
                 178 
                 179 
               
               
                   
               
            
           
         
       
     
     In the case of Table 50, Equation 12 may be expressed as X 0 =Y π(0) =Y 9 , X 1 =Y π(1) =Y 6 , X 2 =Y π(2) =Y 160 , . . . , X 178 =Y π(178) =Y 177 , and X 179 =Y π(179) =Y 176 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups by changing the 0th group to the 9 th  group, the 1 st  group to the 6 th  group, the 2 nd  group to the 160 th  group, . . . , the 178 th  group to the 177 th  group, and the 179 th  group to the 176 th  group. 
     In the case of Table 51, Equation 12 may be expressed as X 0 =Y π(0) =Y 23 , X 1 =Y π(1) =Y 132 , X 2 =Y π(2) =Y 20 , . . . , X 178 =Y π(178) =Y 178 , and X 179 =Y π(179) =Y 179 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups by changing the 0th group to the 23 rd  group, the 1 st  group to the 132 nd  group, the 2 nd  group to the 20 th  group, . . . , the 178 th  group to the 178 th  group, and the 179 th  group to the 179 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 64800, the code rate is 6/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 52 presented below: 
     
       
         
           
               
               
             
               
                 TABLE 52 
               
               
                   
               
             
            
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
               
               
                   
                 46 
                 47 
                 48 
                 49 
                 50 
                 51 
                 52 
                 53 
                 54 
                 55 
                 56 
                 57 
               
               
                   
                 69 
                 70 
                 71 
                 72 
                 73 
                 74 
                 75 
                 76 
                 77 
                 78 
                 79 
                 80 
               
               
                   
                 92 
                 93 
                 94 
                 95 
                 96 
                 97 
                 98 
                 99 
                 100 
                 101 
                 102 
                 103 
               
               
                   
                 115 
                 116 
                 117 
                 118 
                 119 
                 120 
                 121 
                 122 
                 123 
                 124 
                 125 
                 126 
               
               
                   
                 138 
                 139 
                 140 
                 141 
                 142 
                 143 
                 144 
                 145 
                 146 
                 147 
                 148 
                 149 
               
               
                   
                 161 
                 162 
                 163 
                 164 
                 165 
                 166 
                 167 
                 168 
                 169 
                 170 
                 171 
                 172 
               
               
                 6/15, 
                 9 
                 13 
                 130 
                 1 
                 167 
                 91 
                 100 
                 16 
                 110 
                 160 
                 53 
                 112 
               
               
                   
                 12 
                 177 
                 54 
                 178 
                 52 
                 2 
                 7 
                 62 
                 179 
                 15 
                 159 
                 18 
               
               
                   
                 3 
                 14 
                 28 
                 8 
                 49 
                 24 
                 41 
                 0 
                 27 
                 34 
                 35 
                 25 
               
               
                   
                 40 
                 32 
                 22 
                 81 
                 76 
                 95 
                 116 
                 118 
                 129 
                 173 
                 77 
                 164 
               
               
                   
                 151 
                 150 
                 122 
                 148 
                 84 
                 107 
                 111 
                 104 
                 117 
                 105 
                 158 
                 128 
               
               
                   
                 68 
                 162 
                 94 
                 78 
                 48 
                 155 
                 171 
                 169 
                 103 
                 144 
                 137 
                 154 
               
               
                   
                 153 
                 72 
                 63 
                 71 
                 86 
                 133 
                 106 
                 60 
                 127 
                 156 
                 161 
                 152 
               
               
                   
                 163 
                 87 
                 93 
                 88 
                 55 
                 80 
                 79 
                 108 
                 175 
                 69 
                 82 
                 66 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 Code Rate 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                   
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                 45 
               
               
                   
                   
                 58 
                 59 
                 60 
                 61 
                 62 
                 63 
                 64 
                 65 
                 66 
                 67 
                 68 
               
               
                   
                   
                 81 
                 82 
                 83 
                 84 
                 85 
                 86 
                 87 
                 88 
                 89 
                 90 
                 91 
               
               
                   
                   
                 104 
                 105 
                 106 
                 107 
                 108 
                 109 
                 110 
                 111 
                 112 
                 113 
                 114 
               
               
                   
                   
                 127 
                 128 
                 129 
                 130 
                 131 
                 132 
                 133 
                 134 
                 135 
                 136 
                 137 
               
               
                   
                   
                 150 
                 151 
                 152 
                 153 
                 154 
                 155 
                 156 
                 157 
                 158 
                 159 
                 160 
               
               
                   
                   
                 173 
                 174 
                 175 
                 176 
                 177 
                 178 
                 179 
                   
                   
                   
                   
               
               
                   
                 6/15, 
                 75 
                 65 
                 19 
                 5 
                 64 
                 38 
                 21 
                 59 
                 120 
                 58 
                 176 
               
               
                   
                   
                 123 
                 17 
                 20 
                 115 
                 113 
                 39 
                 131 
                 11 
                 6 
                 57 
                 33 
               
               
                   
                   
                 10 
                 31 
                 29 
                 30 
                 42 
                 23 
                 37 
                 43 
                 36 
                 26 
                 4 
               
               
                   
                   
                 99 
                 83 
                 166 
                 51 
                 138 
                 70 
                 114 
                 102 
                 73 
                 96 
                 147 
               
               
                   
                   
                 101 
                 50 
                 45 
                 74 
                 134 
                 135 
                 149 
                 174 
                 61 
                 145 
                 132 
               
               
                   
                   
                 85 
                 172 
                 157 
                 143 
                 140 
                 124 
                 168 
                 121 
                 44 
                 119 
                 109 
               
               
                   
                   
                 142 
                 46 
                 125 
                 98 
                 67 
                 139 
                 126 
                 92 
                 97 
                 89 
                 170 
               
               
                   
                   
                 146 
                 56 
                 136 
                 141 
                 165 
                 47 
                 90 
               
               
                   
               
            
           
         
       
     
     In the case of Table 52, Equation 12 may be expressed as X 0 =Y π(0) =Y 9 , X 1 =Y π(1) =Y 13 , X 2 =Y π(2) =Y 130 , . . . , X 178 =Y π(178) =Y 47 , and X 179 =Y π(179) =Y 90 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groupsby changing the 0 th  group to the 9 th  group, the 1 st  group to the 13 th  group, the 2 nd  group to the 130 th  group, . . . , the 178 th  group to the 47 th  group, and the 179 th  group to the 90 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 64800, the code rate is 8/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 53 presented below: 
     
       
         
           
               
               
             
               
                 TABLE 53 
               
               
                   
               
             
            
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
               
               
                   
                 46 
                 47 
                 48 
                 49 
                 50 
                 51 
                 52 
                 53 
                 54 
                 55 
                 56 
                 57 
               
               
                   
                 69 
                 70 
                 71 
                 72 
                 73 
                 74 
                 75 
                 76 
                 77 
                 78 
                 79 
                 80 
               
               
                   
                 92 
                 93 
                 94 
                 95 
                 96 
                 97 
                 98 
                 99 
                 100 
                 101 
                 102 
                 103 
               
               
                   
                 115 
                 116 
                 117 
                 118 
                 119 
                 120 
                 121 
                 122 
                 123 
                 124 
                 125 
                 126 
               
               
                   
                 138 
                 139 
                 140 
                 141 
                 142 
                 143 
                 144 
                 145 
                 146 
                 147 
                 148 
                 149 
               
               
                   
                 161 
                 162 
                 163 
                 164 
                 165 
                 166 
                 167 
                 168 
                 169 
                 170 
                 171 
                 172 
               
               
                 8/15, 
                 171 
                 43 
                 85 
                 166 
                 176 
                 177 
                 35 
                 32 
                 86 
                 163 
                 25 
                 175 
               
               
                   
                 71 
                 80 
                 75 
                 118 
                 116 
                 70 
                 82 
                 78 
                 72 
                 124 
                 112 
                 111 
               
               
                   
                 53 
                 30 
                 41 
                 69 
                 73 
                 56 
                 50 
                 68 
                 20 
                 17 
                 10 
                 8 
               
               
                   
                 3 
                 39 
                 0 
                 87 
                 84 
                 6 
                 26 
                 46 
                 16 
                 66 
                 51 
                 31 
               
               
                   
                 36 
                 5 
                 4 
                 83 
                 135 
                 113 
                 49 
                 152 
                 103 
                 140 
                 146 
                 160 
               
               
                   
                 61 
                 143 
                 174 
                 167 
                 64 
                 55 
                 131 
                 156 
                 97 
                 145 
                 165 
                 170 
               
               
                   
                 92 
                 151 
                 88 
                 137 
                 90 
                 136 
                 96 
                 133 
                 147 
                 107 
                 99 
                 95 
               
               
                   
                 168 
                 123 
                 122 
                 52 
                 62 
                 94 
                 102 
                 148 
                 98 
                 162 
                 154 
                 114 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 Code Rate 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                   
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                 45 
               
               
                   
                   
                 58 
                 59 
                 60 
                 61 
                 62 
                 63 
                 64 
                 65 
                 66 
                 67 
                 68 
               
               
                   
                   
                 81 
                 82 
                 83 
                 84 
                 85 
                 86 
                 87 
                 88 
                 89 
                 90 
                 91 
               
               
                   
                   
                 104 
                 105 
                 106 
                 107 
                 108 
                 109 
                 110 
                 111 
                 112 
                 113 
                 114 
               
               
                   
                   
                 127 
                 128 
                 129 
                 130 
                 131 
                 132 
                 133 
                 134 
                 135 
                 136 
                 137 
               
               
                   
                   
                 150 
                 151 
                 152 
                 153 
                 154 
                 155 
                 156 
                 157 
                 158 
                 159 
                 160 
               
               
                   
                   
                 173 
                 174 
                 175 
                 176 
                 177 
                 178 
                 179 
                   
                   
                   
                   
               
               
                   
                 8/15, 
                 27 
                 38 
                 74 
                 129 
                 178 
                 29 
                 179 
                 79 
                 121 
                 120 
                 126 
               
               
                   
                   
                 110 
                 22 
                 63 
                 44 
                 60 
                 77 
                 21 
                 130 
                 37 
                 59 
                 19 
               
               
                   
                   
                 9 
                 11 
                 33 
                 42 
                 24 
                 67 
                 18 
                 76 
                 48 
                 47 
                 34 
               
               
                   
                   
                 169 
                 57 
                 15 
                 2 
                 28 
                 13 
                 23 
                 81 
                 7 
                 54 
                 40 
               
               
                   
                   
                 1 
                 108 
                 144 
                 158 
                 93 
                 139 
                 45 
                 115 
                 100 
                 153 
                 104 
               
               
                   
                   
                 134 
                 157 
                 173 
                 149 
                 164 
                 14 
                 58 
                 125 
                 141 
                 128 
                 117 
               
               
                   
                   
                 172 
                 127 
                 150 
                 142 
                 155 
                 65 
                 101 
                 159 
                 91 
                 138 
                 119 
               
               
                   
                   
                 12 
                 161 
                 132 
                 89 
                 105 
                 109 
                 106 
               
               
                   
               
            
           
         
       
     
     In the case of Table 53, Equation 12 may be expressed as X 0 =Y π(0) =Y 171 , X 1 =Y π(1) =Y 43 , X 2 =Y π(2) =Y 85 , . . . , X 178 =Y π(178) =Y 109 , and X 179 =Y π(179) =Y 106 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups by changing the 0th group to the 171 st  group, the 1 st  group to the 43 rd  group, the 2 nd  group to the 85 th  group, . . . , the 178 th  group to the 109 th  group, and the 179 th  group to the 106 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 54 presented below: 
     
       
         
           
               
               
             
               
                 TABLE 54 
               
               
                   
               
             
            
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
               
               
                   
                 46 
                 47 
                 48 
                 49 
                 50 
                 51 
                 52 
                 53 
                 54 
                 55 
                 56 
                 57 
               
               
                   
                 69 
                 70 
                 71 
                 72 
                 73 
                 74 
                 75 
                 76 
                 77 
                 78 
                 79 
                 80 
               
               
                   
                 92 
                 93 
                 94 
                 95 
                 96 
                 97 
                 98 
                 99 
                 100 
                 101 
                 102 
                 103 
               
               
                   
                 115 
                 116 
                 117 
                 118 
                 119 
                 120 
                 121 
                 122 
                 123 
                 124 
                 125 
                 126 
               
               
                   
                 138 
                 139 
                 140 
                 141 
                 142 
                 143 
                 144 
                 145 
                 146 
                 147 
                 148 
                 149 
               
               
                   
                 161 
                 162 
                 163 
                 164 
                 165 
                 166 
                 167 
                 168 
                 169 
                 170 
                 171 
                 172 
               
               
                 10/15, 
                 71 
                 112 
                 72 
                 133 
                 38 
                 57 
                 98 
                 85 
                 43 
                 171 
                 146 
                 100 
               
               
                   
                 40 
                 114 
                 145 
                 75 
                 82 
                 176 
                 14 
                 86 
                 102 
                 36 
                 76 
                 44 
               
               
                   
                 51 
                 92 
                 88 
                 3 
                 56 
                 12 
                 95 
                 63 
                 18 
                 26 
                 68 
                 79 
               
               
                   
                 10 
                 77 
                 42 
                 65 
                 16 
                 78 
                 53 
                 55 
                 84 
                 2 
                 58 
                 74 
               
               
                   
                 59 
                 28 
                 46 
                 61 
                 7 
                 8 
                 27 
                 62 
                 66 
                 23 
                 52 
                 19 
               
               
                   
                 45 
                 37 
                 50 
                 179 
                 6 
                 154 
                 162 
                 173 
                 174 
                 121 
                 113 
                 161 
               
               
                   
                 140 
                 141 
                 165 
                 156 
                 155 
                 143 
                 167 
                 148 
                 139 
                 163 
                 111 
                 127 
               
               
                   
                 115 
                 116 
                 138 
                 160 
                 157 
                 152 
                 158 
                 126 
                 130 
                 159 
                 172 
                 137 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 Code Rate 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                   
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                 45 
               
               
                   
                   
                 58 
                 59 
                 60 
                 61 
                 62 
                 63 
                 64 
                 65 
                 66 
                 67 
                 68 
               
               
                   
                   
                 81 
                 82 
                 83 
                 84 
                 85 
                 86 
                 87 
                 88 
                 89 
                 90 
                 91 
               
               
                   
                   
                 104 
                 105 
                 106 
                 107 
                 108 
                 109 
                 110 
                 111 
                 112 
                 113 
                 114 
               
               
                   
                   
                 127 
                 128 
                 129 
                 130 
                 131 
                 132 
                 133 
                 134 
                 135 
                 136 
                 137 
               
               
                   
                   
                 150 
                 151 
                 152 
                 153 
                 154 
                 155 
                 156 
                 157 
                 158 
                 159 
                 160 
               
               
                   
                   
                 173 
                 174 
                 175 
                 176 
                 177 
                 178 
                 179 
                   
                   
                   
                   
               
               
                   
                 10/15, 
                 135 
                 81 
                 83 
                 136 
                 109 
                 142 
                 123 
                 49 
                 39 
                 73 
                 117 
               
               
                   
                   
                 60 
                 34 
                 64 
                 41 
                 22 
                 99 
                 29 
                 31 
                 20 
                 5 
                 25 
               
               
                   
                   
                 67 
                 149 
                 47 
                 87 
                 15 
                 89 
                 105 
                 1 
                 13 
                 90 
                 4 
               
               
                   
                   
                 69 
                 120 
                 177 
                 70 
                 178 
                 96 
                 33 
                 80 
                 21 
                 35 
                 54 
               
               
                   
                   
                 48 
                 24 
                 17 
                 101 
                 9 
                 30 
                 32 
                 0 
                 91 
                 93 
                 11 
               
               
                   
                   
                 170 
                 131 
                 153 
                 134 
                 107 
                 104 
                 118 
                 128 
                 164 
                 106 
                 166 
               
               
                   
                   
                 108 
                 94 
                 147 
                 150 
                 97 
                 110 
                 175 
                 169 
                 124 
                 144 
                 122 
               
               
                   
                   
                 132 
                 119 
                 168 
                 125 
                 103 
                 129 
                 151 
               
               
                   
               
            
           
         
       
     
     In the case of Table 54, Equation 12 may be expressed as X 0 =Y π(0) =Y 71 , X 1 =Y π(1) =Y 112 , X 2 =Y π(2) =Y 72 , . . . , X 178 =Y π(178) =Y 129 , and X 179 =Y π(179) =Y 151 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups by changing the 0th group to the 71 st  group, the 1 st  group to the 112 th  group, the 2 nd  group to the 72 nd  group, . . . , the 178 th  group to the 129 th  group, and the 179 th  group to the 151′ group. 
     In another example, when the length N ldpc  of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 55 presented below: 
     
       
         
           
               
               
             
               
                 TABLE 55 
               
               
                   
               
             
            
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
               
               
                   
                 46 
                 47 
                 48 
                 49 
                 50 
                 51 
                 52 
                 53 
                 54 
                 55 
                 56 
                 57 
               
               
                   
                 69 
                 70 
                 71 
                 72 
                 73 
                 74 
                 75 
                 76 
                 77 
                 78 
                 79 
                 80 
               
               
                   
                 92 
                 93 
                 94 
                 95 
                 96 
                 97 
                 98 
                 99 
                 100 
                 101 
                 102 
                 103 
               
               
                   
                 115 
                 116 
                 117 
                 118 
                 119 
                 120 
                 121 
                 122 
                 123 
                 124 
                 125 
                 126 
               
               
                   
                 138 
                 139 
                 140 
                 141 
                 142 
                 143 
                 144 
                 145 
                 146 
                 147 
                 148 
                 149 
               
               
                   
                 161 
                 162 
                 163 
                 164 
                 165 
                 166 
                 167 
                 168 
                 169 
                 170 
                 171 
                 172 
               
               
                 10/15, 
                 130 
                 33 
                 69 
                 31 
                 77 
                 142 
                 84 
                 27 
                 175 
                 127 
                 163 
                 18 
               
               
                   
                 70 
                 176 
                 177 
                 5 
                 178 
                 3 
                 179 
                 43 
                 9 
                 4 
                 49 
                 97 
               
               
                   
                 58 
                 87 
                 51 
                 54 
                 2 
                 60 
                 6 
                 73 
                 16 
                 56 
                 85 
                 20 
               
               
                   
                 41 
                 12 
                 63 
                 44 
                 81 
                 67 
                 40 
                 14 
                 98 
                 55 
                 82 
                 168 
               
               
                   
                 21 
                 94 
                 37 
                 25 
                 28 
                 35 
                 7 
                 89 
                 38 
                 96 
                 62 
                 92 
               
               
                   
                 83 
                 34 
                 15 
                 23 
                 36 
                 174 
                 152 
                 162 
                 148 
                 144 
                 156 
                 155 
               
               
                   
                 128 
                 118 
                 157 
                 153 
                 151 
                 117 
                 145 
                 90 
                 119 
                 129 
                 126 
                 149 
               
               
                   
                 120 
                 167 
                 173 
                 100 
                 154 
                 111 
                 147 
                 138 
                 114 
                 141 
                 123 
                 110 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 Code Rate 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                   
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                 45 
               
               
                   
                   
                 58 
                 59 
                 60 
                 61 
                 62 
                 63 
                 64 
                 65 
                 66 
                 67 
                 68 
               
               
                   
                   
                 81 
                 82 
                 83 
                 84 
                 85 
                 86 
                 87 
                 88 
                 89 
                 90 
                 91 
               
               
                   
                   
                 104 
                 105 
                 106 
                 107 
                 108 
                 109 
                 110 
                 111 
                 112 
                 113 
                 114 
               
               
                   
                   
                 127 
                 128 
                 129 
                 130 
                 131 
                 132 
                 133 
                 134 
                 135 
                 136 
                 137 
               
               
                   
                   
                 150 
                 151 
                 152 
                 153 
                 154 
                 155 
                 156 
                 157 
                 158 
                 159 
                 160 
               
               
                   
                   
                 173 
                 174 
                 175 
                 176 
                 177 
                 178 
                 179 
                   
                   
                   
                   
               
               
                   
                 10/15, 
                 137 
                 132 
                 116 
                 79 
                 170 
                 13 
                 30 
                 135 
                 22 
                 68 
                 171 
               
               
                   
                   
                 46 
                 29 
                 108 
                 74 
                 103 
                 64 
                 107 
                 86 
                 19 
                 50 
                 109 
               
               
                   
                   
                 95 
                 11 
                 106 
                 99 
                 75 
                 42 
                 1 
                 32 
                 8 
                 48 
                 17 
               
               
                   
                   
                 26 
                 47 
                 78 
                 24 
                 88 
                 71 
                 80 
                 105 
                 0 
                 10 
                 52 
               
               
                   
                   
                 66 
                 72 
                 57 
                 39 
                 59 
                 45 
                 76 
                 65 
                 53 
                 61 
                 91 
               
               
                   
                   
                 113 
                 172 
                 122 
                 121 
                 161 
                 102 
                 169 
                 150 
                 131 
                 139 
                 136 
               
               
                   
                   
                 143 
                 104 
                 112 
                 158 
                 165 
                 164 
                 146 
                 125 
                 93 
                 115 
                 140 
               
               
                   
                   
                 101 
                 166 
                 159 
                 160 
                 133 
                 134 
                 124 
               
               
                   
               
            
           
         
       
     
     In the case of Table 55, Equation 12 may be expressed as X 0 =Y π(0) =Y 130 , X 1 =Y π(1) =Y 33 , X 2 =Y π(2) =Y 69 , . . . , X 178 =Y π(178) =Y 134 , and X 179 =Y π(179) =Y 124 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups by changing the 0th group to the 130 th  group, the 1 st  group to the 33 rd  group, the 2 nd  group to the 69 th  group, . . . , the 178 th  group to the 134 th  group, and the 179 th  group to the 124 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 64800, the code rate is 12/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 56 presented below: 
     
       
         
           
               
               
             
               
                 TABLE 56 
               
               
                   
               
             
            
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
               
               
                   
                 46 
                 47 
                 48 
                 49 
                 50 
                 51 
                 52 
                 53 
                 54 
                 55 
                 56 
                 57 
               
               
                   
                 69 
                 70 
                 71 
                 72 
                 73 
                 74 
                 75 
                 76 
                 77 
                 78 
                 79 
                 80 
               
               
                   
                 92 
                 93 
                 94 
                 95 
                 96 
                 97 
                 98 
                 99 
                 100 
                 101 
                 102 
                 103 
               
               
                   
                 115 
                 116 
                 117 
                 118 
                 119 
                 120 
                 121 
                 122 
                 123 
                 124 
                 125 
                 126 
               
               
                   
                 138 
                 139 
                 140 
                 141 
                 142 
                 143 
                 144 
                 145 
                 146 
                 147 
                 148 
                 149 
               
               
                   
                 161 
                 162 
                 163 
                 164 
                 165 
                 166 
                 167 
                 168 
                 169 
                 170 
                 171 
                 172 
               
               
                 12/15, 
                 29 
                 176 
                 28 
                 24 
                 167 
                 43 
                 22 
                 32 
                 177 
                 148 
                 172 
                 156 
               
               
                   
                 34 
                 164 
                 179 
                 11 
                 125 
                 63 
                 76 
                 48 
                 113 
                 75 
                 73 
                 83 
               
               
                   
                 106 
                 110 
                 39 
                 86 
                 38 
                 0 
                 119 
                 54 
                 92 
                 87 
                 82 
                 9 
               
               
                   
                 111 
                 16 
                 26 
                 109 
                 126 
                 74 
                 44 
                 97 
                 128 
                 8 
                 118 
                 80 
               
               
                   
                 122 
                 88 
                 85 
                 4 
                 100 
                 69 
                 103 
                 59 
                 5 
                 56 
                 19 
                 95 
               
               
                   
                 20 
                 21 
                 61 
                 33 
                 6 
                 58 
                 96 
                 1 
                 101 
                 71 
                 112 
                 13 
               
               
                   
                 65 
                 123 
                 30 
                 57 
                 105 
                 15 
                 160 
                 145 
                 151 
                 133 
                 161 
                 153 
               
               
                   
                 134 
                 137 
                 168 
                 138 
                 135 
                 152 
                 144 
                 132 
                 107 
                 150 
                 143 
                 162 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 Code Rate 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                   
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                 45 
               
               
                   
                   
                 58 
                 59 
                 60 
                 61 
                 62 
                 63 
                 64 
                 65 
                 66 
                 67 
                 68 
               
               
                   
                   
                 81 
                 82 
                 83 
                 84 
                 85 
                 86 
                 87 
                 88 
                 89 
                 90 
                 91 
               
               
                   
                   
                 104 
                 105 
                 106 
                 107 
                 108 
                 109 
                 110 
                 111 
                 112 
                 113 
                 114 
               
               
                   
                   
                 127 
                 128 
                 129 
                 130 
                 131 
                 132 
                 133 
                 134 
                 135 
                 136 
                 137 
               
               
                   
                   
                 150 
                 151 
                 152 
                 153 
                 154 
                 155 
                 156 
                 157 
                 158 
                 159 
                 160 
               
               
                   
                   
                 173 
                 174 
                 175 
                 176 
                 177 
                 178 
                 179 
                   
                   
                   
                   
               
               
                   
                 12/15, 
                 174 
                 41 
                 23 
                 154 
                 175 
                 37 
                 178 
                 171 
                 36 
                 25 
                 165 
               
               
                   
                   
                 35 
                 115 
                 52 
                 70 
                 18 
                 93 
                 131 
                 45 
                 127 
                 98 
                 49 
               
               
                   
                   
                 68 
                 116 
                 121 
                 12 
                 91 
                 130 
                 62 
                 10 
                 42 
                 78 
                 90 
               
               
                   
                   
                 94 
                 104 
                 114 
                 99 
                 55 
                 72 
                 53 
                 60 
                 84 
                 117 
                 2 
               
               
                   
                   
                 79 
                 14 
                 31 
                 47 
                 66 
                 129 
                 124 
                 3 
                 40 
                 67 
                 51 
               
               
                   
                   
                 81 
                 77 
                 46 
                 7 
                 108 
                 17 
                 120 
                 27 
                 64 
                 89 
                 50 
               
               
                   
                   
                 142 
                 146 
                 158 
                 147 
                 102 
                 149 
                 159 
                 140 
                 139 
                 155 
                 141 
               
               
                   
                   
                 170 
                 169 
                 136 
                 157 
                 173 
                 163 
                 166 
               
               
                   
               
            
           
         
       
     
     In the case of Table 56, Equation 12 may be expressed as X 0 =Y π(0) =Y 29 , X 1 =Y π(1) =Y 176 , X 2 =Y π(2) =Y 28 , . . . , X 178 =Y π(178) =Y 163 , and X 179 =Y π(179) =Y 166 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups by changing the 0 th  group to the 29 th  group, the 1 st  group to the 176 th  group, the 2 nd  group to the 28 th  group, . . . , the 178 th  group to the 163 rd  group, and the 179 th  group to the 166 th  group. 
     As described above, the group interleaver  122  may rearrange the order of the plurality of groups by using Equation 12 and Tables 42 to 56. 
     Since the order of the groups constituting the LDPC codeword is rearranged by the group interleaver  122 , and then the groups are block-interleaved by the block interleaver  124 , which will be described below, “Order of bits groups to be block interleaved” is set forth in Tables 42 to 56 in relation to π(j). 
     The LDPC codeword which is group-interleaved in the above-described method is illustrated in  FIG.  6   . Comparing the LDPC codeword of  FIG.  6    and the LDPC codeword of FIG.  5  before group interleaving, it can be seen that the order of the plurality of groups constituting the LDPC codeword is rearranged. 
     That is, as shown in  FIGS.  5  and  6   , the groups of the LDPC codeword are arranged in order of group X 0 , group X 1 , . . . , group X Ngroup-1  before being group-interleaved, and are arranged in an order of group Y 0 , group Y 1 , . . . , group Y Ngroup-1  after being group-interleaved. 
     In this case, the order of arranging the groups by the group interleaving may be determined based on Tables 27 to 56. 
     The group twist interleaver  123  interleaves bits in a same group. That is, the group twist interleaver  123  may rearrange the order of the bits in the same group by changing the order of the bits in the same group. 
     In this case, the group twist interleaver  123  may rearrange the order of the bits in the same group by cyclic-shifting a predetermined number of bits from among the bits in the same group. 
     For example, as shown in  FIG.  7   , the group twist interleaver  123  may cyclic-shift bits included in the group Y 1  to the right by 1 bit. In this case, the bits located in the 0 th  position, the 1 st  position, the 2 nd  position, . . . , the 358 th  position, and the 359 th  position in the group Y 1  as shown in  FIG.  7    are cyclic-shifted to the right by 1 bit. As a result, the bit located in the 359 th  position before being cyclic-shifted is located in the front of the group Y 1  and the bits located in the 0 th  position, the 1 st  position, the 2 nd  position, . . . , the 358 th  position before being cyclic-shifted are shifted to the right serially by 1 bit and located. 
     In addition, the group twist interleaver  123  may rearrange the order of bits in each group by cyclic-shifting a different number of bits in each group. 
     For example, the group twist interleaver  123  may cyclic-shift the bits included in the group Y 1  to the right by 1 bit, and may cyclic-shift the bits included in the group Y 2  to the right by 3 bits. 
     Changing the order of the bits in the same group as described above is referred to as a group twist. The group twist may be performed to prevent bits mapped onto a single modulation symbol from being connected to a single check node. Accordingly, the group twist interleaver  123  may be omitted according to circumstances. 
     In addition, the group twist interleaver  123  is placed after the group interleaver  122  in the above-described example. However, this is merely an example. That is, the group twist interleaver  123  changes only the order of bits in a certain group and does not change the order of the groups. Therefore, the group twist interleaver  123  may be placed before the group interleaver  122 . 
     The block interleaver  124  interleaves the plurality of groups the order of which has been rearranged. Specifically, the block interleaver  124  may interleave the plurality of groups the order of which has been rearranged by the group interleaver  122 . 
     That is, the group twist interleaver  123  changes only the order of bits in the same group and does not change the order of groups by interleaving. Accordingly, the order of the groups to be block-interleaved by the block interleaver  124  may be determined by the group interleaver  122 . Specifically, the order of the groups to be block-interleaved by the block interleaver  124  may be determined by π(j) defined in Tables 27 to 56. 
     The block interleaver  124  may interleave the plurality of groups the order of which has been rearranged by using at least one column and a plurality of rows. 
     Specifically, the block interleaver  124  may interleave by writing the plurality of groups on each column of the at least one column in group units in a column direction, and reading each row of the at least one column in which the plurality of groups are written in group units in a row direction. 
     Hereinafter, the group located in the j th  position after being interleaved by the group interleaver  122  will be referred to as group Y j . 
     When the number of groups constituting an LDPC codeword is an integer multiple of the number of columns, the block interleaver  124  interleaves the plurality of groups by writing as many groups as the number of groups divided by the number of columns in each column serially in group units. 
     For example, as shown in  FIG.  8   , the block interleaver  124  writes bits included in group Y 0 , group Y 1 , . . . , group Y p−1  in the 1 st  column from the 1 st  row to the R 1   th  row, writes bits included in group Y p , group Y p+1 , . . . , group Y q−1  in the 2nd column from the 1 st  row to the R 1   th  row, . . . , and writes bits included in group Y z , Y z+1 , . . . , group Y Ngroup-1  in the column C from the 1 st  row to the R 1   th  row. The block interleaver  124  may read each row of the plurality of columns in a row direction from the 1 st  row. Each column may include rows from 1 to R 1 . That is, each column is formed of R 1  number of rows. 
     However, when the number of groups of the LDPC codeword is not an integer multiple of the number of columns, the block interleaver  124  may interleave by dividing each column into N number of parts (N is an integer greater than or equal to 2). 
     Specifically, the block interleaver  124  divides each column into a part including as many rows as the number of bits included in groups which can be written in each column in group units, and a part including the other rows, and interleaves the plurality of groups by using the divided parts. 
     The part including as many rows as the number of bits included in the groups which can be written in group units is formed of as many rows as an integer multiple of M. In addition, as described above, the number of codeword bits forming each group may be a divisor of M and thus, a part including columns as many as the number of bits included in each group which can be written by group units may consist of rows as many as the integer multiple of the number of bits forming each group. 
     In this case, the block interleaver  124  writes at least some groups which can be written in each of the plurality of columns in group units from among the plurality of groups in each of the plurality of columns serially, and then writes the other groups in the other area which remains after the at least some groups have been written in group units in each of the plurality of columns. That is, the block interleaver  124  writes the bits included in the at least some writeable group in the first part (that is, part 1) of each column in group units, and then divides the bits included in the other groups and writes the bits in the second part (that is, part 2) of each column. 
     For example, it is assumed that the block interleaver  124  divides each column into the first part including R 1  number of rows and the second part including R 2  number of rows as shown in  FIGS.  9  and  10   . Herein, R 1  corresponds to the number of bits included in the groups which can be written in each column in group units, and R 2  is R 1  subtracted from the total number of rows of each column. 
     In this case, the block interleaver  124  writes the bits included in the groups which can be written in each column in group units in the first part of each column in the column direction. 
     That is, as shown in  FIGS.  9  and  10   , the block interleaver  124  writes the bits included in each of group Y 0 , group Y 1 , . . . , group Y n−1  in the 1 st  to R 1   th  rows of the first part of the 1 st  column, writes bits included in each of group Y n , group Y n+1 , . . . , group Y m−1  in the 1 st  to R 1   th  rows of the first part of the 2 nd  column, . . . , writes bits included in each of group Y e , group Y e+1 , . . . , group Y Ngroup-2  in the 1 st  to R 1   th  rows of the first part of the column C. 
     As described above, the block interleaver  124  writes the bits included in the groups which can be written in each column in group units in the first part of each column in the column direction. 
     Thereafter, the block interleaver  124  divides bits included in the other groups except the groups written in the first part of each column from among the plurality of groups, and writes the bits in the second part of each column in the column direction. In this case, the block interleaver  124  divides the bits included in the other groups except the groups written in the first part of each column by the number of columns, so that the same number of bits are written in the second part of each column, and writes the divided bits in the second part of each column in the column direction. 
     For example, when the last group N group-1  Y of the LDPC codeword remains as shown in  FIG.  9   , the block interleaver  124  divides the bits included in the group Y Ngroup-1  by the number of columns (C), and writes the divided bits in the second part of each column serially. 
     That is, the block interleaver  124  writes the bits in the 1 st  to R 2   th  rows of the second part of the 1 st  column, writes the bits in the 1 st  to R 2   th  rows of the second part of the 2 nd  column, . . . , etc., and writes the bits in the 1 st  to R 2   th  rows of the second part of the column C. In this case, the block interleaver  124  may write the bits in the second part of each column in the column direction as shown in  FIG.  9   . In other words, the bits forming a bit group in the second part may be written not in the same rows but in a plurality of rows. 
     In the above-described example, the block interleaver  124  w ri tes t h   e  bits in the second part in the co lu mn direction. However, this is me re ly an  ex ample. That is, the block interle av er  124  may write the bits in the plurality of  co lumns  of  the second parts in a row direction. In this case, the block interleaver  124  may write the bits in the first part in the same method as described above. 
     Specifically, referring to  FIG.  10   , the block interleaver  124  writes the bits from the 1 st  row of the second part in the 1 st  column to the 1 st  row of the second part in the column C, writes the bits from the 2 nd  row of the second part in the 1 st  column to the 2 nd  row of the second part in the column C, . . . , etc., and writes the bits from the R 2   th  row of the second part in the 1 st  column to the R 2   th  row of the second part in the column C. 
     On the other hand, the block interleaver  124  reads the bits written in each row of each part in the row direction. That is, as shown in  FIGS.  9  and  10   , the block interleaver  124  reads the bits written in each row of the first part of the plurality of columns serially in the row direction, and reads the bits written in each row of the second part of the plurality of columns serially in the row direction. 
     As described above, the block interleaver  124  may interleave the plurality of groups in the methods described above with reference to  FIGS.  8  to  10   . 
     In particular, in the case of  FIG.  9   , the bits included in the group which does not belong to the first part are written in the second part in the column direction and read in the row direction. In view of this, the order of the bits included in the group which does not belong to the first part is rearranged. Since the bits included in the group which does not belong to the first part are interleaved as described above, Bit Error Rate (BER)/Frame Error Rate (FER) performance can be improved in comparison with a case in which such bits are not interleaved. 
     However, the group which does not belong to the first part may not be interleaved as shown in  FIG.  10   . That is, since the block interleaver  124  writes and read the bits included in the group which does not belong to the first part on and from the second part in the row direction, the order of the bits included in the group which does not belong to the first part is not changed and the bits are output to the modulator  130  serially. In this case, the bits included in the group which does not belong to the first part may be output serially and mapped onto a modulation symbol. 
     In  FIGS.  9  and  10   , the last single group of the plurality of groups is written in the second part. However, this is merely an example. The number of groups written in the second part may vary according to the total number of groups of the LDPC codeword, the number of columns and rows or the number of transmit antenna. 
     The block interleaver  124  may have a different configuration according to whether bits included in a same group are mapped onto a single bit of each modulation symbol or bits included in a same group are mapped onto two bits of each modulation symbol. 
     Meanwhile, in case of a system where the block interleaver  124  uses a plurality of antennas, the block interleaver  124  may determine the number of columns in consideration of the number of bits forming a modulation symbol and the number of antennas in use simultaneously. For example, in a case where a plurality of bits included in the same group are respectively mapped onto a single bit of each modulation symbol, and two antennas are used, the block interleaver  124  may determine the number of columns as twice the number of bits forming a modulation symbol 
     First, when bits included in the same group are mapped onto a single bit of each modulation symbol, the block interleaver  124  may have configurations as shown in Tables 57 and 58: 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 57 
               
             
            
               
                   
                   
               
               
                   
                   
                 N ldpc  = 64800 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                   
                   
                 16 
                 64 
                 256 
                 1024 
                 4096 
               
               
                   
                   
                 QPSK 
                 QAM 
                 QAM 
                 QAM 
                 QAM 
                 QAM 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 C 
                 2 
                 4 
                 6 
                 8 
                 10 
                 12 
               
               
                   
                 R 1   
                 32400 
                 16200 
                 10800 
                 7920 
                 6480 
                 5400 
               
               
                   
                 R 2   
                 0 
                 0 
                 0 
                 180 
                 0 
                 0 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                   
                 TABLE 58 
               
             
            
               
                   
                   
               
               
                   
                   
                 N ldpc  = 16200 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                   
                   
                 16 
                 64 
                 256 
                 1024 
                 4096 
               
               
                   
                   
                 QPSK 
                 QAM 
                 QAM 
                 QAM 
                 QAM 
                 QAM 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 C 
                 2 
                 4 
                 6 
                 8 
                 10 
                 12 
               
               
                   
                 R 1   
                 7920 
                 3960 
                 2520 
                 1800 
                 1440 
                 1080 
               
               
                   
                 R 2   
                 180 
                 90 
                 180 
                 225 
                 180 
                 270 
               
               
                   
                   
               
            
           
         
       
     
     Herein, C (or NO is the number of columns of the block interleaver  124 , R 1  is the number of rows constituting the first part in each column, and R 2  i s the number of rows constituting the second part in each column. 
     Referring to Tables 57 and 58, when the number of groups constituting an LDPC codeword is an integer multiple of the number of columns, the block interleaver  124  interleaves without dividing each column. Therefore, R 1  corresponds to the number of rows constituting each column, and R 2  is 0. In addition, when the number of groups constituting an LDPC codeword is not an integer multiple of the number of columns, the block interleaver  124  interleaves the groups by dividing each column into the first part formed of R 1  number of rows, and the second part formed of R 2  number of rows. 
     When the number of columns of the block interleaver  124  is equal to the number of bits constituting a modulation symbol, bits included in a same group are mapped onto a single bit of each modulation symbol as shown in Tables 57 and 58. 
     For example, when N ldpc =64800 and the modulation method is 16-QAM, the block interleaver  124  may use four (4) columns each including 16200 rows. In this case, a plurality of groups of an LDPC codeword are written in the four (4) columns in group units and bits written in the same row in each column are output serially. In this case, since four (4) bits constitute a single modulation symbol in the modulation method of 16-QAM, bits included in the same group and output from a single column may be mapped onto a single bit of each modulation symbol. For example, bits included in a group written in the 1 st  column may be mapped onto the first bit of each modulation symbol. 
     On the other hand, when bits included in a same group are mapped onto two bits of each modulation symbol, the block interleaver  124  may have configurations as shown in Tables 59 and 60: 
     
       
         
           
               
               
             
               
                 TABLE 59 
               
             
            
               
                   
               
               
                   
                 N ldpc  = 64800 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                 16 
                 64 
                 256 
                 1024 
                 4096 
               
               
                   
                 QPSK 
                 QAM 
                 QAM 
                 QAM 
                 QAM 
                 QAM 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 C 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
               
               
                 R 1   
                 64800 
                 32400 
                 21600 
                 16200 
                 12960 
                 10800 
               
               
                 R 2   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                   
                 TABLE 60 
               
             
            
               
                   
                   
               
               
                   
                   
                 N ldpc  = 16200 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                   
                   
                 16 
                 64 
                 256 
                 1024 
                 4096 
               
               
                   
                   
                 QPSK 
                 QAM 
                 QAM 
                 QAM 
                 QAM 
                 QAM 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 C 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
               
               
                   
                 R 1   
                 16200 
                 7920 
                 5400 
                 3960 
                 3240 
                 2520 
               
               
                   
                 R 2   
                 0 
                 180 
                 0 
                 90 
                 0 
                 180 
               
               
                   
                   
               
            
           
         
       
     
     Herein, C (or NO is the number of columns of the block interleaver  124 , R 1  is the number of rows constituting the first part in each column, and R 2  is the number of rows constituting the second part in each column. 
     Referring to Tables 59 and 60, when the number of groups constituting an LDPC codeword is an integer multiple of the number of columns, the block interleaver  124  interleaves without dividing each column. Therefore, R 1  corresponds to the number of rows constituting each column, and R 2  is 0. In addition, when the number of groups constituting an LDPC codeword is not an integer multiple of the number of columns, the block interleaver  124  interleaves the groups by dividing each column into the first part formed of R 1  number of rows, and the second part formed of R 2  number of rows 
     When the number of columns of the block interleaver  124  is half of the number of bits constituting a modulation symbol as shown in Tables 59 and 60, bits included in a same group are mapped onto two bits of each modulation symbol. 
     For example, when N ldpc =64800 and the modulation method is 16-QAM, the block interleaver  124  may use two (2) columns each including 32400 rows in this case, a plurality of groups of an LDPC codeword are written in the two (2) columns in group units and bits written in the same row in each column are output serially. Since four (4) bits constitute a single modulation symbol in the modulation method of 16-QAM, bits output from two rows constitute a single modulation symbol Accordingly, bits included in the same group and output from a single column may be mapped onto two bits of each modulation symbol. For example, bits included in a group written in the 1 st  column may be mapped onto bits existing in any two positions of each modulation symbol. 
     Referring to Tables 57 to 60, the total number of rows of the block interleaver  124 , that is, R 1 +R 2 , is N ldpc /C. 
     In addition, the number of rows of the first part, Ri, is an integer multiple of the number of bits included in each group, M (e.g., M=360), and maybe expressed as └N group /C┘×M and the number of rows of the second part, R 2 , may be N ldpc /C-R 1 . Herein, └N group /C┘ is the largest integer below N ldpc /C. Since R 1  is an integer multiple of the number of bits included in each group, M, bits may be written in R 1  in group units. 
     In addition, when the number of groups of an LDPC codeword is not an integer multiple of the number of columns, it can be seen from Tables 57 to 60 that the block interleaver  124  interleaves a plurality of groups of the LDPC codeword by dividing each column into two parts. 
     Specifically, the length of an LDPC codeword divided by the number of columns is the total number of rows included in the each column. In this case, when the number of groups of the LDPC codeword is an integer multiple of the number of columns, each column is not divided into two parts. However, when the number of groups of the LDPC codeword is not an integer multiple of the number of columns, each column is divided into two parts. 
     For example, it is assumed that the number of columns of the block interleaver  124  is identical to the number of bits constituting a modulation symbol, and an LDPC codeword is formed of 64800 bits as shown in Table 57. In this case, the LDPC codeword is formed of 64800/360(=180) groups. 
     When the modulation method is 16-QAM, each column may have 64800/4(=16200) rows. In this case, since the number of groups of an LDPC codeword divided by the number of columns is 180/4(=45), bits can be written in each column in group units without dividing each column into two parts. That is, bits included in 45 groups, that is, 45×360(=16200) bits can be written in each column. 
     However, when the modulation method is 256-QAM, each column may have 64800/8(=8100) rows. In this case, since the number of groups of an LDPC codeword divided by the number of columns is 180/8=22.5, each column is divided into two parts. 
     In this case, since the bits should be written in the first part of each column in group units, the first part of each column has 22×360(=7920) rows and 7920 bits included in 22 groups may be written. The second part of each column has rows which are the rows of the first part subtracted from the total rows of each column. Accordingly, the second part of each column includes 8100-7920(=180) rows, and 180 bits can be written. In this case, the bits included in the other group which has not been written in the first part are divided and written in the second part of each column. 
     In another example, it is assumed that the number of columns of the block interleaver  124  is half of the number of bits constituting the modulation symbol, and the LDPC codeword is formed of 16200 bits as shown in Table 60. In this case, the LDPC codeword is formed of 16200/360(=45) groups. 
     When the modulation method is 64-QAM, each column may have 16200/3(=5400) rows. In this case, since the number of groups of the LDPC codeword divided by the number of columns is 45/3(=15), bits can be written in each column in group units without dividing each column into two parts. That is, bits included in the 15 groups, that is, 15×360(=5400) bits can be written in each column. 
     However, when the modulation method is 256-QAM, each column may have 16200/4(=4050) rows. In this case, since the number of groups of the LDPC codeword divided by the number of columns is 45/4=11.25, each column is divided into 2 parts. 
     In this case, since the bits should be written in the first part of each column in group units, the first part of each column has 11×360(=3960) rows and 3960 bits included in 11 groups may be written. The second part of each column has rows which are the rows of the first part subtracted from the total rows of each column. Accordingly, the second part of each column includes 4050-3960(=90) rows, and 90 bits can be written. In this case, the bits included in the other group which has not been written in the first part are divided and written in the second part of each column. 
     Hereinafter, the block interleaver of  FIG.  4    according to an exemplary embodiment will be explained in detail with reference to  FIG.  11   . 
     In a group-interleaved LDPC codeword (v 0 , v 1 , . . . , v N     ldpc     -1 ), Y j  is continuously arranged like V={Y 0 , Y 1 , . . . Y N     group     -1 }. 
     The LDPC codeword after group interleaving may be interleaved by the block interleaver  124  as shown in  FIG.  11   . Specifically, an input bit vi is written from the first part to the second part serially in a column direction, and is read from the first part to the second part serially in a row direction. 
     In this case, the number of columns and the number of rows of the first part and the second part of the block interleaver  124  vary according to a modulation method as in Table 61 presented below. 
     Herein, a sum of the number of rows of the first part, Nr i  and the number of rows of the second part, N r2 , is equal to N ldpc /N c  (herein, N c  is the number of columns). In addition, since N r1  is a multiple of 360, a plurality of bit groups may be written in the first part. 
     
       
         
           
               
               
               
               
             
               
                 TABLE 61 
               
             
            
               
                   
               
               
                   
                 Rows in Part 1 N r1   
                 Rows in Part 2 N r2   
                   
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 N ldpc  =  
                 N ldpc  =  
                 N ldpc  =  
                 N ldpc  =  
                 Columns 
               
               
                 Modulation 
                 64800 
                 16200 
                 64800 
                 16200 
                 N c   
               
               
                   
               
               
                  16-QAM 
                 16200 
                 3960 
                  0 
                  90 
                  4 
               
               
                  14-QAM 
                 10800 
                 2520 
                  0 
                 180 
                  6 
               
               
                  256-QAM 
                  7920 
                 1800 
                 180 
                 225 
                  8 
               
               
                 1024-QAM 
                  6480 
                 1440 
                  0 
                 180 
                 10 
               
               
                   
               
            
           
         
       
     
     Hereinafter, an operation of the block interleaver  124  will be explained in detail. 
     Specifically, as shown in  FIG.  11   , the input bit v i (0≤i&lt;N c ×N r1 ) is written in r i  row of c i  column of the first part of the block interleaver  124 . Herein, c i  and r i  are 
     
       
         
           
             
               c 
               i 
             
             ⁢ 
             
               ⌊ 
               
                 i 
                 
                   N 
                   
                     r 
                     ⁢ 
                     1 
                   
                 
               
               ⌋ 
             
           
         
       
     
     and r i =(i mod N rl ), respectively. 
     In addition, the input bit v i (N c ×N rl ≤i&lt;N ldpc ) is written in an r i  row of c i  column of the second part of the block interleaver  124 . Herein, c i  and r i  are 
     
       
         
           
             
               c 
               i 
             
             ⁢ 
             
               ⌊ 
               
                 
                   ( 
                   
                     i 
                     - 
                     
                       
                         N 
                         C 
                       
                       ⨯ 
                       
                         N 
                         
                           r 
                           ⁢ 
                           1 
                         
                       
                     
                   
                   ) 
                 
                 
                   N 
                   
                     r 
                     ⁢ 
                     2 
                   
                 
               
               ⌋ 
             
           
         
       
     
     and r i =N r1 +{(i-N c ×N r2 )mod N 2 }, respectively. 
     An output bit q i (0≤j&lt;N ldpc ) is read from c j  column of r i  row. Herein, r j  and c j  are 
     
       
         
           
             
               r 
               j 
             
             ⁢ 
             
               ⌊ 
               
                 j 
                 
                   N 
                   c 
                 
               
               ⌋ 
             
           
         
       
     
     and c j =(j mod N c ), respectively. 
     For example, when the length N ldpc  of an LDPC codeword is 64800 and the modulation method is 256-QAM, an order of bits output from the block interleaver  124  may be (q 0 , q 1 , q 2 , . . . , q 63357 , q 63358 , q 63359 , q 63360 , q 63361 , . . . , q 64799 )=(v 0 ,v 7920 , v 15840 , . . . , v 47519 , v 55439 , v 63359 , v 63360 , v 63540 , v 64799 ). Herein, the indexes of the right side of the foregoing equation may be specifically expressed for the eight (8) columns as 0, 7920, 15840, 23760, 31680, 39600, 47520, 55440, 1, 7921, 15841, 23761, 31681, 39601, 47521, 55441, . . . , 7919, 15839, 23759, 31679, 39599, 47519, 55439, 63359, 63360, 63540, 63720, 63900, 64080, 64260, 64440, 64620, . . . , 63539, 63719, 63899, 64079, 64259, 64439, 64619, 64799. 
     Referring back to  FIG.  1   , the modulator  130  maps an interleaved LDPC codeword onto modulation symbols. Specifically, the modulator  130  may demultiplex the interleaved LDPC codeword and modulate the demultiplexed LDPC codeword and map it onto a constellation. 
     First, the modulator  130  demultiplexes the interleaved LDPC codeword. To achieve this, the modulator  130  may include a demultiplexer shown in  FIG.  12  or  13    to demultiplex the interleaved LDPC codeword. 
     The demultiplexer demultiplexes the interleaved LDPC codeword. Specifically, the demultiplexer performs serial-to-parallel conversion with respect to the interleaved LDPC codeword, and demultiplexes the interleaved LDPC codeword into a cell having a predetermined number of bits (or a data cell) 
     For example, as shown in  FIG.  12   , the demultiplexer receives the LDPC codeword Q=(q 0 , q 1 , q 2 , . . . ) output from the interleaver  120 , outputs the received LDPC codeword bits to one of a plurality of substreams serially, converts the input LDPC codeword bits into cells, and outputs the cells. 
     Herein, the number of substreams, Nsubstreams, may be equal to the number of bits constituting a modulation symbol, η mod , and the number of bits constituting the cell may be equal toN ldpc /η mod . η mod  varies according to a modulation method and the number of generated cells varies according to the length N ldpc  of the LDPC codeword as in Table 62 presented below: 
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 62 
               
               
                   
                   
               
               
                   
                   
                   
                 Number 
                 Number 
               
               
                   
                   
                   
                 of output 
                 of output 
               
               
                   
                 Modulation 
                   
                 data cells for  
                 data cells for  
               
               
                   
                 mode 
                 η MOD   
                 N ldpc  = 64 800 
                 N ldpc  = 16 200 
               
               
                   
                   
               
             
            
               
                   
                 QPSK 
                  2 
                 32 400 
                 8 100 
               
               
                   
                  16-QAM 
                  4 
                 16 200 
                 4 050 
               
               
                   
                  64-QAM 
                  6 
                 10 800 
                 2 700 
               
               
                   
                  256-QAM 
                  8 
                  8 100 
                 2 025 
               
               
                   
                 1024-QAM 
                 10 
                  6 480 
                 1 620 
               
               
                   
                   
               
            
           
         
       
     
     Bits having the same index in each of the plurality of sub-streams may constitute a same cell. That is, in  FIG.  12   , each cell may be expressed as (y 0,0 , y 1,0 , . . . , y η MOD-1,0), (y 0,1 , y 1,1 , . . . , y η MOD-1,1). 
     The demultiplexer may demultiplex an input LDPC codeword bits in various methods. That is, the demultiplexer may change an order of the LDPC codeword bits and output the bits to each of the plurality of substreams, or may output the bits to each of the plurality of streams serially without changing the order of the LDPC codeword bits. These operations may be determined according to the number of columns used for interleaving in the block interleaver  124 . 
     Specifically, when the block interleaver  124  includes as many columns as half of the number of bits constituting a modulation symbol, the demultiplexer may change the order of the input LDPC codeword bits and output the bits to each of the plurality of sub-streams. An example of a method for changing the order is illustrated in Table 63 presented below: 
     
       
         
           
               
               
               
             
               
                 TABLE 63 
               
               
                   
               
             
            
               
                   
                 Modulation format 
                 QPSM 
               
            
           
           
               
               
               
               
            
               
                   
                 input bit di mod N substreams   
                 0 
                 1 
               
               
                   
               
               
                   
                 output bit-number e 
                 0 
                 1 
               
               
                   
               
            
           
           
               
               
               
            
               
                   
                 Modulation format 
                 16 QAM 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 input bit di mod N substreams   
                 0 
                 1 
                 2 
                 3 
               
               
                   
               
               
                   
                 output bit-number e 
                 0 
                 2 
                 1 
                 3 
               
               
                   
               
            
           
           
               
               
            
               
                 Modulation format 
                 64 QAM 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 input bit di mod N substreams   
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
               
               
                   
               
               
                 output bit-number e 
                 0 
                 3 
                 1 
                 4 
                 2 
                 5 
               
               
                   
               
            
           
           
               
               
            
               
                 Modulation format 
                 256 QAM 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 input bit di mod N substreams   
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
               
               
                   
               
               
                 output bit-number e 
                 0 
                 4 
                 1 
                 5 
                 2 
                 6 
                 3 
                 7 
               
               
                   
               
            
           
           
               
               
            
               
                 Modulation format 
                 1024 QAM 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
            
               
                 input bit di mod N substreams   
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
               
               
                   
               
               
                 output bit-number e 
                 0 
                 5 
                 1 
                 6 
                 2 
                 7 
                 3 
                 8 
                 4 
                 9 
               
               
                   
               
            
           
           
               
               
            
               
                 Modulation format 
                 4096 QAM 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 input bit di mod N substreams   
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
               
               
                   
               
               
                 output bit-number e 
                 0 
                 6 
                 1 
                 7 
                 2 
                 8 
                 3 
                 9 
                 4 
                 10 
                 5 
                 11 
               
               
                   
               
            
           
         
       
     
     According to Table 63, when the modulation method is 16-QAM for example, the number of substreams is four (4) since the number of bits constituting the modulation symbol is four (4) in the case of 16-QAM. In this case, the demultiplexer may output, from among the serially input bits, bits with an index i satisfying i mod 4=0 to the 0 th  substream, bits with an index i satisfying i mod 4=1 to the 2 nd  substream, bits with an index i satisfying i mode 4=2 to the 1 st  substream, and bits with an index i satisfying i mode 4=3 to the 3 rd  substream. 
     Accordingly, the LDPC codeword bits input to the demultiplexer, (q 0 , q 1 , q 2 , may be output as cells like (y 0,0 , y 1,0 , y 2,0 , y 3,0 )=(q 0 , q 2 , q 1 , q 3 ), (y 0,1 , y 1,1 , y 2,1 , y 3,1 )=(q 4 , q 6 , q 5 , q 7 ), . . . . 
     When the block interleaver  124  includes the same number of columns as the number of bits constituting a modulation symbol, the demultiplexer may output the input LDPC codeword bits to each of the plurality of streams serially without changing the order of the bits. That is, as shown in  FIG.  13   , the demultiplexer may output the input LDPC codeword bits (q 0 , q 1 , q 2 , . . . ) to each of the sub streams serially, and accordingly, each cell may be configured as (y 0,0 , y 1,0 , . . . , y η MOD-1,0)=(q 0 , q 1 , . . . , q η MOD−1), (y 0,1 , y 1,1 , . . . , y η MOD-1,1)=q η MOD, q η MOD+1, . . . , q 2×η MOD−1), . . . . 
     In the above-described example, the demultiplexer outputs the input LDPC codeword bits to each of the plurality of streams serially without changing the order of the bits. However, this is merely an example. That is, according to an exemplary embodiment, when the block interleaver  124  includes the same number of columns as the number of bits constituting a modulation symbol, the demultiplexer may be omitted. 
     The modulator  130  may map the demultiplexed LDPC codeword onto modulation symbols. However, when the demultiplexer is omitted as described above, the modulator  130  may map LDPC codeword bits output from the interleaver  120 , that is, block-interleaved LDPC codeword bits, onto modulation symbols. 
     The modulator  130  may modulate bits (that is, cells) output from a demultiplexer in various modulation methods such as QPSK, 16-QAM, 64-QAM, 256-QAM, 1024-QAM, 4096-QAM, etc. When the modulation method is QPSK, 16-QAM, 64-QAM, 256-QAM, 1024-QAM and 4096-QAM, the number of bits constituting a modulation symbol, η MOD  (that is, a modulation degree), may be 2, 4, 6, 8, 10 and 12, respectively. 
     In this case, since each cell output from the demultiplexer is formed of as many bits as the number of bits constituting a modulation symbol, the modulator  130  may generate a modulation symbol by mapping each cell output from the demultiplexer onto a constellation point serially. Herein, a modulation symbol corresponds to a constellation point on the constellation. 
     However, when the demultiplexer is omitted, the modulator  130  may generate modulation symbols by grouping a predetermined number of bits from interleaved bits sequentially and mapping the predetermined number of bits onto constellation points. In this case, the modulator  130  may generate the modulation symbols by using T I NIO D  number of bits sequentially according to a modulation method. 
     The modulator  130  may modulate by mapping cells output from the demultiplexer onto constellation points in a uniform constellation (UC) method. 
     The uniform constellation method refers to a method for mapping a modulation symbol onto a constellation point so that a real number component Re(z q ) and an imaginary number component Im(z q ) of a constellation point have symmetry and the modulation symbol is placed at equal intervals. Accordingly, at least two of modulation symbols mapped onto constellation points in the uniform constellation method may have the same demodulation performance. 
     Examples of the method for generating a modulation symbol in the uniform constellation method according to an exemplary embodiment are illustrated in Tables 64 to 71 presented below, and an example of a case of a uniform constellation 64-QAM is illustrated in  FIG.  14   . 
     
       
         
           
               
               
               
             
               
                 TABLE 64 
               
               
                   
               
             
            
               
                 
                   
                 
                 1 
                 0 
               
               
                 Re(z q ) 
                 −1  
                 1 
               
               
                   
               
               
                     indicates data missing or illegible when filed 
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                 TABLE 65 
               
               
                   
               
             
            
               
                 
                   
                 
                 1 
                 0 
               
               
                 Im(z q ) 
                 −1  
                 1 
               
               
                   
               
               
                     indicates data missing or illegible when filed 
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
             
               
                 TABLE 66 
               
               
                   
               
             
            
               
                 
                   
                 
                 1 
                 1 
                 0 
                 0 
               
               
                 
                   
                 
                 0 
                 1 
                 1 
                 0 
               
               
                 Re(z q ) 
                 −3  
                 −1  
                 1 
                 3 
               
               
                   
               
               
                     indicates data missing or illegible when filed 
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
             
               
                 TABLE 67 
               
               
                   
               
             
            
               
                 
                   
                 
                 1 
                 1 
                 0 
                 0 
               
               
                 
                   
                 
                 0 
                 1 
                 1 
                 0 
               
               
                 Im(z q ) 
                 −3  
                 −1  
                 1 
                 3 
               
               
                   
               
               
                     indicates data missing or illegible when filed 
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 68 
               
               
                   
               
             
            
               
                 y 0,q   
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
               
               
                 y 2,q   
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
               
               
                 y 4,q   
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
               
               
                 Re(z q ) 
                 −7 
                 −5 
                 −3 
                 −1 
                 1 
                 3 
                 5 
                 7 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 69 
               
               
                   
               
             
            
               
                 y 1,q   
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
               
               
                 y 3,q   
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
               
               
                 y 5,q   
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
               
               
                 Im(z q ) 
                 −7 
                 −5 
                 −3 
                 −1 
                 1 
                 3 
                 5 
                 7 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 70 
               
               
                   
               
             
            
               
                 y 0,q   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 y 2,q   
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
               
               
                 y 4,q   
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
               
               
                 y 6,q   
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
               
               
                 Re(z q ) 
                 −15 
                 −13 
                 −11 
                 −9 
                 −7 
                 −5 
                 −3 
                 −1 
                 1 
                 3 
                 5 
                 7 
                 9 
                 11 
                 13 
                 15 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 71 
               
               
                   
               
             
            
               
                 y 1,q   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 y 3,q   
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
               
               
                 y 5,q   
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
               
               
                 y 7,q   
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
               
               
                 Im(z q ) 
                 −15 
                 −13 
                 −11 
                 −9 
                 −7 
                 −5 
                 −3 
                 −1 
                 1 
                 3 
                 5 
                 7 
                 9 
                 11 
                 13 
                 15 
               
               
                   
               
            
           
         
       
     
     Tables 64 and 65 are used for determining a real number component Re(z q ) and an imaginary number component Im(z q ) when the modulation is performed in a QPSK method, Tables 66 and 67 are used for determining a real number component Re(z q ) and an imaginary number component Im(z q ) when the modulation is performed in a 16-QAM method, Tables 68 and 69 are used for determining a real number component Re(z q ) and an imaginary number component Im(z q ) when the modulation is performed in a 64-QAM method, and Tables 70 and 71 are used for determining a real number component Re(z q ) and an imaginary number component Im(z q ) when the modulation is performed in a 256-QAM method 
     Referring to Tables 64 to 71, performance (e.g., reliability) varies according to whether a plurality of bits constituting a modulation symbol correspond to most significant bits (MSBs) or least significant bits (LSBs) 
     For example, in the case of 16-QAM, from among four (4) bits constituting a modulation symbol, each of the first and second bits determines a sign of each of the real number component Re(z q ) and the imaginary number component Im(z q ) of a constellation point onto which a modulation symbol is mapped, and the third and fourth bits determine a size of the constellation point onto which the modulation symbol is mapped 
     In this case, the first and second bits for determining, the sign from among the four (4) bits constituting the modulation symbol have a higher reliability than the third and fourth bits for determining the size. 
     In another example, in the case of 64-QAM, from among six (6) bits constituting a modulation symbol, each of the first and second bits determines a sign of each of the real number component Re(z q ) and the imaginary number component Im(z q ) of a constellation point onto which the modulation symbol is mapped. In addition, the third to sixth bits determine a size of the constellation point onto which the modulation symbol is mapped. From among these bits, the third and fourth bits determine a relatively large size, and the fifth and sixth bits determine a relatively small size (for example, the third bit determines which of sizes (-7, -5) and (-3, -1) corresponds to the constellation point onto which the modulation symbol is mapped, and, when (-7, -5) is determined by the third bit, the fourth bit determines which of -7 and -5 corresponds to the size of the constellation point.). 
     In this case, the first and second bits for determining the sign from among the six bits constituting the modulation symbol have the highest reliability, and the third and fourth bits for determining the relatively large size has the higher reliability than the fifth and sixth bits for determining the relatively small size. 
     As described above, in the case of the uniform constellation method, the bits constituting a modulation symbol have different reliability according to mapping locations in the modulation symbol. 
     The modulator  130  may modulate by mapping cells output from the demultiplexer onto constellation points in a non-uniform constellation (NUC) method. 
     Specifically, the modulator  130  may modulate bits output from the demultiplexer in various modulation methods such as non-uniform 16-QAM, non-uniform 64-QAM, non-uniform 256-QAM, non-uniform 1024-QAM, non-uniform 4096-QAM, etc. 
     Hereinafter, a method for generating a modulation symbol by using the non-uniform constellation method according to an exemplary embodiment will be explained. 
     First, the non-uniform constellation method has the following characteristics: 
     In the non-uniform constellation method, the constellation points may not regularly be arranged unlike in the uniform constellation method. Accordingly, when the non-uniform constellation method is used, performance for a signal-to-noise ratio (SNR) less than a specific value can be improved and a high SNR gain can be obtained in comparison to the uniform constellation method. 
     In addition, the characteristics of the constellation may be determined by one or more parameters such as a distance between constellation points. Since the constellation points are regularly distributed in the uniform constellation, the number of parameters for specifying the uniform constellation method may be one (1). However, the number of parameters necessary for specifying the non-uniform constellation method is relatively larger and the number of parameters increases as the constellation (e.g., the number of constellation points) increases. 
     In the case of the non-uniform constellation method, an x-axis and a y-axis may be designed to be symmetric to each other or may be designed to be asymmetric to each other. When the x-axis and the y-axis are designed to be asymmetric to each other, improved performance can be guaranteed, but decoding complexity may increase. 
     Hereinafter, an example of a case in which the x-axis and the y-axis are designed to be asymmetric to each other will be explained. In this case, once a constellation point of the first quadrant is defined, locations of constellation points in the other three quadrants may be determined as follows. For example, when a set of constellation points defined for the first quadrant is X, the set becomes—conj(X) in the case of the second quadrant, becomes conj(X) in the case of the third quadrant, and becomes—(X) in the case of the fourth quadrant. 
     That is, once the first quadrant is defined, the other quadrants may be expressed as follows: 
     1 Quarter (first quadrant)=X 
     2 Quarter (second quadrant)=-conj (X) 
     3 Quarter (third quadrant)=conj (X) 
     4 Quarter (fourth quadrant)=-X 
     Specifically, when the non-uniform M-QAM is used, M number of constellation points may be defined as z={z 0 , z 1 , . . . , z M-1 }. In this case, when the constellation points existing in the first quadrant are defined as {x 0 , x 1 , x 2 , . . . , x M/4-1 }, z may be defined as follows: 
     from z 0  to z M/4-1 =from x 0  to x M/4    
     from z M/4  to z 2×M/4-1 =-conj(from x 0  to x M/4 ) 
     from z 2×M/4  to z 3×M/4-1 =conj(from x 0  to x M/4 ) 
     from z 3×M/4  to z 4×M/4-1 =-(from x 0  to x M/4 ) 
     Accordingly, the modulator  130  may map the bits [y 0 , . . . , y m-1 ] output from the demultiplexer onto constellation points in the non-uniform constellation method by mapping the output bits onto z L  having an index of 
     
       
         
           
             L 
             = 
             
               
                 ∑ 
                 
                   i 
                   = 
                   0 
                 
                 
                   m 
                   - 
                   1 
                 
               
               
                 
                   ( 
                   
                     
                       y 
                       1 
                     
                     ⨯ 
                     
                       2 
                       
                         m 
                         - 
                         1 
                       
                     
                   
                   ) 
                 
                 . 
               
             
           
         
       
     
     An example of the constellation of the non-uniform constellation method is illustrated in  FIGS.  15  to  19   . 
     An example of the method for modulating asymmetrically in the non-uniform constellation method in the modulator  130  is illustrated as in Tables 72 to 77 presented below. That is, according to an exemplary embodiment, modulation is performed in the non-uniform constellation method by defining constellation points existing in the first quadrant and defining constellations points existing in the other quadrants based on Tables 72 to 77. 
     
       
         
           
               
               
               
               
               
               
             
               
                 TABLE 72 
               
               
                   
               
             
            
               
                 x/Shape 
                 R6/15 
                 R7/15 
                 R8/15 
                 R9/15 
                 R10/15 
               
               
                   
               
               
                 x0 
                 0.4530 + 0.2663i 
                 1.2103 + 0.5026i 
                 0.4819 + 0.2575i 
                 0.4909 + 1.2007i 
                 0.2173 + 0.4189i 
               
               
                 x1 
                 0.2663 + 0.4530i 
                 0.5014 + 1.2103i 
                 0.2575 + 0.4819i 
                 1.2007 + 0.4909i 
                 0.6578 + 0.2571i 
               
               
                 x2 
                 1.2092 + 0.5115i 
                 0.4634 + 0.2624i 
                 1.2068 + 0.4951i 
                 0.2476 + 0.5065i 
                 0.4326 + 1.1445i 
               
               
                 x3 
                 0.5115 + 1.2092i 
                 0.2624 + 0.4627i 
                 0.4951 + 1.2068i 
                 0.5053 + 0.2476i 
                 1.2088 + 0.5659i 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 x/Shape 
                 R11/15 
                 R12/15 
                 R13/15 
               
               
                   
               
               
                   
                 x0 
                 0.9583 + 0.9547i 
                 0.2999 + 0.2999i 
                 0.9517 + 0.9511i 
               
               
                   
                 x1 
                 0.9547 + 0.2909i 
                 0.9540 + 0.2999i 
                 0.9524 + 0.3061i 
               
               
                   
                 x2 
                 0.2921 + 0.9583i 
                 0.2999 + 0.9540i 
                 0.3067 + 0.9524i 
               
               
                   
                 x3 
                 0.2909 + 0.2927i 
                 0.9540 + 0.9540i 
                 0.3061 + 0.3067i 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
             
               
                 TABLE 73 
               
               
                   
               
             
            
               
                 x/Shape 
                 R64_6/15 
                 R64_7/15 
                 R64_8/15 
                 R64_9/15 
                 R64_10/15 
               
               
                   
               
               
                 x0 
                 0.4387 + 1.6023i 
                 0.3352 + 0.6028i 
                 1.4827 + 0.2920i 
                 0.3547 + 0.6149i 
                 1.4388 + 0.2878i 
               
               
                 x1 
                 1.6023 + 0.4387i 
                 0.2077 + 0.6584i 
                 1.2563 + 0.8411i 
                 0.1581 + 0.6842i 
                 1.2150 + 0.8824i 
               
               
                 x2 
                 0.8753 + 1.0881i 
                 0.1711 + 0.3028i 
                 1.0211 + 0.2174i 
                 0.1567 + 0.2749i 
                 1.0386 + 0.2219i 
               
               
                 x3 
                 1.0881 + 0.8753i 
                 0.1556 + 0.8035i 
                 0.8798 + 0.5702i 
                 0.1336 + 0.2700i 
                 0.8494 + 0.6145i 
               
               
                 x4 
                 0.2202 + 0.9238i 
                 0.6028 + 0.3345i 
                 0.2920 + 1.4827i 
                 0.6177 + 0.4030i 
                 0.2931 + 1.4656i 
               
               
                 x5 
                 0.2019 + 0.7818i 
                 0.6577 + 0.2084i 
                 0.8410 + 1.2563i 
                 0.7262 + 0.1756i 
                 0.8230 + 1.2278i 
               
               
                 x6 
                 0.3049 + 0.8454i 
                 0.3021 + 0.1711i 
                 0.2174 + 1.0211i 
                 0.3568 + 0.1756i 
                 0.2069 + 1.0649i 
               
               
                 x7 
                 0.2653 + 0.7540i 
                 0.3028 + 0.1556i 
                 0.5702 + 0.8798i 
                 0.3771 + 0.1336i 
                 0.5677 + 0.8971i 
               
               
                 x8 
                 0.7818 + 0.2019i 
                 0.5556 + 0.8922i 
                 0.3040 + 0.1475i 
                 0.5639 + 0.8864i 
                 0.4119 + 0.1177i 
               
               
                 x9 
                 0.9238 + 0.2202i 
                 0.2352 + 1.0190i 
                 0.3028 + 0.1691i 
                 0.1980 + 1.0277i 
                 0.3998 + 0.2516i 
               
               
                 x10 
                 0.7540 + 0.2653i 
                 0.8450 + 1.2619i 
                 0.6855 + 0.1871i 
                 0.8199 + 1.2515i 
                 0.7442 + 0.1559i 
               
               
                 x11 
                 0.8454 + 0.3049i 
                 0.2922 + 1.4894i 
                 0.6126 + 0.3563i 
                 0.2854 + 1.4691i 
                 0.5954 + 0.4328i 
               
               
                 x12 
                 0.2675 + 0.2479i 
                 0.8929 + 0.5549i 
                 0.1475 + 0.3040i 
                 0.8654 + 0.6058i 
                 0.1166 + 0.1678i 
               
               
                 x13 
                 0.2479 + 0.2675i 
                 1.0197 + 0.2359i 
                 0.1691 + 0.3028i 
                 1.0382 + 0.2142i 
                 0.1582 + 0.3325i 
               
               
                 x14 
                 0.2890 + 0.2701i 
                 1.2626 + 0.8457i 
                 0.1871 + 0.6855i 
                 1.2362 + 0.8416i 
                 0.1355 + 0.7408i 
               
               
                 x15 
                 0.2701 + 0.2890i 
                 1.4894 + 0.2922i 
                 0.3563 + 0.6126i 
                 1.4663 + 0.2973i 
                 0.3227 + 0.6200i 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 x/Shape 
                 R64_11/15 
                 R64_12/15 
                 R64_13/15 
               
               
                   
               
               
                   
                 x0 
                 0.3317 + 0.6970i 
                 1.0854 + 0.5394i 
                 0.4108 + 0.7473i 
               
               
                   
                 x1 
                 0.1386 + 0.8824i 
                 0.7353 + 0.4623i 
                 0.1343 + 0.5338i 
               
               
                   
                 x2 
                 0.1323 + 0.4437i 
                 1.0474 + 0.1695i 
                 0.1570 + 0.9240i 
               
               
                   
                 x3 
                 0.1015 + 0.1372i 
                 0.7243 + 0.1504i 
                 0.1230 + 0.1605i 
               
               
                   
                 x4 
                 0.5682 + 0.4500i 
                 1.0693 + 0.9408i 
                 0.6285 + 0.4617i 
               
               
                   
                 x5 
                 0.6739 + 0.1435i 
                 0.7092 + 0.8073i 
                 0.3648 + 0.3966i 
               
               
                   
                 x6 
                 0.3597 + 0.3401i 
                 1.4261 + 0.2216i 
                 0.6907 + 0.1541i 
               
               
                   
                 x7 
                 0.3660 + 0.1204i 
                 0.6106 + 1.1783i 
                 0.3994 + 0.1308i 
               
               
                   
                 x8 
                 0.6004 + 0.8922i 
                 0.1392 + 0.4078i 
                 0.7268 + 0.8208i 
               
               
                   
                 x9 
                 0.2120 + 1.2253i 
                 0.4262 + 0.4205i 
                 1.0463 + 0.9495i 
               
               
                   
                 x10 
                 0.9594 + 1.0714i 
                 0.1407 + 0.1336i 
                 0.1866 + 1.2733i 
               
               
                   
                 x11 
                 0.5829 + 1.3995i 
                 0.4265 + 0.1388i 
                 0.5507 + 1.1793i 
               
               
                   
                 x12 
                 0.8439 + 0.5675i 
                 0.1388 + 0.7057i 
                 0.9283 + 0.5140i 
               
               
                   
                 x13 
                 0.9769 + 0.1959i 
                 0.4197 + 0.7206i 
                 1.2648 + 0.5826i 
               
               
                   
                 x14 
                 1.2239 + 0.6760i 
                 0.1682 + 1.0316i 
                 0.9976 + 0.1718i 
               
               
                   
                 x15 
                 1.3653 + 0.2323i 
                 0.2287 + 1.3914i 
                 1.3412 + 0.1944i 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
             
               
                 TABLE 74 
               
               
                   
               
             
            
               
                 x/Shape 
                 NUC_64_6/15 
                 NUC_64_7/15 
                 NUC_64_8/15 
                 NUC_64_9/15 
                 NUC_64_10/15 
               
               
                   
               
               
                 x0 
                 0.4387 + 1.6023i 
                 0.3352 + 0.6028i 
                 1.4827 + 0.2920i 
                 0.3547 + 0.6149i 
                 1.4388 + 0.2878i 
               
               
                 x1 
                 1.6023 + 0.4387i 
                 0.2077 + 0.6584i 
                 1.2563 + 0.8411i 
                 0.1581 + 0.6842i 
                 1.2150 + 0.8824i 
               
               
                 x2 
                 0.8753 + 1.0881i 
                 0.1711 + 0.3028i 
                 1.0211 + 0.2174i 
                 0.1567 + 0.2749i 
                 1.0386 + 0.2219i 
               
               
                 x3 
                 1.0881 + 0.8753i 
                 0.1556 + 0.8035i 
                 0.8798 + 0.5702i 
                 0.1336 + 0.2700i 
                 0.8494 + 0.6145i 
               
               
                 x4 
                 0.2202 + 0.9238i 
                 0.6028 + 0.3345i 
                 0.2920 + 1.4827i 
                 0.6177 + 0.4030i 
                 0.2931 + 1.4656i 
               
               
                 x5 
                 0.2019 + 0.7818i 
                 0.6577 + 0.2084i 
                 0.8410 + 1.2563i 
                 0.7262 + 0.1756i 
                 0.8230 + 1.2278i 
               
               
                 x6 
                 0.3049 + 0.8454i 
                 0.3021 + 0.1711i 
                 0.2174 + 1.0211i 
                 0.3568 + 0.1756i 
                 0.2069 + 1.0649i 
               
               
                 x7 
                 0.2653 + 0.7540i 
                 0.3028 + 0.1556i 
                 0.5702 + 0.8798i 
                 0.3771 + 0.1336i 
                 0.5677 + 0.8971i 
               
               
                 x8 
                 0.7818 + 0.2019i 
                 0.5556 + 0.8922i 
                 0.3040 + 0.1475i 
                 0.5639 + 0.8864i 
                 0.4119 + 0.1177i 
               
               
                 x9 
                 0.9238 + 0.2202i 
                 0.2352 + 1.0190i 
                 0.3028 + 0.1691i 
                 0.1980 + 1.0277i 
                 0.3998 + 0.2516i 
               
               
                 x10 
                 0.7540 + 0.2653i 
                 0.8450 + 1.2619i 
                 0.6855 + 0.1871i 
                 0.8199 + 1.2515i 
                 0.7442 + 0.1559i 
               
               
                 x11 
                 0.8454 + 0.3049i 
                 0.2922 + 1.4894i 
                 0.6126 + 0.3563i 
                 0.2854 + 1.4691i 
                 0.5954 + 0.4328i 
               
               
                 x12 
                 0.2675 + 0.2479i 
                 0.8929 + 0.5549i 
                 0.1475 + 0.3040i 
                 0.8654 + 0.6058i 
                 0.1166 + 0.1678i 
               
               
                 x13 
                 0.2479 + 0.2675i 
                 1.0197 + 0.2359i 
                 0.1691 + 0.3028i 
                 1.0382 + 0.2142i 
                 0.1582 + 0.3325i 
               
               
                 x14 
                 0.2890 + 0.2701i 
                 1.2626 + 0.8457i 
                 0.1871 + 0.6855i 
                 1.2362 + 0.8416i 
                 0.1355 + 0.7408i 
               
               
                 x15 
                 0.2701 + 0.2890i 
                 1.4894 + 0.2922i 
                 0.3563 + 0.6126i 
                 1.4663 + 0.2973i 
                 0.3227 + 0.6200i 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 x/Shape 
                 NUC_64_11/15 
                 NUC_64_12/15 
                 NUC_64_13/15 
               
               
                   
               
               
                   
                 x0 
                 0.3317 + 0.6970i 
                 1.0854 + 0.5394i 
                 0.8624 + 1.1715i 
               
               
                   
                 x1 
                 0.1386 + 0.8824i 
                 0.7353 + 0.4623i 
                 1.1184 + 0.8462i 
               
               
                   
                 x2 
                 0.1323 + 0.4437i 
                 1.0474 + 0.1695i 
                 0.2113 + 1.3843i 
               
               
                   
                 x3 
                 0.1015 + 0.1372i 
                 0.7243 + 0.1504i 
                 0.7635 + 0.7707i 
               
               
                   
                 x4 
                 0.5682 + 0.4500i 
                 1.0693 + 0.9408i 
                 1.1796 + 0.1661i 
               
               
                   
                 x5 
                 0.6739 + 0.1435i 
                 0.7092 + 0.8073i 
                 1.0895 + 0.4882i 
               
               
                   
                 x6 
                 0.3597 + 0.3401i 
                 1.4261 + 0.2216i 
                 0.8101 + 0.1492i 
               
               
                   
                 x7 
                 0.3660 + 0.1204i 
                 0.6106 + 1.1783i 
                 0.7482 + 0.4477i 
               
               
                   
                 x8 
                 0.6004 + 0.8922i 
                 0.1392 + 0.4078i 
                 0.1524 + 0.9943i 
               
               
                   
                 x9 
                 0.2120 + 1.2253i 
                 0.4262 + 0.4205i 
                 0.1482 + 0.6877i 
               
               
                   
                 x10 
                 0.9594 + 1.0714i 
                 0.1407 + 0.1336i 
                 0.4692 + 1.0853i 
               
               
                   
                 x11 
                 0.5829 + 1.3995i 
                 0.4265 + 0.1388i 
                 0.4492 + 0.7353i 
               
               
                   
                 x12 
                 0.8439 + 0.5675i 
                 0.1388 + 0.7057i 
                 0.1578 + 0.1319i 
               
               
                   
                 x13 
                 0.9769 + 0.1959i 
                 0.4197 + 0.7206i 
                 0.1458 + 0.4025i 
               
               
                   
                 x14 
                 1.2239 + 0.6760i 
                 0.1682 + 1.0316i 
                 0.4763 + 0.1407i 
               
               
                   
                 x15 
                 1.3653 + 0.2323i 
                 0.2287 + 1.3914i 
                 0.4411 + 0.4267i 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                 TABLE 75 
               
               
                   
               
               
                 x/Shape 
                 7/15 
                 13/15 
               
               
                   
               
             
            
               
                 x0  
                 0.1543 + 0.3088i 
                 1.4293 + 0.2286i 
               
               
                 x1  
                 0.1719 + 0.3074i 
                 0.6234 + 1.1799i 
               
               
                 x2  
                 0.2021 + 0.6601i 
                 1.0719 + 0.9247i 
               
               
                 x3  
                 0.3396 + 0.6009i 
                 0.6841 + 0.8071i 
               
               
                 x4  
                 0.3080 + 0.1543i 
                 1.0440 + 0.1692i 
               
               
                 x5  
                 0.3069 + 0.1716i 
                 0.7232 + 0.1541i 
               
               
                 x6  
                 0.6607 + 0.2018i 
                 1.0639 + 0.5312i 
               
               
                 x7  
                 0.6011 + 0.3395i 
                 0.7147 + 0.4706i 
               
               
                 x8  
                 0.2936 + 1.4847i 
                 0.2128 + 1.4368i 
               
               
                 x9  
                 0.8412 + 1.2593i 
                 0.1990 + 1.0577i 
               
               
                 x10 
                 0.2321 + 1.0247i 
                 0.1176 + 0.6586i 
               
               
                 x11 
                 0.5629 + 0.8926i 
                 0.3691 + 0.7533i 
               
               
                 x12 
                 1.4850 + 0.2935i 
                 0.1457 + 0.1261i 
               
               
                 x13 
                 1.2599 + 0.8426i 
                 0.4329 + 0.1380i 
               
               
                 x14 
                 1.0247 + 0.2320i 
                 0.1424 + 0.3819i 
               
               
                 x15 
                 0.8925 + 0.5631i 
                 0.4216 + 0.4265i 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
             
               
                 TABLE 76 
               
               
                   
               
             
            
               
                 x/Shape 
                 R6/15 
                 R7/15 
                 R8/15 
                 R9/15 
                 R10/15 
               
               
                   
               
               
                 x0 
                 0.6800 + 1.6926i 
                 1.2905 + 1.3099i 
                 1.0804 + 1.3788i 
                 1.3231 + 1.1506i 
                 1.6097 + 0.1548i 
               
               
                 x1 
                 0.3911 + 1.3645i 
                 1.0504 + 0.9577i 
                 1.0487 + 0.9862i 
                 0.9851 + 1.2311i 
                 1.5549 + 0.4605i 
               
               
                 x2 
                 0.2191 + 1.7524i 
                 1.5329 + 0.8935i 
                 1.6464 + 0.7428i 
                 1.1439 + 0.8974i 
                 1.3226 + 0.1290i 
               
               
                 x3 
                 0.2274 + 1.4208i 
                 1.1577 + 0.8116i 
                 1.3245 + 0.9414i 
                 0.9343 + 0.9271i 
                 1.2772 + 0.3829i 
               
               
                 x4 
                 0.8678 + 1.2487i 
                 1.7881 + 0.2509i 
                 0.7198 + 1.2427i 
                 1.5398 + 0.7962i 
                 1.2753 + 1.0242i 
               
               
                 x5 
                 0.7275 + 1.1667i 
                 1.4275 + 0.1400i 
                 0.8106 + 1.0040i 
                 0.9092 + 0.5599i 
                 1.4434 + 0.7540i 
               
               
                 x6 
                 0.8747 + 1.0470i 
                 1.4784 + 0.5201i 
                 0.5595 + 1.0317i 
                 1.2222 + 0.6574i 
                 1.0491 + 0.8476i 
               
               
                 x7 
                 0.7930 + 1.0406i 
                 1.3408 + 0.4346i 
                 0.6118 + 0.9722i 
                 0.9579 + 0.6373i 
                 1.1861 + 0.6253i 
               
               
                 x8 
                 0.2098 + 0.9768i 
                 0.7837 + 0.5867i 
                 1.6768 + 0.2002i 
                 0.7748 + 1.5867i 
                 0.9326 + 0.0970i 
               
               
                 x9 
                 0.2241 + 1.0454i 
                 0.8250 + 0.6455i 
                 0.9997 + 0.6844i 
                 0.6876 + 1.2489i 
                 0.8962 + 0.2804i 
               
               
                 x10 
                 0.1858 + 0.9878i 
                 0.8256 + 0.5601i 
                 1.4212 + 0.4769i 
                 0.5992 + 0.9208i 
                 1.1044 + 0.1102i 
               
               
                 x11 
                 0.1901 + 1.0659i 
                 0.8777 + 0.6110i 
                 1.1479 + 0.6312i 
                 0.6796 + 0.9743i 
                 1.0648 + 0.3267i 
               
               
                 x12 
                 0.5547 + 0.8312i 
                 1.0080 + 0.1843i 
                 0.6079 + 0.6566i 
                 0.5836 + 0.5879i 
                 0.7325 + 0.6071i 
               
               
                 x13 
                 0.5479 + 0.8651i 
                 1.0759 + 0.1721i 
                 0.7284 + 0.6957i 
                 0.6915 + 0.5769i 
                 0.8260 + 0.4559i 
               
               
                 x14 
                 0.6073 + 0.8182i 
                 1.0056 + 0.2758i 
                 0.5724 + 0.7031i 
                 0.5858 + 0.7058i 
                 0.8744 + 0.7153i 
               
               
                 x15 
                 0.5955 + 0.8420i 
                 1.0662 + 0.2964i 
                 0.6302 + 0.7259i 
                 0.6868 + 0.6793i 
                 0.9882 + 0.5300i 
               
               
                 x16 
                 1.4070 + 0.1790i 
                 0.8334 + 1.5554i 
                 0.1457 + 1.4010i 
                 1.6118 + 0.1497i 
                 0.1646 + 1.6407i 
               
               
                 x17 
                 1.7227 + 0.2900i 
                 0.8165 + 1.1092i 
                 0.1866 + 1.7346i 
                 0.9511 + 0.1140i 
                 0.4867 + 1.5743i 
               
               
                 x18 
                 1.3246 + 0.2562i 
                 0.6092 + 1.2729i 
                 0.1174 + 1.1035i 
                 1.2970 + 0.1234i 
                 0.1363 + 1.3579i 
               
               
                 x19 
                 1.3636 + 0.3654i 
                 0.6728 + 1.1456i 
                 0.1095 + 1.0132i 
                 1.0266 + 0.1191i 
                 0.4023 + 1.3026i 
               
               
                 x20 
                 1.3708 + 1.2834i 
                 0.3061 + 1.7469i 
                 0.4357 + 1.3636i 
                 1.5831 + 0.4496i 
                 1.0542 + 1.2584i 
               
               
                 x21 
                 1.6701 + 0.8403i 
                 0.1327 + 1.4056i 
                 0.5853 + 1.6820i 
                 0.9328 + 0.3586i 
                 0.7875 + 1.4450i 
               
               
                 x22 
                 1.1614 + 0.7909i 
                 0.3522 + 1.3414i 
                 0.3439 + 1.0689i 
                 1.2796 + 0.3894i 
                 0.8687 + 1.0407i 
               
               
                 x23 
                 1.2241 + 0.7367i 
                 0.2273 + 1.3081i 
                 0.3234 + 0.9962i 
                 1.0188 + 0.3447i 
                 0.6502 + 1.1951i 
               
               
                 x24 
                 0.9769 + 0.1863i 
                 0.5007 + 0.8098i 
                 0.1092 + 0.6174i 
                 0.5940 + 0.1059i 
                 0.0982 + 0.9745i 
               
               
                 x25 
                 0.9452 + 0.2057i 
                 0.5528 + 0.8347i 
                 0.1074 + 0.6307i 
                 0.7215 + 0.1100i 
                 0.2842 + 0.9344i 
               
               
                 x26 
                 1.0100 + 0.2182i 
                 0.4843 + 0.8486i 
                 0.1109 + 0.6996i 
                 0.5863 + 0.1138i 
                 0.1142 + 1.1448i 
               
               
                 x27 
                 0.9795 + 0.2417i 
                 0.5304 + 0.8759i 
                 0.1076 + 0.7345i 
                 0.6909 + 0.1416i 
                 0.3385 + 1.0973i 
               
               
                 x28 
                 0.8241 + 0.4856i 
                 0.1715 + 0.9147i 
                 0.3291 + 0.6264i 
                 0.5843 + 0.3604i 
                 0.6062 + 0.7465i 
               
               
                 x29 
                 0.8232 + 0.4837i 
                 0.1540 + 0.9510i 
                 0.3126 + 0.6373i 
                 0.6970 + 0.3592i 
                 0.4607 + 0.8538i 
               
               
                 x30 
                 0.8799 + 0.5391i 
                 0.1964 + 0.9438i 
                 0.3392 + 0.6999i 
                 0.5808 + 0.3250i 
                 0.7263 + 0.8764i 
               
               
                 x31 
                 0.8796 + 0.5356i 
                 0.1788 + 0.9832i 
                 0.3202 + 0.7282i 
                 0.6678 + 0.3290i 
                 0.5450 + 1.0067i 
               
               
                 x32 
                 0.1376 + 0.3342i 
                 0.3752 + 0.1667i 
                 0.9652 + 0.1066i 
                 0.1406 + 1.6182i 
                 0.2655 + 0.0746i 
               
               
                 x33 
                 0.1383 + 0.3292i 
                 0.3734 + 0.1667i 
                 0.9075 + 0.1666i 
                 0.1272 + 1.2984i 
                 0.2664 + 0.0759i 
               
               
                 x34 
                 0.1363 + 0.3322i 
                 0.3758 + 0.1661i 
                 0.9724 + 0.1171i 
                 0.1211 + 0.9644i 
                 0.4571 + 0.0852i 
               
               
                 x35 
                 0.1370 + 0.3273i 
                 0.3746 + 0.1649i 
                 0.9186 + 0.1752i 
                 0.1220 + 1.0393i 
                 0.4516 + 0.1062i 
               
               
                 x36 
                 0.1655 + 0.3265i 
                 0.4013 + 0.1230i 
                 0.6342 + 0.1372i 
                 0.1124 + 0.6101i 
                 0.2559 + 0.1790i 
               
               
                 x37 
                 0.1656 + 0.3227i 
                 0.4001 + 0.1230i 
                 0.6550 + 0.1495i 
                 0.1177 + 0.6041i 
                 0.2586 + 0.1772i 
               
               
                 x38 
                 0.1634 + 0.3246i 
                 0.4037 + 0.1230i 
                 0.6290 + 0.1393i 
                 0.1136 + 0.7455i 
                 0.3592 + 0.2811i 
               
               
                 x39 
                 0.1636 + 0.3208i 
                 0.4019 + 0.1218i 
                 0.6494 + 0.1504i 
                 0.1185 + 0.7160i 
                 0.3728 + 0.2654i 
               
               
                 x40 
                 0.1779 + 0.6841i 
                 0.6025 + 0.3934i 
                 1.3127 + 0.1240i 
                 0.4324 + 1.5679i 
                 0.7706 + 0.0922i 
               
               
                 x41 
                 0.1828 + 0.6845i 
                 0.5946 + 0.3928i 
                 0.9572 + 0.4344i 
                 0.3984 + 1.2825i 
                 0.7407 + 0.2260i 
               
               
                 x42 
                 0.1745 + 0.6828i 
                 0.6116 + 0.3879i 
                 1.2403 + 0.2631i 
                 0.3766 + 0.9534i 
                 0.6180 + 0.0927i 
               
               
                 x43 
                 0.1793 + 0.6829i 
                 0.6019 + 0.3837i 
                 1.0254 + 0.4130i 
                 0.3668 + 1.0301i 
                 0.6019 + 0.1658i 
               
               
                 x44 
                 0.3547 + 0.6009i 
                 0.7377 + 0.1618i 
                 0.6096 + 0.4214i 
                 0.3667 + 0.5995i 
                 0.6007 + 0.4980i 
               
               
                 x45 
                 0.3593 + 0.6011i 
                 0.7298 + 0.1582i 
                 0.6773 + 0.4284i 
                 0.3328 + 0.5960i 
                 0.6673 + 0.3928i 
               
               
                 x46 
                 0.3576 + 0.5990i 
                 0.7274 + 0.1782i 
                 0.5995 + 0.4102i 
                 0.3687 + 0.7194i 
                 0.4786 + 0.3935i 
               
               
                 x47 
                 0.3624 + 0.5994i 
                 0.7165 + 0.1746i 
                 0.6531 + 0.4101i 
                 0.3373 + 0.6964i 
                 0.5176 + 0.3391i 
               
               
                 x48 
                 0.2697 + 0.1443i 
                 0.1509 + 0.2425i 
                 0.1250 + 0.1153i 
                 0.1065 + 0.1146i 
                 0.0757 + 0.1003i 
               
               
                 x49 
                 0.2704 + 0.1433i 
                 0.1503 + 0.2400i 
                 0.1252 + 0.1158i 
                 0.1145 + 0.1108i 
                 0.0753 + 0.1004i 
               
               
                 x50 
                 0.2644 + 0.1442i 
                 0.1515 + 0.2437i 
                 0.1245 + 0.1152i 
                 0.1053 + 0.1274i 
                 0.0777 + 0.4788i 
               
               
                 x51 
                 0.2650 + 0.1432i 
                 0.1503 + 0.2425i 
                 0.1247 + 0.1156i 
                 0.1134 + 0.1236i 
                 0.0867 + 0.4754i 
               
               
                 x52 
                 0.2763 + 0.1638i 
                 0.1285 + 0.2388i 
                 0.3768 + 0.1244i 
                 0.1111 + 0.3821i 
                 0.1023 + 0.2243i 
               
               
                 x53 
                 0.2768 + 0.1626i 
                 0.1279 + 0.2419i 
                 0.3707 + 0.1237i 
                 0.1186 + 0.3867i 
                 0.1010 + 0.2242i 
               
               
                 x54 
                 0.2715 + 0.1630i 
                 0.1279 + 0.2431i 
                 0.3779 + 0.1260i 
                 0.1080 + 0.3431i 
                 0.1950 + 0.3919i 
               
               
                 x55 
                 0.2719 + 0.1618i 
                 0.1279 + 0.2406i 
                 0.3717 + 0.1252i 
                 0.1177 + 0.3459i 
                 0.1881 + 0.3969i 
               
               
                 x56 
                 0.6488 + 0.1696i 
                 0.3394 + 0.5764i 
                 0.1161 + 0.3693i 
                 0.3644 + 0.1080i 
                 0.0930 + 0.8122i 
               
               
                 x57 
                 0.6462 + 0.1706i 
                 0.3364 + 0.5722i 
                 0.1157 + 0.3645i 
                 0.3262 + 0.1104i 
                 0.2215 + 0.7840i 
               
               
                 x58 
                 0.6456 + 0.1745i 
                 0.3328 + 0.5758i 
                 0.1176 + 0.3469i 
                 0.3681 + 0.1173i 
                 0.0937 + 0.6514i 
               
               
                 x59 
                 0.6431 + 0.1753i 
                 0.3303 + 0.5698i 
                 0.1171 + 0.3424i 
                 0.3289 + 0.1196i 
                 0.1540 + 0.6366i 
               
               
                 x60 
                 0.5854 + 0.3186i 
                 0.1491 + 0.6316i 
                 0.3530 + 0.3899i 
                 0.3665 + 0.3758i 
                 0.4810 + 0.6306i 
               
               
                 x61 
                 0.5862 + 0.3167i 
                 0.1461 + 0.6280i 
                 0.3422 + 0.3808i 
                 0.3310 + 0.3795i 
                 0.3856 + 0.7037i 
               
               
                 x62 
                 0.5864 + 0.3275i 
                 0.1509 + 0.6280i 
                 0.3614 + 0.3755i 
                 0.3672 + 0.3353i 
                 0.3527 + 0.5230i 
               
               
                 x63 
                 0.5873 + 0.3254i 
                 0.1473 + 0.6225i 
                 0.3509 + 0.3656i 
                 0.3336 + 0.3402i 
                 0.3100 + 0.5559i 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 x/Shape 
                 R11/15 
                 R12/15 
                 R13/15 
               
               
                   
               
               
                   
                 x0 
                 0.3105 + 0.3382i 
                 1.1014 + 1.1670i 
                 0.3556 + 0.3497i 
               
               
                   
                 x1 
                 0.4342 + 0.3360i 
                 0.8557 + 1.2421i 
                 0.3579 + 0.4945i 
               
               
                   
                 x2 
                 0.3149 + 0.4829i 
                 1.2957 + 0.8039i 
                 0.5049 + 0.3571i 
               
               
                   
                 x3 
                 0.4400 + 0.4807i 
                 1.0881 + 0.8956i 
                 0.5056 + 0.5063i 
               
               
                   
                 x4 
                 0.1811 + 0.3375i 
                 0.5795 + 1.2110i 
                 0.2123 + 0.3497i 
               
               
                   
                 x5 
                 0.0633 + 0.3404i 
                 0.6637 + 1.4215i 
                 0.2116 + 0.4900i 
               
               
                   
                 x6 
                 0.1818 + 0.4851i 
                 0.6930 + 1.0082i 
                 0.0713 + 0.3489i 
               
               
                   
                 x7 
                 0.0633 + 0.4815i 
                 0.8849 + 0.9647i 
                 0.0690 + 0.4960i 
               
               
                   
                 x8 
                 0.3084 + 0.1971i 
                 1.2063 + 0.5115i 
                 0.3527 + 0.2086i 
               
               
                   
                 x9 
                 0.4356 + 0.1993i 
                 1.0059 + 0.4952i 
                 0.3497 + 0.0713i 
               
               
                   
                 x10 
                 0.3098 + 0.0676i 
                 1.4171 + 0.5901i 
                 0.4960 + 0.2123i 
               
               
                   
                 x11 
                 0.4342 + 0.0691i 
                 1.0466 + 0.6935i 
                 0.4974 + 0.0698i 
               
               
                   
                 x12 
                 0.1775 + 0.1985i 
                 0.6639 + 0.6286i 
                 0.2086 + 0.2079i 
               
               
                   
                 x13 
                 0.0640 + 0.1978i 
                 0.8353 + 0.5851i 
                 0.2094 + 0.0690i 
               
               
                   
                 x14 
                 0.1775 + 0.0676i 
                 0.6879 + 0.8022i 
                 0.0676 + 0.2079i 
               
               
                   
                 x15 
                 0.0647 + 0.0669i 
                 0.8634 + 0.7622i 
                 0.0698 + 0.0683i 
               
               
                   
                 x16 
                 0.7455 + 0.3411i 
                 0.1213 + 1.4366i 
                 0.3586 + 0.7959i 
               
               
                   
                 x17 
                 0.5811 + 0.3396i 
                 0.1077 + 1.2098i 
                 0.3571 + 0.6392i 
               
               
                   
                 x18 
                 0.7556 + 0.4669i 
                 0.0651 + 0.9801i 
                 0.5034 + 0.8271i 
               
               
                   
                 x19 
                 0.5862 + 0.4756i 
                 0.2009 + 1.0115i 
                 0.5063 + 0.6600i 
               
               
                   
                 x20 
                 0.9556 + 0.3280i 
                 0.3764 + 1.4264i 
                 0.2146 + 0.7862i 
               
               
                   
                 x21 
                 1.1767 + 0.3091i 
                 0.3237 + 1.2130i 
                 0.2109 + 0.6340i 
               
               
                   
                 x22 
                 0.9673 + 0.4720i 
                 0.5205 + 0.9814i 
                 0.0713 + 0.8093i 
               
               
                   
                 x23 
                 1.2051 + 0.5135i 
                 0.3615 + 1.0163i 
                 0.0698 + 0.6467i 
               
               
                   
                 x24 
                 0.7367 + 0.2015i 
                 0.0715 + 0.6596i 
                 0.2799 + 1.0862i 
               
               
                   
                 x25 
                 0.5811 + 0.2015i 
                 0.2116 + 0.6597i 
                 0.2806 + 1.2755i 
               
               
                   
                 x26 
                 0.7316 + 0.0669i 
                 0.0729 + 0.8131i 
                 0.4328 + 0.9904i 
               
               
                   
                 x27 
                 0.5782 + 0.0669i 
                 0.2158 + 0.8246i 
                 0.4551 + 1.1812i 
               
               
                   
                 x28 
                 0.9062 + 0.1971i 
                 0.5036 + 0.6467i 
                 0.2309 + 0.9414i 
               
               
                   
                 x29 
                 1.2829 + 0.1185i 
                 0.3526 + 0.6572i 
                 0.1077 + 1.3891i 
               
               
                   
                 x30 
                 0.9156 + 0.0735i 
                 0.5185 + 0.8086i 
                 0.0772 + 0.9852i 
               
               
                   
                 x31 
                 1.1011 + 0.0735i 
                 0.3593 + 0.8245i 
                 0.0802 + 1.1753i 
               
               
                   
                 x32 
                 0.3244 + 0.8044i 
                 1.2545 + 0.1010i 
                 0.8301 + 0.3727i 
               
               
                   
                 x33 
                 0.4589 + 0.8218i 
                 1.0676 + 0.0956i 
                 0.8256 + 0.5256i 
               
               
                   
                 x34 
                 0.3207 + 0.6415i 
                 1.4782 + 0.1667i 
                 0.6593 + 0.3668i 
               
               
                   
                 x35 
                 0.4509 + 0.6371i 
                 0.8981 + 0.0882i 
                 0.6623 + 0.5182i 
               
               
                   
                 x36 
                 0.1920 + 0.8196i 
                 0.5518 + 0.0690i 
                 1.0186 + 0.3645i 
               
               
                   
                 x37 
                 0.0633 + 0.8167i 
                 0.6903 + 0.0552i 
                 1.0001 + 0.5242i 
               
               
                   
                 x38 
                 0.1811 + 0.6371i 
                 0.5742 + 0.1987i 
                 1.1857 + 0.2725i 
               
               
                   
                 x39 
                 0.0640 + 0.6415i 
                 0.7374 + 0.1564i 
                 1.3928 + 0.3408i 
               
               
                   
                 x40 
                 0.3331 + 1.0669i 
                 1.2378 + 0.3049i 
                 0.8011 + 0.2227i 
               
               
                   
                 x41 
                 0.4655 + 1.0087i 
                 1.0518 + 0.3032i 
                 0.7981 + 0.0735i 
               
               
                   
                 x42 
                 0.3433 + 1.2865i 
                 1.4584 + 0.3511i 
                 0.6459 + 0.2198i 
               
               
                   
                 x43 
                 0.5004 + 1.5062i 
                 0.9107 + 0.2603i 
                 0.6430 + 0.0713i 
               
               
                   
                 x44 
                 0.1971 + 1.0051i 
                 0.6321 + 0.4729i 
                 0.9681 + 0.2205i 
               
               
                   
                 x45 
                 0.0735 + 1.0298i 
                 0.7880 + 0.4392i 
                 0.9615 + 0.0735i 
               
               
                   
                 x46 
                 0.1498 + 1.5018i 
                 0.6045 + 0.3274i 
                 1.3327 + 0.1039i 
               
               
                   
                 x47 
                 0.0865 + 1.2553i 
                 0.7629 + 0.2965i 
                 1.1359 + 0.0809i 
               
               
                   
                 x48 
                 0.7811 + 0.8080i 
                 0.0596 + 0.0739i 
                 0.8382 + 0.8709i 
               
               
                   
                 x49 
                 0.6167 + 0.8153i 
                 0.1767 + 0.0731i 
                 0.8145 + 0.6934i 
               
               
                   
                 x50 
                 0.7636 + 0.6255i 
                 0.0612 + 0.2198i 
                 0.6645 + 0.8486i 
               
               
                   
                 x51 
                 0.6000 + 0.6327i 
                 0.1815 + 0.2192i 
                 0.6600 + 0.6786i 
               
               
                   
                 x52 
                 0.9898 + 0.7680i 
                 0.4218 + 0.0715i 
                 1.1612 + 0.6949i 
               
               
                   
                 x53 
                 1.5855 + 0.1498i 
                 0.2978 + 0.0725i 
                 0.9785 + 0.6942i 
               
               
                   
                 x54 
                 0.9476 + 0.6175i 
                 0.4337 + 0.2115i 
                 1.3698 + 0.6259i 
               
               
                   
                 x55 
                 1.4625 + 0.4015i 
                 0.3057 + 0.2167i 
                 1.2183 + 0.4841i 
               
               
                   
                 x56 
                 0.8276 + 1.0225i 
                 0.0667 + 0.5124i 
                 0.7989 + 1.0498i 
               
               
                   
                 x57 
                 0.6313 + 1.0364i 
                 0.2008 + 0.5095i 
                 0.4395 + 1.4203i 
               
               
                   
                 x58 
                 0.8815 + 1.2865i 
                 0.0625 + 0.3658i 
                 0.6118 + 1.0246i 
               
               
                   
                 x59 
                 0.6342 + 1.2705i 
                 0.1899 + 0.3642i 
                 0.6303 + 1.2421i 
               
               
                   
                 x60 
                 1.0422 + 0.9593i 
                 0.4818 + 0.4946i 
                 1.0550 + 0.8924i 
               
               
                   
                 x61 
                 1.2749 + 0.8538i 
                 0.3380 + 0.5050i 
                 0.8612 + 1.2800i 
               
               
                   
                 x62 
                 1.1556 + 1.1847i 
                 0.4571 + 0.3499i 
                 1.2696 + 0.8969i 
               
               
                   
                 x63 
                 1.4771 + 0.6742i 
                 0.3216 + 0.3599i 
                 1.0342 + 1.1181i 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
             
               
                 TABLE 77 
               
             
            
               
                   
               
               
                 CR 6/15 
                 CR 8/15 
                 CR 10/15 
                 CR 12/15 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Label (int.) 
                 Constellation 
                 Label (int.) 
                 Constellation 
                 Label (int.) 
                 Constellation 
                 Label (int.) 
                 Constellation 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 0 
                 0.6800 + 1.6926i 
                 0 
                 1.0804 + 1.3788i 
                 0 
                 1.6097 + 0.1548i 
                 0 
                 1.1980 + 1.1541i 
               
               
                 1 
                 0.3911 + 1.3645i 
                 1 
                 1.0487 + 0.9862i 
                 1 
                 1.5549 + 0.4605i 
                 1 
                 0.9192 + 1.2082i 
               
               
                 2 
                 0.2191 + 1.7524i 
                 2 
                 1.6464 + 0.7428i 
                 2 
                 1.3226 + 0.1290i 
                 2 
                 1.2778 + 0.8523i 
               
               
                 3 
                 0.2274 + 1.4208i 
                 3 
                 1.3245 + 0.9414i 
                 3 
                 1.2772 + 0.3829i 
                 3 
                 1.0390 + 0.9253i 
               
               
                 4 
                 0.8678 + 1.2487i 
                 4 
                 0.7198 + 1.2427i 
                 4 
                 1.2753 + 1.0242i 
                 4 
                 0.6057 + 1.2200i 
               
               
                 5 
                 0.7275 + 1.1667i 
                 5 
                 0.8106 + 1.0040i 
                 5 
                 1.4434 + 0.7540i 
                 5 
                 0.7371 + 1.4217i 
               
               
                 6 
                 0.8747 + 1.0470i 
                 6 
                 0.5595 + 1.0317i 
                 6 
                 1.0491 + 0.8476i 
                 6 
                 0.6678 + 1.0021i 
               
               
                 7 
                 0.7930 + 1.0406i 
                 7 
                 0.6188 + 0.9722i 
                 7 
                 1.1861 + 0.6253i 
                 7 
                 0.8412 + 0.9448i 
               
               
                 8 
                 0.2098 + 0.9768i 
                 8 
                 1.6768 + 0.2202i 
                 8 
                 0.9326 + 0.0970i 
                 8 
                 1.1228 + 0.5373i 
               
               
                 9 
                 0.2241 + 1.0454i 
                 9 
                 0.9997 + 0.6844i 
                 9 
                 0.8962 + 0.2804i 
                 9 
                 1.0048 + 0.5165i 
               
               
                 10 
                 0.1858 + 0.9878i 
                 10 
                 1.4212 + 0.4769i 
                 10 
                 1.1044 + 0.1102i 
                 10 
                 1.4321 + 0.6343i 
               
               
                 11 
                 0.1901 + 1.0659i 
                 11 
                 1.1479 + 0.6312i 
                 11 
                 1.0648 + 0.3267i 
                 11 
                 1.0245 + 0.7152i 
               
               
                 12 
                 0.5547 + 0.8312i 
                 12 
                 0.6079 + 0.6566i 
                 12 
                 0.7325 + 0.6071i 
                 12 
                 0.6384 + 0.6073i 
               
               
                 13 
                 0.5479 + 0.8651i 
                 13 
                 0.7284 + 0.6957i 
                 13 
                 0.8260 + 0.4559i 
                 13 
                 0.8175 + 0.5684i 
               
               
                 14 
                 0.6073 + 0.8182i 
                 14 
                 0.5724 + 0.7031i 
                 14 
                 0.8744 + 0.7153i 
                 14 
                 0.6568 + 0.7801i 
               
               
                 15 
                 0.5955 + 0.8420i 
                 15 
                 0.6302 + 0.7259i 
                 15 
                 0.9882 + 0.5300i 
                 15 
                 0.8311 + 0.7459i 
               
               
                 16 
                 1.4070 + 0.1790i 
                 16 
                 0.1457 + 1.4010i 
                 16 
                 0.1646 + 1.6407i 
                 16 
                 0.1349 + 1.4742i 
               
               
                 17 
                 1.7227 + 0.2900i 
                 17 
                 0.1866 + 1.7346i 
                 17 
                 0.4867 + 1.5743i 
                 17 
                 0.1105 + 1.2309i 
               
               
                 18 
                 1.3246 + 0.2562i 
                 18 
                 0.1174 + 1.1035i 
                 18 
                 0.1363 + 1.3579i 
                 18 
                 0.0634 + 0.9796i 
               
               
                 19 
                 1.3636 + 0.3654i 
                 19 
                 0.1095 + 1.0132i 
                 19 
                 0.4023 + 1.3026i 
                 19 
                 0.1891 + 1.0198i 
               
               
                 20 
                 1.3708 + 1.2834i 
                 20 
                 0.4357 + 1.3636i 
                 20 
                 1.0542 + 1.2584i 
                 20 
                 0.4142 + 1.4461i 
               
               
                 21 
                 1.6701 + 0.8403i 
                 21 
                 0.5853 + 1.6820i 
                 21 
                 0.7875 + 1.4450i 
                 21 
                 0.3323 + 1.2279i 
               
               
                 22 
                 1.1614 + 0.7909i 
                 22 
                 0.3439 + 1.0689i 
                 22 
                 0.8687 + 1.0407i 
                 22 
                 0.4998 + 0.9827i 
               
               
                 23 
                 1.2241 + 0.7367i 
                 23 
                 0.3234 + 0.9962i 
                 23 
                 0.6502 + 1.1951i 
                 23 
                 0.3467 + 1.0202i 
               
               
                 24 
                 0.9769 + 0.1863i 
                 24 
                 0.1092 + 0.6174i 
                 24 
                 0.0982 + 0.9745i 
                 24 
                 0.0680 + 0.6501i 
               
               
                 25 
                 0.9452 + 0.2057i 
                 25 
                 0.1074 + 0.6307i 
                 25 
                 0.2842 + 0.9344i 
                 25 
                 0.2016 + 0.6464i 
               
               
                 26 
                 1.0100 + 0.2182i 
                 26 
                 0.1109 + 0.6996i 
                 26 
                 0.1142 + 1.1448i 
                 26 
                 0.0719 + 0.8075i 
               
               
                 27 
                 0.9795 + 0.2417i 
                 27 
                 0.1076 + 0.7645i 
                 27 
                 0.3385 + 1.0973i 
                 27 
                 0.2088 + 0.8146i 
               
               
                 28 
                 0.8241 + 0.4856i 
                 28 
                 0.3291 + 0.6264i 
                 28 
                 0.6062 + 0.7465i 
                 28 
                 0.4809 + 0.6296i 
               
               
                 29 
                 0.8232 + 0.4837i 
                 29 
                 0.3126 + 0.6373i 
                 29 
                 0.4607 + 0.8538i 
                 29 
                 0.3374 + 0.6412i 
               
               
                 30 
                 0.8799 + 0.5391i 
                 30 
                 0.3392 + 0.6999i 
                 30 
                 0.7263 + 0.8764i 
                 30 
                 0.4955 + 0.8008i 
               
               
                 31 
                 0.8796 + 0.5356i 
                 31 
                 0.3202 + 0.7282i 
                 31 
                 0.5450 + 1.0067i 
                 31 
                 0.3431 + 0.8141i 
               
               
                 32 
                 0.1376 + 0.3342i 
                 32 
                 0.9652 + 0.1066i 
                 32 
                 0.2655 + 0.0746i 
                 32 
                 1.2731 + 0.1108i 
               
               
                 33 
                 0.1383 + 0.3292i 
                 33 
                 0.9075 + 0.1666i 
                 33 
                 0.2664 + 0.0759i 
                 33 
                 1.0794 + 0.0977i 
               
               
                 34 
                 0.1363 + 0.3322i 
                 34 
                 0.9724 + 0.1171i 
                 34 
                 0.4571 + 0.0852i 
                 34 
                 1.5126 + 0.1256i 
               
               
                 35 
                 0.1370 + 0.3273i 
                 35 
                 0.9186 + 0.1752i 
                 35 
                 0.4516 + 0.1062i 
                 35 
                 0.9029 + 0.0853i 
               
               
                 36 
                 0.1655 + 0.3265i 
                 36 
                 0.6342 + 0.1372i 
                 36 
                 0.2559 + 0.1790i 
                 36 
                 0.5429 + 0.0694i 
               
               
                 37 
                 0.1656 + 0.3227i 
                 37 
                 0.6550 + 0.1495i 
                 37 
                 0.2586 + 0.1772i 
                 37 
                 0.6795 + 0.0559i 
               
               
                 38 
                 0.1634 + 0.3246i 
                 38 
                 0.6290 + 0.1393i 
                 38 
                 0.3592 + 0.2811i 
                 38 
                 0.5628 + 0.1945i 
               
               
                 39 
                 0.1636 + 0.3208i 
                 39 
                 0.6494 + 0.1504i 
                 39 
                 0.3728 + 0.2654i 
                 39 
                 0.7326 + 0.1410i 
               
               
                 40 
                 0.1779 + 0.6841i 
                 40 
                 1.3127 + 0.1240i 
                 40 
                 0.7706 + 0.0922i 
                 40 
                 1.2283 + 0.3217i 
               
               
                 41 
                 0.1828 + 0.6845i 
                 41 
                 0.9572 + 0.4344i 
                 41 
                 0.7407 + 0.2260i 
                 41 
                 1.0269 + 0.3261i 
               
               
                 42 
                 0.1745 + 0.6828i 
                 42 
                 1.2403 + 0.2631i 
                 42 
                 0.6180 + 0.0927i 
                 42 
                 1.4663 + 0.3716i 
               
               
                 43 
                 0.1793 + 0.6829i 
                 43 
                 1.0254 + 0.4130i 
                 43 
                 0.6019 + 0.1658i 
                 43 
                 0.9085 + 0.2470i 
               
               
                 44 
                 0.3547 + 0.6009i 
                 44 
                 0.6096 + 0.4214i 
                 44 
                 0.6007 + 0.4980i 
                 44 
                 0.6160 + 0.4549i 
               
               
                 45 
                 0.3593 + 0.6011i 
                 45 
                 0.6773 + 0.4284i 
                 45 
                 0.6673 + 0.3928i 
                 45 
                 0.7818 + 0.4247i 
               
               
                 46 
                 0.3576 + 0.5990i 
                 46 
                 0.5595 + 0.4102i 
                 46 
                 0.4786 + 0.3935i 
                 46 
                 0.5938 + 0.3170i 
               
               
                 47 
                 0.3624 + 0.5994i 
                 47 
                 0.6531 + 0.4101i 
                 47 
                 0.5176 + 0.3391i 
                 47 
                 0.7600 + 0.2850i 
               
               
                 48 
                 0.2697 + 0.1443i 
                 48 
                 0.1250 + 0.1153i 
                 48 
                 0.0757 + 0.1003i 
                 48 
                 0.0595 + 0.0707i 
               
               
                 49 
                 0.2704 + 0.1433i 
                 49 
                 0.1252 + 0.1158i 
                 49 
                 0.0753 + 0.1004i 
                 49 
                 0.1722 + 0.0706i 
               
               
                 50 
                 0.2644 + 0.1442i 
                 50 
                 0.1245 + 0.1152i 
                 50 
                 0.0777 + 0.4788i 
                 50 
                 0.0599 + 0.2119i 
               
               
                 51 
                 0.2650 + 0.1432i 
                 51 
                 0.1247 + 0.1156i 
                 51 
                 0.0867 + 0.4754i 
                 51 
                 0.1748 + 0.2114i 
               
               
                 52 
                 0.2763 + 0.1638i 
                 52 
                 0.3768 + 0.1244i 
                 52 
                 0.1023 + 0.2243i 
                 52 
                 0.4134 + 0.0701i 
               
               
                 53 
                 0.2768 + 0.1626i 
                 53 
                 0.3707 + 0.1237i 
                 53 
                 0.1010 + 0.2242i 
                 53 
                 0.2935 + 0.0705i 
               
               
                 54 
                 0.2715 + 0.1630i 
                 54 
                 0.3779 + 0.1260i 
                 54 
                 0.1950 + 0.3919i 
                 54 
                 0.4231 + 0.2066i 
               
               
                 55 
                 0.2719 + 0.1618i 
                 55 
                 0.3717 + 0.1252i 
                 55 
                 0.1881 + 0.3969i 
                 55 
                 0.2979 + 0.2100i 
               
               
                 56 
                 0.6488 + 0.1696i 
                 56 
                 0.1161 + 0.3693i 
                 56 
                 0.0930 + 0.8122i 
                 56 
                 0.0638 + 0.5002i 
               
               
                 57 
                 0.6462 + 0.1706i 
                 57 
                 0.1157 + 0.3645i 
                 57 
                 0.2215 + 0.7840i 
                 57 
                 0.1905 + 0.4966i 
               
               
                 58 
                 0.6456 + 0.1745i 
                 58 
                 0.1176 + 0.3469i 
                 58 
                 0.0937 + 0.6514i 
                 58 
                 0.0612 + 0.3552i 
               
               
                 59 
                 0.6431 + 0.1753i 
                 59 
                 0.1171 + 0.3424i 
                 59 
                 0.1540 + 0.6366i 
                 59 
                 0.1810 + 0.3533i 
               
               
                 60 
                 0.5854 + 0.3186i 
                 60 
                 0.3530 + 0.3899i 
                 60 
                 0.4810 + 0.6306i 
                 60 
                 0.4630 + 0.4764i 
               
               
                 61 
                 0.5862 + 0.3167i 
                 61 
                 0.3422 + 0.3808i 
                 61 
                 0.3856 + 0.7307i 
                 61 
                 0.3231 + 0.4895i 
               
               
                 62 
                 0.5864 + 0.3275i 
                 62 
                 0.3614 + 0.3755i 
                 62 
                 0.3527 + 0.5230i 
                 62 
                 0.4416 + 0.3397i 
               
               
                 63 
                 0.5873 + 0.3254i 
                 63 
                 0.3509 + 0.3656i 
                 63 
                 0.3100 + 0.5559i 
                 63 
                 0.3083 + 0.3490i 
               
               
                   
               
            
           
         
       
     
     Table 72 indicates non-uniform 16-QAM, Tables 73 to 75 indicate non-uniform 64-QAM, and tables 76 and 77 indicate non-uniform 256-QAM, and different mapping methods may be applied according to a code rate. 
     On the other hand, when the non-uniform constellation is designed to have the x-axis and the y-axis symmetric to each other, constellation points may be expressed similarly to those of uniform QAM and an example is illustrated as in Tables 78 to 81 presented below: 
     
       
         
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 78 
               
               
                   
               
             
            
               
                 y 0,q   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 y 2,q   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 y 4,q   
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
               
               
                 y 6,q   
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
               
               
                 y 8,q   
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
               
               
                 Re(z q ) 
                 −x 15   
                 −x 14   
                 −x 13   
                 −x 12   
                 −x 11   
                 −x 10   
                 −x 9   
                 −x 8   
                 −x 7   
                 −x 6   
                 −x 5   
                 −x 4   
                 −x 3   
                 −x 2   
                 −x 1   
                 −1  
               
               
                 y 0,q   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 y 2,q   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 y 4,q   
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
               
               
                 y 6,q   
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
               
               
                 y 8,q   
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
               
               
                 Re(z q ) 
                 1 
                 x 1   
                 x 2   
                 x 3   
                 x 4   
                 x 5   
                 x 6   
                 x 7   
                 x 8   
                 x 9   
                 x 10   
                 x 11   
                 x 12   
                 x 13   
                 x 14   
                 x 15   
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 79 
               
               
                   
               
             
            
               
                 y 1,q   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 y 3,q   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 y 5,q   
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
               
               
                 y 7,q   
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
               
               
                 y 9,q   
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
               
               
                 Im(z q ) 
                 −x 15   
                 −x 14   
                 −x 13   
                 −x 12   
                 −x 11   
                 −x 10   
                 −x 9   
                 −x 8   
                 −x 7   
                 −x 6   
                 −x 5   
                 −x 4   
                 −x 3   
                 −x 2   
                 −x 1   
                 −1  
               
               
                 y 1,q   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 y 3,q   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 y 5,q   
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
               
               
                 y 7,q   
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 0 
                 0 
               
               
                 y 9,q   
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
               
               
                 Im(z q ) 
                 1 
                 x 1   
                 x 2   
                 x 3   
                 x 4   
                 x 5   
                 x 6   
                 x 7   
                 x 8   
                 x 9   
                 x 10   
                 x 11   
                 x 12   
                 x 13   
                 x 14   
                 x 15   
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 80 
               
               
                   
               
               
                 x/Shape 
                 R6/15 
                 R7/15 
                 R8/15 
                 R9/15 
                 R10/15 
                 R11/15 
                 R12/15 
                 R13/15 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 x1 
                 1.0003 
                 1 
                 1.0005 
                 1 
                 1.0772 
                 1.16666667 
                 2.5983 
                 2.85714286 
               
               
                 x2 
                 1.0149 
                 1.04 
                 2.0897 
                 2.78571429 
                 2.8011 
                 3.08333333 
                 4.5193 
                 4.85714286 
               
               
                 x3 
                 1.0158 
                 1.04 
                 2.0888 
                 2.78571429 
                 2.9634 
                 3.33333333 
                 6.1649 
                 6.85714286 
               
               
                 x4 
                 2.6848 
                 3 
                 3.9945 
                 4.85714286 
                 4.8127 
                 5.16666667 
                 8.2107 
                 8.85714286 
               
               
                 x5 
                 2.6903 
                 3.04 
                 3.9931 
                 4.85714286 
                 5.1864 
                 5.75 
                 9.9594 
                 11 
               
               
                 x6 
                 2.882 
                 3.28 
                 5.3843 
                 6.85714286 
                 6.7838 
                 7.41666667 
                 12.0321 
                 13.2857143 
               
               
                 x7 
                 2.8747 
                 3.32 
                 5.3894 
                 6.85714286 
                 7.5029 
                 8.5 
                 13.9574 
                 15.7142857 
               
               
                 x8 
                 4.7815 
                 5.24 
                 7.5206 
                 9.14285714 
                 9.238 
                 10.0833333 
                 16.2598 
                 18.1428571 
               
               
                 x9 
                 4.7619 
                 5.32 
                 7.6013 
                 9.28571429 
                 10.32 
                 11.5833333 
                 18.4269 
                 20.7142857 
               
               
                 x10 
                 5.5779 
                 6.04 
                 9.3371 
                 11.5714286 
                 12.0115 
                 13.3333333 
                 20.9273 
                 23.4285714 
               
               
                 x11 
                 5.6434 
                 6.28 
                 9.8429 
                 12.2142857 
                 13.5356 
                 15.25 
                 23.4863 
                 26.2857143 
               
               
                 x12 
                 7.3854 
                 8.24 
                 11.9255 
                 14.6428571 
                 15.6099 
                 17.3333333 
                 26.4823 
                 29.2857143 
               
               
                 x13 
                 7.8797 
                 8.84 
                 13.3962 
                 16.4285714 
                 17.7524 
                 19.75 
                 29.7085 
                 32.4285714 
               
               
                 x14 
                 9.635 
                 11.04 
                 15.8981 
                 19.4285714 
                 20.5256 
                 22.4166667 
                 33.6247 
                 35.7142857 
               
               
                 x15 
                 11.7874 
                 13.68 
                 19.1591 
                 23.2857143 
                 24.1254 
                 25.5833333 
                 38.5854 
                 39.4285714 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 81 
               
               
                   
                   
               
               
                   
                 x/Shape 
                 9/15 
                 11/15 
                 13/15 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 x0  
                 1 
                 1.275373 
                 2.968204 
               
               
                   
                 x1  
                 2.753666 
                 3.224572 
                 4.986168 
               
               
                   
                 x2  
                 2.754654 
                 3.680802 
                 6.996148 
               
               
                   
                 x3  
                 4.810415 
                 5.509975 
                 9.073992 
               
               
                   
                 x4  
                 4.814368 
                 6.346779 
                 11.17465 
               
               
                   
                 x5  
                 6.797569 
                 8.066609 
                 13.35998 
               
               
                   
                 x6  
                 6.812391 
                 9.353538 
                 15.60908 
               
               
                   
                 x7  
                 9.044328 
                 11.04938 
                 17.97794 
               
               
                   
                 x8  
                 9.195366 
                 12.69977 
                 20.46238 
               
               
                   
                 x9  
                 11.42332 
                 14.55533 
                 23.10439 
               
               
                   
                 x10 
                 12.08725 
                 16.56972 
                 25.93383 
               
               
                   
                 x11 
                 14.46334 
                 18.82536 
                 28.98772 
               
               
                   
                 x12 
                 16.26146 
                 21.364 
                 32.30898 
               
               
                   
                 x13 
                 19.19229 
                 24.26295 
                 36.0013 
               
               
                   
                 x14 
                 22.97401 
                 27.70588 
                 40.26307 
               
               
                   
                   
               
            
           
         
       
     
     Tables 78 and 79 are tables for determining the real number component Re(z q ) and the imaginary number component Im(z q ) when modulation is performed in the non-uniform 1024-QAM method. That is, Table 78 indicates the real number part of the 1024-QAM, and Table 79 indicates the imaginary number part of the 1024-QAM. In addition, Tables 80 and 81 illustrate an example of a case in which modulation is performed in the non-uniform 1024-QAM method, and show xi values of Tables 78 and 79. 
     Since the non-uniform constellation method does not symmetrically map the modulation symbol onto the constellation point as shown in Tables 72 to 77, modulation symbols mapped onto constellation points may have different decoding performance. That is, bits constituting a modulation symbol may have different performance. 
     For example, referring to  FIG.  15    illustrating an example of a case in which modulation is performed in the non-uniform 64-QAM method, a modulation symbol 10 may be configured as (y 0 , y 1 , y 2 , y 3 , y 4 , y 5 )=(0, 0, 1, 0, 1, 0), and performance (e.g., capacity) of bits constituting the modulation symbol 10 may have a relationship of C(y 0 )&gt;C(y 1 )&gt;C(y 2 )&gt;C(y 3 )&gt;C(y 4 )&gt;C(y 5 ). 
     In addition, it is obvious that the constellation in the uniform constellation method and the non-uniform constellation method may be rotated and/or scaled (herein, the same or different scaling factor may be applied to a real number axis and an imaginary number axis), and other variations can be applied. In addition, the illustrated constellation indicates relevant locations of the constellation points and another constellation can be derived by rotation, scaling and/or other appropriate conversion. 
     As described above, the modulator  130  may map modulation symbols onto constellation points by using uniform constellation methods and non-uniform constellation methods. In this case, bits constituting a modulation symbol may have different performance as described above. 
     LDPC codeword bits may have different codeword characteristics according to a configuration of a parity check matrix. That is, the LDPC codeword bits may have different codeword characteristics according to the number of 1 existing in the columns of the parity check matrix, that is, a column degree. 
     Accordingly, the interleaver  120  may interleave to map the LDPC codeword bits onto modulation symbols by considering both the codeword characteristic of the LDPC codeword bits and the reliability of the bits constituting a modulation symbol. 
     In particular, since bits constituting a modulation symbol have different performance when a non-uniform QAM is used, the block interleaver  124  configures the number of columns to be identical to the number of bits constituting a modulation symbol such that one of a plurality of groups of an LDPC codeword can be mapped onto bits each of which exists on a same location of each modulation symbol. 
     That is, when LDPC codeword bits of high decoding performance are mapped onto high reliability bits from among bits of each modulation symbol, a receiver side may show high decoding performance, but there is a problem that the LDPC codeword bits of the high decoding performance are not received. In addition, when the LDPC codeword bits of high decoding performance are mapped onto low reliability bits from among the bits of the modulation symbol, initial reception performance is excellent, and thus, overall performance is also excellent. However, when many bits showing poor decoding performance are received, error propagation may occur. 
     Accordingly, when LDPC codeword bits are mapped onto modulation symbols, an LDPC codeword bit having a specific codeword characteristic is mapped onto a specific bit of a modulation symbol by considering both codeword characteristics of the LDPC codeword bits and reliability of the bits of the modulation symbol, and is transmitted to a receiver side. Accordingly, the receiver side can achieve both the high reception performance and the high decoding performance. 
     In this case, since the LDPC codeword is divided into groups each formed of M (=360) number of bits having the same codeword characteristic and the bits are mapped respectively onto a bit of a specific location of each modulation symbol in group units, bits having a specific codeword characteristic can be mapped onto the specific location of each modulation symbol more effectively. In addition, as described above, the number of bits forming a group may be a divisor of M. However, in this specification, the number of codeword bits forming a group will be limited to M for convenience of explanation. 
     That is, the modulator  130  can map bits included in a predetermined group from among the plurality of groups constituting the LDPC codeword onto a predetermined bit of each modulation symbol. Herein, each of the plurality of groups may be formed of M(=360) bits. 
     For example, in the case of 16-QAM, bits included in a predetermined group from among the plurality of groups may be mapped onto a first bit of each modulation symbol, or may be mapped onto a first bit and a second bit. 
     The modulator  130  can map bits included in a predetermined group from among the plurality of groups onto a predetermined bit of each modulation symbol for the following reasons. 
     As described above, the block interleaver  124  interleaves a plurality of groups of an LDPC codeword in group units, the demultiplexer demultiplexes bits output from the block interleaver  124 , and the modulator  130  maps demultiplexed bits (that is, cells) onto modulation symbols serially. 
     Accordingly, the group interleaver  122 , which is placed before the block interleaver  124 , interleaves the LDPC codeword in group units such that groups including bits to be mapped onto bits of specific locations of a modulation symbol can be written in the same column of the block interleaver  124 , considering a demultiplexing operation of the demultiplexer. 
     Specifically, the group interleaver  122  may rearrange the order of a plurality of groups of an LDPC codeword in group units such that groups including bits to be mapped onto the same location of different modulation symbols are serially arranged adjacent to one another, thereby allowing the block interleaver  122  to write a predetermined group on a predetermined column. That is, the group interleaver  122  interleaves the plurality of groups of the LDPC codeword in group units based on the above-described Tables 27 to 56, so that groups including bits to be mapped onto the same location of each modulation symbol are arranged to be adjacent to one another, and the block interleaver  124  interleaves by writing the adjacent groups on the same column. 
     Accordingly, the modulator  130  may generate a modulation symbol by mapping a bit output from a predetermined column of the block interleaver  124  onto a predetermined bit of the modulation symbol. In this case, bits included in one group may be mapped onto one bit of each modulation symbol or may be mapped onto two bits of each modulation symbol. 
     To explain detail, a case in which an LDPC codeword having a length of 16200 is modulated in the non-uniform 64-QAM method will be explained. 
     The group interleaver  122  divides the LDPC codeword into 16200/360(=45) groups, and interleaves the plurality of groups in group units. 
     In this case, the group interleaver  122  determines the number of groups to be written in each column of the block interleaver  124  based on the number of columns of the block interleaver  124 , and interleaves the plurality of groups in group units based on the determined number of groups. 
     Herein, groups written in a same column of the block interleaver  124  may be mapped onto a single specific bit or two specific bits from among bits constituting each modulation symbol according to the number of columns of the block interleaver  124 . Thus, the group interleaver  122  interleaves the plurality of groups in group units such that groups including bits required to be mapped onto a predetermined bit of each modulation symbol are adjacent to one another and serially arranged, considering bit characteristic of the modulation symbol. In this case, the group interleaver  122  may use the above-described Tables 27 to 56. 
     Accordingly, the groups which are adjacent to one another in the LDPC codeword interleaved in group units may be written in the same column of the block interleaver  124 , and the bits written in the same column may be mapped onto a single specific bit or two specific bits of each modulation symbol by the modulator  130 . 
     For example, it is assumed that the block interleaver  124  includes as many columns as the number of bits constituting a modulation symbol, that is, six (6) columns. In this case, each column of the block interleaver  124  may be divided into a first part including 2520 rows and a second part including 180 rows, as shown in Table 58 or 61. 
     Accordingly, the group interleaver  122  performs group interleaving such that 2520/360(=7) groups to be written in the first part of each column of the block interleaver  124  from among the plurality of groups are serially arranged to be adjacent to one another. Accordingly, the block interleaver  124  writes the seven (7) groups on the first part of each column and divides the bits included in the other three (3) groups and writes these bits on the second part of each column. 
     Thereafter, the block interleaver  124  reads the bits written in each row of the first part of the plurality of columns in the row direction, and reads the bits written in each row of the second part of the plurality of columns in the row direction. 
     That is, the block interleaver  124  may output the bits written in each row of the plurality of columns, from the bit written in the first row of the first column to the bit written in the first row of the sixth column, sequentially like (q 0 ,q 1 ,q 2 ,q 3 ,q 4 ,q 5 ,q 6 ,q 7 ,q 8 ,q 9 ,q 10 ,q 11 , . . . ). 
     In this case, when the demultiplexer is not used or the demultiplexer outputs serially bits input to the demultiplexer without changing the order of the bits, the LDPC codeword bits output from the block interleaver  124 , (q 0 , q 1 ,q 2 , q 3 , q 4 , q 5 ), etc. are modulated by the modulator  130 . That is, the LDPC codeword bits output from the block interleaver  124 , (q 0 , q 1 ,q 2 , q 3 , q 4 , q 5 ), , etc. configure cells (y 0,0 ,y 1,0 , . . . ,y 5,0 ), (y 0,1 ,y 1,1 , . . . , y 5,1 ), . . . , etc. and the modulator  130  generates a modulation symbol by mapping the cells onto constellation points. 
     Accordingly, the modulator  130  may map bits output from a same column of the block interleaver  124  onto a single specific bit of bits constituting each modulation symbol. For example, the modulator  130  may map bits included in a group written in the first column of the block interleaver  124 , that is, (q 0 , q 6 , . . . ), onto the first bit of each modulation symbol, and also, all bits written in the first column may be bits which are determined to be mapped onto the first bit of each modulation symbol according to a codeword characteristic of the LDPC codeword bits and the reliability of the bits constituting the modulation symbol. 
     As described above, the group interleaver  122  may interleave a plurality of groups of an LDPC codeword in group units such that the groups including bits to be mapped onto a single bit of a specific location of each modulation symbol are written in a specific column of the block interleaver  124 . 
     On the other hand, it is assumed that the block interleaver  124  includes as many columns as half of the number of bits constituting a modulation symbol, that is, three (3) columns. In this case, each column of the block interleaver  124  is not divided into parts as shown in Table 60 and 5400 bits are written in each column. 
     Accordingly, the group interleaver  122  performs group interleaving such that 5400/360(=15) groups to be written in each column of the block interleaver  124  from among the plurality of groups are serially arranged to be adjacent to one another. Accordingly, the block interleaver  124  writes the 15 groups on each column. 
     Thereafter, the block interleaver  124  may read bits written in each row of the plurality of columns in the row direction. 
     That is, the block interleaver  124  may output the bits written in each row of the plurality of columns, from the bit written in the first row of the first column to the bit written in the first row of the third column, sequentially like (q 0 ,q 1 ,q 2 , q 3 , q 4 , q 5 , q 6 , q 7 , q 8 , q 9 , q 10 ,q 11 , . . . ). 
     In this case, the demultiplexer demultiplexes the LDPC codeword bits output from the block interleaver  124  based on Table 63 described above, and output cells likes (y 00 , y 1,0 , . . . , y 5,0 )=(q 0 , q 2 , q 4 , q 1 , q 3 , q 5 ), (y 0,1 ,y 1,1 , . . . , y 5,1 )=(q 6 , q 8 , q 10 ,q 7 , q 9 , q 11 ). . . , etc. and the modulator  130  generates a modulation symbol by mapping the cells onto constellation points. 
     Accordingly, the modulator  130  may map bits output from the same column of the block interleaver  124  onto two specific bits of each modulation symbol. For example, the modulator  130  may map (q 0 , q 6 , . . . ) from among the bits (q 0 , q 3 , q 6 , q 9 , . . . ) included in the group written in the first column in the block interleaver  124  onto the first bit of each modulation symbol, and may map (q 3 , q 9 , . . . ) on the fifth bit of each modulation symbol. The bits written in the first column are bits which are determined to be mapped onto the first bit and the fifth bit of each modulation symbol according to the codeword characteristic of the LDPC codeword bits and the reliability of the bits constituting the modulation symbol. Herein, the first bit of the modulation symbol is a bit for determining a sign of the real number component Re(z q ) of a constellation point onto which the modulation symbol is mapped, and the fifth bit of the modulation symbol is a bit for determining a relatively small size of the constellation point onto which the modulation symbol is mapped. 
     As described above, the group interleaver  122  may interleave the plurality of groups of the LDPC codeword in group units such that groups including bits to be mapped onto two bits of specific locations of a modulation symbol are written in a specific column of the block interleaver  124 . 
     Hereinafter, exemplary embodiments will be explained in detail. 
     First, according to a first exemplary embodiment, it is assumed that the encoder  110  performs LDPC encoding at a code rate of 10/15, 11/15, 12/15 and 13/15 and generates an LDPC codeword formed of 16200 bits (N ldpc =16200), and the modulator  130  uses the non-uniform 16-QAM modulation method corresponding to the code rate based on Table 72. 
     In this case, the group interleaver  122  may perform group interleaving by using Equation 11 described above and Table 82 presented below: 
     
       
         
           
               
             
               
                 TABLE 82 
               
               
                   
               
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                   
               
               
                 10/15, 11/15, 
                 7 
                 17 
                 33 
                 31 
                 26 
                 10 
                 32 
                 41 
                 28 
                 8 
                 24 
                 42 
                 20 
                 9 
                 35 
                 43 
                 22 
                 12 
                 38 
                 3 
                 5 
                 14 
                 37 
               
               
                 12/15, 13/15  
                 40 
                 19 
                 16 
                 27 
                 39 
                 25 
                 4 
                 21 
                 1 
                 23 
                 18 
                 36 
                 0 
                 6 
                 11 
                 34 
                 2 
                 29 
                 15 
                 30 
                 13 
                 44 
               
               
                   
               
            
           
         
       
     
     Table 82 defines π(j) in Equation 11 and is identical to Table 27 described above. 
     The group interleaver  122  may perform group interleaving by using Equation 12 described above and Table 83 presented below: 
     
       
         
           
               
             
               
                 TABLE 83 
               
               
                   
               
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                   
               
               
                 10/15, 11/15, 
                 35 
                 31 
                 39 
                 19 
                 29 
                 20 
                 36 
                 0 
                 9 
                 13 
                 5 
                 37 
                 17 
                 43 
                 21 
                 41 
                 25 
                 1 
                 33 
                 24 
                 12 
                 30 
                 16 
               
               
                 12/15, 13/15  
                 32 
                 10 
                 28 
                 4 
                 26 
                 8 
                 40 
                 42 
                 3 
                 6 
                 2 
                 38 
                 14 
                 34 
                 22 
                 18 
                 27 
                 23 
                 7 
                 11 
                 15 
                 44 
               
               
                   
               
            
           
         
       
     
     Table 83 defines π(j) in Equation 12 and is identical to Table 42 described above. 
     Herein, a result of group interleaving based on Equation 11 and Table 82 and a result of group interleaving based on Equation 12 and Table 83 are identical to each other. This is because Equation 11 and Equation 12 have an inverse relationship to each other, and Table 82 and Table 83 have an inverse relationship to each other. This is applied to exemplary embodiments presented below. 
     In these cases, the block interleaver  124  in which the number of columns is four (4), the number of rows of the first part is 3960(=360 ×11), and the number of rows of the second part is 180 according to Table 57 or 61 may be used. 
     Accordingly, 11 groups (X 7 , X 17 , X 33 , X 31 , X 26 , X 10 , X 32 , X 41 , X 28 , X 8 , X 24 ) constituting an LDPC codeword are input to the first part of the first column of the block interleaver  124 , 11 groups (X 42 , X 20 , X 9 , X 35 , X 43 , X 22 , X 12 , X 38 , X 3 , X 5 , X 14 ) are input to the first part of the second column of the block interleaver  124 , 11 groups (X 37 , X 40 , X 19 , X 16 , X 27 , X 39 , X 25 , X 4 , X 21 , X 1 , X 23 ) are input to the first part of the third column of the block interleaver  124 , and 11 groups (X 18 , X 36 , X 0 , X 6 , X 11 , X 34 , X 2 , X 29 , X 15 , X 30 , X 13 ) are input to the first part of the fourth column of the block interleaver  124 . 
     In addition, a group X 44  is input to the second part of the block interleaver  124 . Specifically, bits constituting the group X 44  are input to the rows of the first column of the second part serially, input to the rows of the second column serially, input to the rows of the third column serially, and finally input to the rows of the fourth column serially. 
     In addition, the block interleaver  124  may output the bits input to the first row to the last row of each column serially, and the bits output from the block interleaver  124  may be input to the modulator  130  serially. In this case, the demultiplexer may be omitted or the demultiplexer may output the input bits serially without changing the order of the bits. 
     Accordingly, one bit included in each of groups X 7 , X 42 , X 37  and X 18  constitute a single modulation symbol. 
     According to an exemplary embodiment, one bit included in each of the groups X 7 , X 42 , X 37  and X 18  constitute a single modulation symbol based on group interleaving and block interleaving. In addition to the above-described method, other methods for constituting a single modulation symbol with one bit included in each of the groups X 7 , X 42 , X 37  and X 18  may be included in the inventive concept. 
     The performance achieved when a method according to a first exemplary embodiment is used is illustrated in  FIG.  20   . Referring to  FIG.  20   , when the non-uniform 16-QAM modulation method is used, high bit error rate and frame error rate (BER/FER) performance can be shown in a specific SNR region. 
     A receiver apparatus to be described later and correspond to the transmitter apparatus  100  which performs the above-described operations may include a demodulator corresponding the modulator  130 , a deinterleaver corresponding to the interleaver  120  (that is, the parity interleaver  121 , the group interleaver  122  and the block interleaver  124 ), and a decoder corresponding to the encoder  110 . These demodulator, deinterleaver and decoder may correspond to a demodulator, a deinterlever and a decoder to be explained later in reference to  FIG.  27   , respectively. 
     According to a second exemplary embodiment, it is assumed that the encoder  110  performs LDPC encoding at a code rate of 6/15, 7/15, 8/15 and 9/15 and generates an LDPC codeword formed of 16200 bits (N ldpc =16200), and the modulator  130  uses the non-uniform 64-QAM modulation method corresponding to a code rate based on Tables 73 or 75. 
     In this case, the group interleaver  122  may perform group interleaving by using Equation 11 described above and Table 84 presented below: 
     
       
         
           
               
             
               
                 TABLE 84 
               
               
                   
               
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                   
               
               
                 6/15, 7/15, 
                 32 
                 4 
                 23 
                 27 
                 35 
                 24 
                 16 
                 39 
                 5 
                 22 
                 33 
                 40 
                 18 
                 13 
                 8 
                 6 
                 37 
                 34 
                 0 
                 15 
                 21 
                 38 
                 30 
               
               
                 8/15, 9/15  
                 26 
                 14 
                 17 
                 10 
                 31 
                 25 
                 28 
                 12 
                 1 
                 29 
                 9 
                 41 
                 3 
                 20 
                 19 
                 36 
                 11 
                 7 
                 2 
                 42 
                 43 
                 44 
               
               
                   
               
            
           
         
       
     
     Table 84 defines π(j) in Equation 11 and is identical to Table 29 described above. 
     The group interleaver  122  may perform group interleaving by using Equation 12 described above and Table 85 presented below: 
     
       
         
           
               
             
               
                 TABLE 85 
               
               
                   
               
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                   
               
               
                 6/15, 7/15, 
                 18 
                 31 
                 41 
                 35 
                 1 
                 8 
                 15 
                 40 
                 14 
                 33 
                 26 
                 39 
                 30 
                 13 
                 24 
                 19 
                 6 
                 25 
                 12 
                 37 
                 36 
                 20 
                 9 
               
               
                 8/15, 9/15  
                 2 
                 5 
                 28 
                 23 
                 3 
                 29 
                 32 
                 22 
                 27 
                 0 
                 10 
                 17 
                 4 
                 38 
                 16 
                 21 
                 7 
                 11 
                 34 
                 42 
                 43 
                 44 
               
               
                   
               
            
           
         
       
     
     Table 85 defines π(j) in Equation 12 and is identical to Table 44 described above. 
     In these cases, the block interleaver  124  in which the number of columns is six (6), the number of rows of the first part is 2520(=360×7), and the number of rows of the second part is 180 according to Table 58 or 61 may be used. In this case, the output of the block interleaver  124  is input to the modulator  133 , and the demultiplexer may be omitted or the demultiplexer may output the input bits serially without changing the order of the bits. 
     The operations of the block interleaver  124  and the modulator  130  are the same as in the first exemplary embodiment, and thus, a detailed description thereof is omitted. 
     A receiver apparatus to be described later and correspond to the transmitter apparatus  100  which performs the above-described operations may include a demodulator corresponding the modulator  130 , a deinterleaver corresponding to the interleaver  120  (that is, the parity interleaver  121 , the group interleaver  122  and the block interleaver  124 ), and a decoder corresponding to the encoder  110 . These demodulator, deinterleaver and decoder may correspond to a demodulator, a deinterlever and a decoder to be explained later in reference to  FIG.  27   , respectively. 
     The performance achieved when a method according to the second exemplary embodiment is used is illustrated in  FIG.  21   . Referring to  FIG.  21   , when the non-uniform 64-QAM modulation method is used, high BER/FER performance can be shown in a specific SNR region. 
     According to a third exemplary embodiment, it is assumed that the encoder  110  performs LDPC encoding at a code rate of 10/15, 11/15, 12/15, and 13/15 and generates an LDPC codeword formed of 16200 bits (N ldpc =16200), and the modulator  130  uses the non-uniform 256-QAM modulation method corresponding to the code rate based on Tables 76 and 77. 
     In this case, the group interleaver  122  may perform group interleaving by using Equation 11 described above and Table 86 presented below: 
     
       
         
           
               
             
               
                 TABLE 86 
               
               
                   
               
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                   
               
               
                 10/15, 11/15, 
                 28 
                 6 
                 15 
                 8 
                 0 
                 22 
                 37 
                 35 
                 21 
                 26 
                 7 
                 12 
                 27 
                 1 
                 32 
                 33 
                 13 
                 11 
                 10 
                 18 
                 34 
                 9 
                 39 
               
               
                 12/15, 13/15  
                 38 
                 24 
                 17 
                 29 
                 25 
                 5 
                 16 
                 30 
                 2 
                 4 
                 19 
                 23 
                 14 
                 20 
                 3 
                 31 
                 36 
                 40 
                 41 
                 42 
                 43 
                 44 
               
               
                   
               
            
           
         
       
     
     Table 86 defines π(j) in Equation 11 and is identical to Table 31 described above. 
     The group interleaver  122  may perform group interleaving by using Equation 12 described above and Table 87 presented below: 
     
       
         
           
               
             
               
                 TABLE 87 
               
               
                   
               
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                   
               
               
                 10/15, 11/15, 
                 4 
                 13 
                 31 
                 37 
                 32 
                 28 
                 1 
                 10 
                 3 
                 21 
                 18 
                 17 
                 11 
                 16 
                 35 
                 2 
                 29 
                 25 
                 19 
                 33 
                 36 
                 8 
                 5 
               
               
                 12/15, 13/15  
                 34 
                 24 
                 27 
                 9 
                 12 
                 0 
                 26 
                 30 
                 38 
                 14 
                 15 
                 20 
                 7 
                 39 
                 6 
                 23 
                 22 
                 40 
                 41 
                 42 
                 43 
                 44 
               
               
                   
               
            
           
         
       
     
     Table 87 defines π(j) in Equation 12 and is identical to Table 46 described above. 
     In these cases, the block interleaver  124  in which the number of columns is eight (8), the number of rows of the first part is 1800(=360×5), and the number of rows of the second part is 225 according to Table 58 or 61 may be used. In this case, the output of the block interleaver  124  is input to the modulator  133 , and the demultiplexer may be omitted or the demultiplexer may output the input bits serially without changing the order of the bits. 
     The operations of the block interleaver  124  and the modulator  130  are the same as in the first exemplary embodiment, and thus, a detailed description thereof is omitted. 
     A receiver apparatus to be described later and correspond to the transmitter apparatus  100  which performs the above-described operations may include a demodulator corresponding the modulator  130 , a deinterleaver corresponding to the interleaver  120  (that is, the parity interleaver  121 , the group interleaver  122  and the block interleaver  124 ), and a decoder corresponding to the encoder  110 . These demodulator, deinterleaver and decoder may correspond to a demodulator, a deinterlever and a decoder to be explained later in reference to  FIG.  27   , respectively. 
     According to a fourth exemplary embodiment, it is assumed that the encoder  110  performs LDPC encoding at a code rate of 6/15, 7/15, 8/15 and 9/15 and generates an LDPC codeword formed of 16200 bits (N ldpc =16200), and the modulator  130  uses the non-uniform 1024-QAM modulation method corresponding to the code rate based on Tables 78 to 81. 
     In this case, the group interleaver  122  may perform group interleaving by using Equation 11 described above and Table 88 presented below: 
     
       
         
           
               
             
               
                 TABLE 88 
               
               
                   
               
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                   
               
               
                 6/15, 7/15, 
                 16 
                 13 
                 1 
                 25 
                 24 
                 33 
                 4 
                 29 
                 32 
                 30 
                 0 
                 17 
                 22 
                 18 
                 8 
                 9 
                 27 
                 11 
                 37 
                 35 
                 12 
                 15 
                 10 
               
               
                 8/15, 9/15  
                 20 
                 5 
                 6 
                 36 
                 38 
                 2 
                 26 
                 14 
                 7 
                 19 
                 3 
                 21 
                 23 
                 31 
                 34 
                 28 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
               
               
                   
               
            
           
         
       
     
     Table 88 defines π(j) in Equation 11 and is identical to Table 33 described above. 
     The group interleaver  122  may perform group interleaving by using Equation 12 described above and Table 89 presented below: 
     
       
         
           
               
             
               
                 TABLE 89 
               
               
                   
               
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                   
               
               
                 6/15, 7/15, 
                 10 
                 2 
                 28 
                 33 
                 6 
                 24 
                 25 
                 31 
                 14 
                 15 
                 22 
                 17 
                 20 
                 1 
                 30 
                 21 
                 0 
                 11 
                 13 
                 32 
                 23 
                 34 
                 12 
               
               
                 8/15, 9/15  
                 35 
                 4 
                 3 
                 29 
                 16 
                 38 
                 7 
                 9 
                 36 
                 8 
                 5 
                 37 
                 19 
                 26 
                 18 
                 27 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
               
               
                   
               
            
           
         
       
     
     Table 89 defines π(j) in Equation 12 and is identical to Table 48 described above. 
     In these cases, the block interleaver  124  in which the number of columns is 10, the number of rows of the first part is 1440(=360×4), and the number of rows of the second part is 180 according to Table 58 or 61 may be used. In this case, the output of the block interleaver  124  is input to the modulator  133 , and the demultiplexer may be omitted or the demultiplexer may output the input bits serially without changing the order of the bits. 
     The operations of the block interleaver  124  and the modulator  130  are the same as in the first exemplary embodiment, and thus, a detailed description thereof is omitted. 
     A receiver apparatus to be described later and correspond to the transmitter apparatus  100  which performs the above-described operations may include a demodulator corresponding the modulator  130 , a deinterleaver corresponding to the interleaver  120  (that is, the parity interleaver  121 , the group interleaver  122  and the block interleaver  124 ), and a decoder corresponding to the encoder  110 . These demodulator, deinterleaver and decoder may correspond to a demodulator, a deinterlever and a decoder to be explained later in reference to  FIG.  27   , respectively. 
     The performance achieved when a method according to the fourth exemplary embodiment is used is illustrated in  FIG.  22   . Referring to  FIG.  22   , when the non-uniform 1024-QAM modulation method according to an exemplary embodiment is used, high BER/FER performance can be shown in a specific SNR region. 
     According to a fifth exemplary embodiment, it is assumed that the encoder  110  performs LDPC encoding at a code rate of 6/15, 7/15, 8/15 and 9/15 and generates an LDPC codeword formed of 64800 bits (N ldpc =64800), and the modulator  130  uses the non-uniform 256-QAM modulation method corresponding to the code rate based on Tables 76 and 77. 
     In this case, the group interleaver  122  may perform group interleaving by using Equation 11 described above and Table 90 presented below: 
     
       
         
           
               
             
               
                 TABLE 90 
               
               
                   
               
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                 45 
               
               
                   
                 46 
                 47 
                 48 
                 49 
                 50 
                 51 
                 52 
                 53 
                 54 
                 55 
                 56 
                 57 
                 58 
                 59 
                 60 
                 61 
                 62 
                 63 
                 64 
                 65 
                 66 
                 67 
                 68 
               
               
                   
                 69 
                 70 
                 71 
                 72 
                 73 
                 74 
                 75 
                 76 
                 77 
                 78 
                 79 
                 80 
                 81 
                 82 
                 83 
                 84 
                 85 
                 86 
                 87 
                 88 
                 89 
                 90 
                 91 
               
               
                   
                 92 
                 93 
                 94 
                 95 
                 96 
                 97 
                 98 
                 99 
                 100 
                 101 
                 102 
                 103 
                 104 
                 105 
                 106 
                 107 
                 108 
                 109 
                 110 
                 111 
                 112 
                 113 
                 114 
               
               
                   
                 115 
                 116 
                 117 
                 118 
                 119 
                 120 
                 121 
                 122 
                 123 
                 124 
                 125 
                 126 
                 127 
                 128 
                 129 
                 130 
                 131 
                 132 
                 133 
                 134 
                 135 
                 136 
                 137 
               
               
                   
                 138 
                 139 
                 140 
                 141 
                 142 
                 143 
                 144 
                 145 
                 146 
                 147 
                 148 
                 149 
                 150 
                 151 
                 152 
                 153 
                 154 
                 155 
                 156 
                 157 
                 158 
                 159 
                 160 
               
               
                   
                 161 
                 162 
                 163 
                 164 
                 165 
                 166 
                 167 
                 168 
                 169 
                 170 
                 171 
                 172 
                 173 
                 174 
                 175 
                 176 
                 177 
                 178 
                 179 
                   
                   
                   
                   
               
               
                 6/15, 
                 48 
                 4 
                 15 
                 97 
                 108 
                 76 
                 1 
                 174 
                 61 
                 0 
                 59 
                 71 
                 120 
                 175 
                 167 
                 114 
                 65 
                 98 
                 101 
                 19 
                 112 
                 109 
                 152 
               
               
                 7/15, 
                 138 
                 35 
                 62 
                 43 
                 86 
                 153 
                 73 
                 173 
                 165 
                 23 
                 49 
                 91 
                 5 
                 169 
                 99 
                 77 
                 149 
                 26 
                 36 
                 25 
                 56 
                 156 
                 155 
               
               
                 8/15, 
                 110 
                 80 
                 58 
                 42 
                 40 
                 103 
                 159 
                 83 
                 127 
                 111 
                 63 
                 89 
                 11 
                 52 
                 144 
                 142 
                 133 
                 154 
                 44 
                 96 
                 93 
                 66 
                 122 
               
               
                 9/15  
                 123 
                 79 
                 141 
                 51 
                 21 
                 17 
                 45 
                 126 
                 150 
                 3 
                 168 
                 41 
                 106 
                 124 
                 64 
                 147 
                 78 
                 8 
                 118 
                 113 
                 39 
                 69 
                 140 
               
               
                   
                 14 
                 131 
                 82 
                 134 
                 55 
                 33 
                 50 
                 84 
                 28 
                 105 
                 6 
                 145 
                 7 
                 27 
                 132 
                 92 
                 115 
                 164 
                 74 
                 10 
                 68 
                 102 
                 67 
               
               
                   
                 30 
                 151 
                 18 
                 148 
                 129 
                 53 
                 100 
                 22 
                 107 
                 16 
                 170 
                 143 
                 121 
                 38 
                 57 
                 95 
                 90 
                 172 
                 81 
                 158 
                 171 
                 32 
                 119 
               
               
                   
                 37 
                 24 
                 130 
                 136 
                 161 
                 75 
                 29 
                 9 
                 47 
                 60 
                 162 
                 146 
                 137 
                 157 
                 70 
                 104 
                 31 
                 34 
                 166 
                 128 
                 117 
                 125 
                 2 
               
               
                   
                 13 
                 85 
                 88 
                 135 
                 116 
                 12 
                 163 
                 20 
                 46 
                 87 
                 94 
                 139 
                 54 
                 72 
                 160 
                 176 
                 177 
                 178 
                 179 
               
               
                   
               
            
           
         
       
     
     Table 90 defines π(j) in Equation 11 and is identical to Table 35 described above. 
     The group interleaver  122  may perform group interleaving by using Equation 12 described above and Table 91 presented below: 
     
       
         
           
               
             
               
                 TABLE 91 
               
               
                   
               
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                 45 
               
               
                   
                 46 
                 47 
                 48 
                 49 
                 50 
                 51 
                 52 
                 53 
                 54 
                 55 
                 56 
                 57 
                 58 
                 59 
                 60 
                 61 
                 62 
                 63 
                 64 
                 65 
                 66 
                 67 
                 68 
               
               
                   
                 69 
                 70 
                 71 
                 72 
                 73 
                 74 
                 75 
                 76 
                 77 
                 78 
                 79 
                 80 
                 81 
                 82 
                 83 
                 84 
                 85 
                 86 
                 87 
                 88 
                 89 
                 90 
                 91 
               
               
                   
                 92 
                 93 
                 94 
                 95 
                 96 
                 97 
                 98 
                 99 
                 100 
                 101 
                 102 
                 103 
                 104 
                 105 
                 106 
                 107 
                 108 
                 109 
                 110 
                 111 
                 112 
                 113 
                 114 
               
               
                   
                 115 
                 116 
                 117 
                 118 
                 119 
                 120 
                 121 
                 122 
                 123 
                 124 
                 125 
                 126 
                 127 
                 128 
                 129 
                 130 
                 131 
                 132 
                 133 
                 134 
                 135 
                 136 
                 137 
               
               
                   
                 138 
                 139 
                 140 
                 141 
                 142 
                 143 
                 144 
                 145 
                 146 
                 147 
                 148 
                 149 
                 150 
                 151 
                 152 
                 153 
                 154 
                 155 
                 156 
                 157 
                 158 
                 159 
                 160 
               
               
                   
                 161 
                 162 
                 163 
                 164 
                 165 
                 166 
                 167 
                 168 
                 169 
                 170 
                 171 
                 172 
                 173 
                 174 
                 175 
                 176 
                 177 
                 178 
                 179 
                   
                   
                   
                   
               
               
                 6/15, 
                 9 
                 6 
                 160 
                 78 
                 1 
                 35 
                 102 
                 104 
                 86 
                 145 
                 111 
                 58 
                 166 
                 161 
                 92 
                 2 
                 124 
                 74 
                 117 
                 19 
                 168 
                 73 
                 122 
               
               
                 7/15, 
                 32 
                 139 
                 42 
                 40 
                 105 
                 100 
                 144 
                 115 
                 154 
                 136 
                 97 
                 155 
                 24 
                 41 
                 138 
                 128 
                 89 
                 50 
                 80 
                 49 
                 26 
                 64 
                 75 
               
               
                 8/15, 
                 169 
                 146 
                 0 
                 33 
                 98 
                 72 
                 59 
                 120 
                 173 
                 96 
                 43 
                 129 
                 48 
                 10 
                 147 
                 8 
                 25 
                 56 
                 83 
                 16 
                 67 
                 114 
                 112 
               
               
                 9/15  
                 90 
                 152 
                 11 
                 174 
                 29 
                 110 
                 143 
                 5 
                 38 
                 85 
                 70 
                 47 
                 133 
                 94 
                 53 
                 99 
                 162 
                 27 
                 170 
                 163 
                 57 
                 131 
                 34 
               
               
                   
                 107 
                 66 
                 171 
                 130 
                 65 
                 3 
                 17 
                 37 
                 121 
                 18 
                 113 
                 51 
                 153 
                 101 
                 81 
                 123 
                 4 
                 21 
                 46 
                 55 
                 20 
                 88 
                 15 
               
               
                   
                 108 
                 165 
                 158 
                 87 
                 137 
                 12 
                 127 
                 68 
                 69 
                 82 
                 159 
                 76 
                 54 
                 157 
                 119 
                 140 
                 93 
                 106 
                 62 
                 95 
                 164 
                 141 
                 150 
               
               
                   
                 23 
                 172 
                 91 
                 71 
                 61 
                 126 
                 60 
                 103 
                 149 
                 84 
                 118 
                 39 
                 77 
                 116 
                 22 
                 28 
                 63 
                 45 
                 44 
                 151 
                 134 
                 52 
                 175 
               
               
                   
                 142 
                 148 
                 167 
                 109 
                 31 
                 156 
                 14 
                 79 
                 36 
                 125 
                 135 
                 132 
                 30 
                 7 
                 13 
                 179 
                 178 
                 177 
                 176 
               
               
                   
               
            
           
         
       
     
     Table 91 defines π(j) in Equation 12 and is identical to Table 50 described above. 
     In these cases, the block interleaver  124  in which the number of columns is 8, the number of rows of the first part is 7920(=360×22), and the number of rows of the second part is 180 according to Table 58 or 61 may be used. In this case, the output of the block interleaver  124  is input to the modulator  133 , and the demultiplexer (not shown) may be omitted or the demultiplexer (not shown) may output the input bits serially without changing the order of the bits. 
     The operations of the block interleaver  124  and the modulator  130  are the same as in the first exemplary embodiment, and thus, a detailed description thereof is omitted. 
     A receiver apparatus to be described later and correspond to the transmitter apparatus  100  which performs the above-described operations may include a demodulator corresponding the modulator  130 , a deinterleaver corresponding to the interleaver  120  (that is, the parity interleaver  121 , the group interleaver  122  and the block interleaver  124 ), and a decoder corresponding to the encoder  110 . These demodulator, deinterleaver and decoder may correspond to a demodulator, a deinterlever and a decoder to be explained later in reference to  FIG.  27   , respectively. 
     In the first to fifth exemplary embodiments, when the grouping interleaving is performed by using Equation 11, a value of π(j) is applied as an index of an input group, and, when the group interleaving is performed by using Equation 12, a value of π(j) is applied as an index of an output group. Therefore, Equation 11 and 12 have an inverse relationship 
     In addition, the above-described first to fifth exemplary embodiments are merely an example for explaining the above inverse relationship and various tables described in this description may have the same inverse relationship like the first to fifth exemplary embodiments. 
     The transmitter apparatus  100  may modulate a signal mapped onto a constellation and may transmit the signal to the receiver apparatus (for example, a receiver apparatus  2700  of  FIG.  27   ). For example, the transmitter apparatus  200  may map a signal mapped onto a constellation onto an Orthogonal Frequency Division Multiplexing (OFDM) frame by using the OFDM method, and may transmit the signal to the receiver apparatus  2700  via an allocated channel. 
     Exemplary Embodiment 2: Use of Block-Row Interleaver 
     According to another exemplary embodiment, the interleaver  120  may interleave an LDPC codeword in other methods, different from the methods described in the exemplary embodiment 1 beginning at paragraph [0127] above, and may map bits included in a predetermined group from among a plurality of groups constituting the interleaved LDPC codeword onto a predetermined bit of a modulation symbol. This will be explained in detail with reference to  FIG.  23   . 
     Referring to  FIG.  23   , the interleaver  120  includes a parity interleaver  121 , a group interleaver (or a group-wise interleaver  122 ), a group twist interleaver  123  and a block-row interleaver  125 . Herein, the parity interleaver  121  and the group twist interleaver  123  perform the same functions as in the exemplary embodiment 1 described above. and thus, a detailed description of these elements is omitted. 
     The group interleaver  122  may divide a parity-interleaved LDPC codeword into a plurality of groups, and may rearrange the order of the plurality of groups. 
     In this case, the operation of dividing the parity-interleaved LDPC codeword into the plurality of groups is the same as in the exemplary embodiment 1, and thus, a detailed description thereof is omitted. 
     The group interleaver  122  interleaves an LDPC codeword in group units. That is, the group interleaver  122  may rearrange the order of the plurality of groups in the LDPC codeword in group units by changing locations of the plurality of groups constituting the LDPC codeword. 
     In this case, the group interleaver  122  may interleave the LDPC codeword in group units by using Equation 13 
       Y j =X π(j) (0≤j&lt;N group )   (13),
 
     where x i  is the j th  group before group interleaving, and Y is the j th  group after group interleaving. 
     In addition, π(j) is a parameter indicating an interleaving order and is determined by at least one of a length of an LDPC codeword, a code rate and a modulation method. 
     According to an exemplary embodiment, an example of π(j) may be defined as in Tables 92 to 106 presented below. 
     For example, when the length N ldpc  of the LDPC codeword is 16200, the code rate is 10/15, 11/15, 12/15 and 13/15, and the modulation method is 16-QAM, π(j) may be defined as in Table 92 or 93 presented below: 
     
       
         
           
               
             
               
                 TABLE 92 
               
               
                   
               
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                   
               
               
                 10/15, 11/15, 
                 7 
                 42 
                 37 
                 18 
                 17 
                 20 
                 40 
                 36 
                 33 
                 9 
                 19 
                 0 
                 31 
                 35 
                 16 
                 6 
                 26 
                 43 
                 27 
                 11 
                 10 
                 22 
                 39 
               
               
                 12/15, 13/15  
                 34 
                 32 
                 12 
                 25 
                 2 
                 41 
                 38 
                 4 
                 29 
                 28 
                 3 
                 21 
                 15 
                 8 
                 5 
                 1 
                 30 
                 24 
                 14 
                 23 
                 13 
                 44 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 93 
               
               
                   
               
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                  0 
                  1 
                  2 
                  3 
                  4 
                  5 
                  6 
                  7 
                  8 
                  9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                   
               
               
                 10/15, 11/15, 
                  6 
                 15 
                 25 
                  4 
                 34 
                  7 
                 24 
                  0 
                 11 
                 14 
                 43 
                 20 
                 21 
                 30 
                 40 
                 31 
                 12 
                 13 
                 38 
                  5 
                  8 
                 32 
                 36 
               
               
                 12/15, 13/15  
                 33 
                  9 
                 17 
                 37 
                 35 
                 23 
                 18 
                 39 
                  1 
                 22 
                  3 
                 44 
                 28 
                  2 
                 19 
                 41 
                 26 
                 10 
                 16 
                 42 
                 27 
                 29 
               
               
                   
               
            
           
         
       
     
     In the case of Table 92, Equation 13 may be expressed as Y 0 =X π(0) =X 7 , Y 1 =X π(1) =X 42 , Y 2 =X π(2) =X 37 , . . . , Y 43 =X π(43) =X 13 , and Y 44 =X π(44) =X 44 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups in group units by changing the 7 th  group to the 0 th  group, the 42 nd  group to the 1 st  group, the 37 th  group to the 2 nd  group, . . . , the 13 th  group to the 43 rd  group, and the 44 th  group to the 44 th  group. 
     In the case of Table 93, Equation 13 may be expressed as Y 0 =X π(0) =X 6 , Y 1 =X π(1) =x 15 , Y 2 =X π(2) =X 25 , . . . , Y 43 =X π(43) =X 27 , and Y 44 =X π(44) =X 29 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups in group units by changing the 6 th  group to the 0 th  group, the 15 th  group to the 1 st  group, the 25 th  group to the 2 nd  group, . . . , the 27 th  group to the 43 rd  group, and the 29 th  group to the 44 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 16200, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 64-QAM, π(j) may be defined as in Table 94 or 95 presented below: 
     
       
         
           
               
             
               
                 TABLE 94 
               
               
                   
               
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                  0 
                  1 
                  2 
                  3 
                  4 
                  5 
                  6 
                  7 
                  8 
                  9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                   
               
               
                 6/15, 7/15, 
                 32 
                 39 
                  8 
                 38 
                 25 
                  3 
                  4 
                  5 
                  6 
                 30 
                 28 
                 20 
                 23 
                 22 
                 37 
                 26 
                 12 
                 19 
                 27 
                 33 
                 34 
                 14 
                  1 
               
               
                 8/15, 9/15  
                 36 
                 35 
                 40 
                  0 
                 17 
                 29 
                 11 
                 24 
                 18 
                 15 
                 10 
                  9 
                  7 
                 16 
                 13 
                 21 
                 31 
                 41 
                  2 
                 42 
                 43 
                 44 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 95 
               
               
                   
               
             
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                  0 
                 1 
                  2 
                  3 
                  4 
                  5 
                  6 
                  7 
                 8 
                  9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                 6/15, 7/15, 
                 32 
                 4 
                 23 
                 27 
                 35 
                 24 
                 16 
                 39 
                 5 
                 22 
                 33 
                 40 
                 18 
                 13 
                  8 
                  6 
                 37 
                 34 
                  0 
                 15 
                 21 
                 38 
                 30 
               
               
                 8/15, 9/15  
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
               
               
                 6/15, 7/15, 
                 26 
                 14 
                 17 
                 10 
                 31 
                 25 
                 28 
                 12 
                  1 
                 29 
                  9 
                 41 
                  3 
                 20 
                 19 
                 36 
                 11 
                  7 
                  2 
                 42 
                 43 
                 44 
               
               
                 8/15, 9/15  
               
               
                   
               
            
           
         
       
     
     In the case of Table 94, Equation 13 may be expressed as Y 0 =X π(0) =X 32 , Y 1 =X π(1) =X 39 , Y 2 =X π(2) =X 8 , . . . , Y 43 =X π(43) =X 43 , and Y 44 =X π(44) =X 44 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups in group units by changing the 32 nd  group to the 0 th  group, the 39 th  group to the 1 st  group, the 8 th  group to the 2 nd  group, . . . , the 43 rd  group to the 43 rd  group, and the 44 th  group to the 44 th  group. 
     In the case of Table 95, Equation 13 may be expressed as Y 0 =X π(0) =X 32 , Y 1 =X π(1) =X 4 , Y 2 =X π(2) =X 23 , . . . , Y 43 =X π(43) =X 43 , and Y 44 =X π(44) =X 44 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups in group units by changing the 32 nd  group to the 0 th  group, the 4 th  group to the 1 st  group, the 23 th  group to the 2 nd  group, . . . , the 43 rd  group to the 43 rd  group, and the 44 th  group to the 44 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 16200, the code rate is 10/15, 11/15, 12/15 and 13/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 96 or 97 presented below: 
     
       
         
           
               
             
               
                 TABLE 96 
               
               
                   
               
             
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                  0 
                  1 
                 2 
                  3 
                  4 
                  5 
                  6 
                  7 
                 8 
                  9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                 10/15, 11/15, 
                 28 
                 22 
                 7 
                 33 
                 34 
                 17 
                 30 
                 14 
                 6 
                 37 
                 12 
                 13 
                  9 
                 29 
                  2 
                 20 
                 15 
                 35 
                 27 
                 11 
                 39 
                 25 
                  4 
               
               
                 12/15, 13/15  
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
               
               
                 10/15, 11/15, 
                  3 
                  8 
                 21 
                  1 
                 10 
                 38 
                  5 
                 19 
                 31 
                  0 
                 26 
                 32 
                 18 
                 24 
                 16 
                 23 
                 36 
                 40 
                 41 
                 42 
                 43 
                 44 
               
               
                 12/15, 13/15  
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 97 
               
               
                   
               
             
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                  0 
                 1 
                  2 
                  3 
                  4 
                  5 
                  6 
                  7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                 10/15, 11/15, 
                 21 
                 9 
                 13 
                 17 
                 33 
                 38 
                 44 
                 42 
                 8 
                 1 
                 11 
                 16 
                 18 
                 37 
                 39 
                  3 
                 30 
                 22 
                 12 
                  6 
                 31 
                  5 
                 41 
               
               
                 12/15, 13/15  
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
               
               
                 10/15, 11/15, 
                 35 
                  0 
                 23 
                 14 
                 15 
                  7 
                 19 
                 43 
                 32 
                 20 
                 24 
                 10 
                  2 
                 34 
                 36 
                 40 
                  4 
                 25 
                 26 
                 27 
                 28 
                 29 
               
               
                 12/15, 13/15  
               
               
                   
               
            
           
         
       
     
     In the case of Table 96, Equation 13 may be expressed as Y 0 =X π(0) =X 28 , Y 1 =X π(1) =X 22 , Y 2 =X π(2) =X 7 , . . . , Y 43 =X π(43) =X 43 , and Y 44 =X π(44) =X 44 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups in group units by changing the 28 th  group to the 0 th  group, the 22 nd  group to the 1 st  group, the 7 th  group to the 2 nd  group, . . . , the 43 rd  group to the 43 rd  group, and the 44 th  group to the 44 th  group. 
     In the case of Table 97, Equation 13 may be expressed as Y 0 =X π(0) =X 21 , Y 1 =X π(1) =X 9 , Y 2 =X π(2) =X 13 , . . . , Y 43 =X π(43) =X 28 , and Y 44 =X π(44) =X 29 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups in group units by changing the 21 st  group to the 0 th  group, the 9 th  group to the 1 st  group, the 13 th  group to the 2 nd  group, . . . , the 28 th  group to the 43 rd  group, and the 29 th  group to the 44 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 16200, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 1024-QAM, π(j) may be defined as in Table 98 or 99 presented below: 
     
       
         
           
               
             
               
                 TABLE 98 
               
               
                   
               
             
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                  0 
                  1 
                  2 
                  3 
                  4 
                  5 
                 6 
                 7 
                  8 
                  9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                 6/15, 7/15, 
                 16 
                 24 
                 32 
                 22 
                 27 
                 12 
                 5 
                 2 
                 19 
                 31 
                 13 
                 33 
                 30 
                 18 
                 11 
                 15 
                  6 
                 26 
                  3 
                 34 
                  1 
                  4 
                  0 
               
               
                 8/15, 9/15  
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
               
               
                 6/15, 7/15, 
                  8 
                 37 
                 10 
                 36 
                 14 
                 21 
                 28 
                 25 
                 29 
                 17 
                  9 
                 35 
                 20 
                 38 
                  7 
                 23 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
               
               
                 8/15, 9/15  
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 99 
               
               
                   
               
             
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                  0 
                  1 
                 2 
                 3 
                 4 
                  5 
                  6 
                  7 
                 8 
                  9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                 6/15, 7/15, 
                 16 
                 34 
                 8 
                 7 
                 1 
                 40 
                 24 
                 30 
                 0 
                 33 
                 12 
                 13 
                 11 
                 44 
                 21 
                 10 
                 27 
                 42 
                 23 
                 25 
                 14 
                 15 
                  4 
               
               
                 8/15, 9/15  
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
               
               
                 6/15, 7/15, 
                  9 
                 18 
                 28 
                 41 
                 26 
                 35 
                 22 
                 19 
                 17 
                  6 
                  5 
                 31 
                 20 
                 32 
                 36 
                 29 
                 43 
                  2 
                  3 
                 37 
                 38 
                 39 
               
               
                 8/15, 9/15  
               
               
                   
               
            
           
         
       
     
     In the case of Table 98, Equation 13 may be expressed as Y 0 =X π(0) =X 16 , Y 1 =X π(1) =X 24 , Y 2 =X π(2) =X 32 , . . . , Y 43 =X π(43) =X 43 , and Y 44 =X π(44) =X 44 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups in group units by changing the 16 th  group to the 0 th  group, the 24 th  group to the 1 st  group, the 32 nd  group to the 2 nd  group, . . . , the 43 rd  group to the 43 rd  group, and the 44 th  group to the 44 th  group. 
     In the case of Table 99, Equation 13 may be expressed as Y 0 =X π(0) =X 16 , Y 1 =X π(1) =X 34 , Y 2 =X π(2) =X 8 , . . . , Y 43 =X π(43) =X 38 , and Y 44 =X π(44) =X 39 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups in group units by changing the 16 th  group to the 0 th  group, the 34 th  group to the 1 st  group, the 8 th  group to the 2 nd  group, . . . , the 38 th  group to the 43 rd  group, and the 39 th  group to the 44 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 64800, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 100 or 101 presented below: 
     
       
         
           
               
             
               
                 TABLE 100 
               
               
                   
               
             
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                  0 
                  1 
                  2 
                  3 
                  4 
                  5 
                  6 
                  7 
                 8 
                  9 
                  10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                  18 
                  19 
                 20 
                 21 
                  22 
               
               
                 6/15, 7/15, 
                 48 
                 152 
                 156 
                 93 
                 113 
                 74 
                 172 
                 31 
                 4 
                 138 
                 155 
                 66 
                 39 
                 10 
                 81 
                 34 
                 15 
                 35 
                 110 
                 122 
                 69 
                 68 
                 158 
               
               
                 8/15, 9/15  
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                  23 
                 24 
                 25 
                 26 
                  27 
                  28 
                  29 
                  30 
                  31 
                  32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                  39 
                 40 
                 41 
                 42 
                  43 
                  44 
                 45 
               
               
                 6/15, 7/15, 
                 166 
                 97 
                 62 
                 80 
                 123 
                 140 
                 102 
                 171 
                 128 
                 108 
                 43 
                 58 
                 79 
                 14 
                 67 
                 32 
                 117 
                 76 
                 86 
                 42 
                 141 
                 131 
                 30 
               
               
                 8/15, 9/15  
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                  46 
                  47 
                 48 
                  49 
                 50 
                 51 
                 52 
                  53 
                 54 
                 55 
                  56 
                 57 
                  58 
                 59 
                  60 
                 61 
                 62 
                 63 
                 64 
                  65 
                 66 
                 67 
                 68 
               
               
                 6/15, 7/15, 
                 119 
                 125 
                  1 
                 153 
                 40 
                 51 
                 82 
                 151 
                 37 
                  2 
                 174 
                 73 
                 103 
                 21 
                 134 
                 18 
                 24 
                 13 
                 61 
                 173 
                 159 
                 17 
                 55 
               
               
                 8/15, 9/15  
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                  69 
                  70 
                 71 
                 72 
                  73 
                 74 
                 75 
                 76 
                  77 
                  78 
                 79 
                 80 
                 81 
                  82 
                  83 
                 84 
                 85 
                  86 
                  87 
                 88 
                 89 
                  90 
                  91 
               
               
                 6/15, 7/15, 
                 148 
                 130 
                 85 
                  0 
                 165 
                 83 
                 45 
                 33 
                 129 
                 136 
                 88 
                 59 
                 23 
                 127 
                 126 
                 50 
                 53 
                 161 
                 135 
                 71 
                 49 
                 111 
                 150 
               
               
                 8/15, 9/15  
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 92 
                  93 
                 94 
                  95 
                  96 
                 97 
                 98 
                 99 
                 100 
                 101 
                 102 
                 103 
                 104 
                 105 
                 106 
                 107 
                 108 
                 109 
                 110 
                 111 
                 112 
                 113 
                 114 
               
               
                 6/15, 7/15, 
                 84 
                 100 
                 75 
                 116 
                 120 
                 91 
                 63 
                  3 
                  28 
                  22 
                  29 
                  12 
                 175 
                  5 
                  89 
                 168 
                 105 
                 107 
                  9 
                 163 
                 167 
                 169 
                  11 
               
               
                 8/15, 9/15  
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 115 
                 116 
                 117 
                 118 
                 119 
                 120 
                 121 
                 122 
                 123 
                 124 
                 125 
                 126 
                 127 
                 128 
                 129 
                 130 
                 131 
                 132 
                 133 
                 134 
                 135 
                 136 
                 137 
               
               
                 6/15, 7/15, 
                  41 
                  6 
                  16 
                  47 
                  20 
                 114 
                  99 
                  52 
                 106 
                 145 
                 170 
                  60 
                  46 
                  65 
                  77 
                 144 
                 124 
                  7 
                 143 
                 162 
                  87 
                  98 
                 149 
               
               
                 8/15, 9/15  
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 138 
                 139 
                 140 
                 141 
                 142 
                 143 
                 144 
                 145 
                 146 
                 147 
                 148 
                 149 
                 150 
                 151 
                 152 
                 153 
                 154 
                 155 
                 156 
                 157 
                 158 
                 159 
                 160 
               
               
                 6/15, 7/15, 
                 142 
                  64 
                  27 
                 121 
                 146 
                  94 
                 101 
                  26 
                 133 
                 147 
                 132 
                  38 
                 137 
                 139 
                  19 
                  36 
                 154 
                  78 
                  92 
                  57 
                 157 
                  54 
                 112 
               
               
                 8/15, 9/15  
               
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                   
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                   
                   
                 Code Rate 
                 161 
                 162 
                 163 
                 164 
                 165 
                 166 
                 167 
                 168 
                 169 
                 170 
                 171 
                 172 
                 173 
                 174 
                 175 
                 176 
                 177 
                 178 
                 179 
               
               
                   
                   
                   
                 6/15, 7/15, 
                  25 
                  44 
                  8 
                 115 
                  95 
                  70 
                  72 
                 109 
                  56 
                  96 
                 118 
                 164 
                  90 
                 104 
                 160 
                 176 
                 177 
                 178 
                 179 
               
               
                   
                   
                   
                 8/15, 9/15  
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 101 
               
               
                   
               
             
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                  0 
                 1 
                  2 
                  3 
                  4 
                  5 
                 6 
                  7 
                  8 
                 9 
                 10 
                 11 
                  12 
                  13 
                  14 
                  15 
                 16 
                 17 
                  18 
                 19 
                  20 
                  21 
                  22 
               
               
                 6/15, 7/15, 
                 48 
                 4 
                 15 
                 97 
                 108 
                 76 
                 1 
                 174 
                 61 
                 0 
                 59 
                 71 
                 120 
                 175 
                 167 
                 114 
                 65 
                 98 
                 101 
                 19 
                 112 
                 109 
                 152 
               
               
                 8/15, 9/15  
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                  23 
                 24 
                 25 
                 26 
                 27 
                  28 
                 29 
                  30 
                  31 
                 32 
                 33 
                 34 
                 35 
                  36 
                 37 
                 38 
                  39 
                 40 
                 41 
                 42 
                 43 
                  44 
                  45 
               
               
                 6/15, 7/15, 
                 138 
                 35 
                 62 
                 43 
                 86 
                 153 
                 73 
                 173 
                 165 
                 23 
                 49 
                 91 
                  5 
                 169 
                 99 
                 77 
                 149 
                 26 
                 36 
                 25 
                 56 
                 156 
                 155 
               
               
                 8/15, 9/15  
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                  46 
                 47 
                 48 
                 49 
                 50 
                  51 
                  52 
                 53 
                  54 
                 55 
                 56 
                 57 
                 58 
                 59 
                  60 
                  61 
                  62 
                  63 
                 64 
                 65 
                 66 
                 67 
                  68 
               
               
                 6/15, 7/15, 
                 110 
                 80 
                 58 
                 42 
                 40 
                 103 
                 159 
                 83 
                 127 
                 11 
                 63 
                 89 
                 11 
                 52 
                 144 
                 142 
                 133 
                 154 
                 44 
                 96 
                 93 
                 66 
                 122 
               
               
                 8/15, 9/15  
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                  69 
                 70 
                  71 
                 72 
                 73 
                 74 
                 75 
                  76 
                  77 
                 78 
                  79 
                 80 
                  81 
                  82 
                 83 
                  84 
                 85 
                 86 
                  87 
                  88 
                 89 
                 90 
                  91 
               
               
                 6/15, 7/15, 
                 123 
                 79 
                 141 
                 51 
                 21 
                 17 
                 45 
                 126 
                 150 
                  3 
                 168 
                 41 
                 106 
                 124 
                 64 
                 147 
                 78 
                  8 
                 118 
                 113 
                 39 
                 69 
                 140 
               
               
                 8/15, 9/15  
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 92 
                  93 
                 94 
                  95 
                 96 
                 97 
                 98 
                 99 
                 100 
                 101 
                 102 
                 103 
                 104 
                 105 
                 106 
                 107 
                 108 
                 109 
                 110 
                 111 
                 112 
                 113 
                 114 
               
               
                 6/15, 7/15, 
                 14 
                 131 
                 82 
                 134 
                 55 
                 33 
                 50 
                 84 
                  28 
                 105 
                  6 
                 145 
                  7 
                  27 
                 132 
                  92 
                 115 
                 164 
                  74 
                  10 
                  68 
                 102 
                  67 
               
               
                 8/15, 9/15  
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 115 
                 116 
                 117 
                 118 
                 119 
                 120 
                 121 
                 122 
                 123 
                 124 
                 125 
                 126 
                 127 
                 128 
                 129 
                 130 
                 131 
                 132 
                 133 
                 134 
                 135 
                 136 
                 137 
               
               
                 6/15, 7/15, 
                  30 
                 151 
                  18 
                 148 
                 129 
                  53 
                 100 
                  22 
                 107 
                  16 
                 170 
                 143 
                 121 
                  38 
                  57 
                  95 
                  90 
                 172 
                  81 
                 158 
                 171 
                  32 
                 119 
               
               
                 8/15, 9/15  
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 138 
                 139 
                 140 
                 141 
                 142 
                 143 
                 144 
                 145 
                 146 
                 147 
                 148 
                 149 
                 150 
                 151 
                 152 
                 153 
                 154 
                 155 
                 156 
                 157 
                 158 
                 159 
                 160 
               
               
                 6/15, 7/15, 
                  37 
                  24 
                 130 
                 136 
                 161 
                  75 
                  29 
                  9 
                  47 
                  60 
                 162 
                 146 
                 137 
                 157 
                  70 
                 104 
                  31 
                  34 
                 166 
                 128 
                 117 
                 125 
                  2 
               
               
                 8/15, 9/15  
               
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                   
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                   
                   
                 Code Rate 
                 161 
                 162 
                 163 
                 164 
                 165 
                 166 
                  167 
                 168 
                 169 
                 170 
                 171 
                 172 
                 173 
                 174 
                 175 
                 176 
                 177 
                 178 
                 179 
               
               
                   
                   
                   
                 6/15, 7/15, 
                  13 
                  85 
                  88 
                 135 
                 116 
                  12 
                 1963 
                  20 
                  46 
                  87 
                  94 
                 139 
                  54 
                  72 
                 160 
                 176 
                 177 
                 178 
                 179 
               
               
                   
                   
                   
                 8/15, 9/15  
               
               
                   
               
            
           
         
       
     
     In the case of Table 100, Equation 13 may be expressed as Y 0 =X π(0) =X 48 , Y 1 =X π(1) =X 152 , Y 2 =X π(2) =X 156 , . . . , Y 178 =X π(178) =X 178 , and Y 179 =X π(179) =X 179 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups in group units by changing the 48 th  group to the 0 th  group, the 152 nd  group to the 1 st  group, the 156 th  group to the 2 nd  group, . . . , the 178 th  group to the 178 th  group, and the 179 th  group to the 179 th  group. 
     In the case of Table 101, Equation 13 may be expressed as Y 0 =X π(0) =X 48 , Y 1 =X π(1) =X 4 , Y 2 =X π(2) =X 15 , . . . , Y 178 =X π(178) =X 178 , and Y 179 =X π(179) =X 179 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups in group units by changing the 48 th  group to the 0 th  group, the 4 th  group to the 1 st  group, the 15 th  group to the 2 nd  group, . . . , the 178 th  group to the 178 th  group, and the 179 th  group to the 179 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 64800, the code rate is 6/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 102 presented below: 
     
       
         
           
               
             
               
                 TABLE 102 
               
               
                   
               
             
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                  0 
                  1 
                  2 
                  3 
                  4 
                 5 
                  6 
                  7 
                 8 
                  9 
                  10 
                  11 
                  12 
                 13 
                  14 
                  15 
                 16 
                 17 
                  18 
                  19 
                  20 
                 21 
                  22 
               
               
                 6/15 
                 53 
                 71 
                 135 
                 172 
                 164 
                 8 
                 114 
                 126 
                 3 
                 63 
                 106 
                 154 
                 159 
                 98 
                 143 
                 120 
                 28 
                 51 
                 151 
                 115 
                 179 
                 11 
                 108 
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                  23 
                 24 
                 25 
                  26 
                  27 
                 28 
                 29 
                  30 
                  31 
                 32 
                 33 
                  34 
                 35 
                  36 
                 37 
                  38 
                  39 
                 40 
                 41 
                 42 
                  43 
                  44 
                 45 
               
               
                 6/15 
                 147 
                 46 
                 57 
                 178 
                 170 
                  5 
                 39 
                 109 
                 129 
                 68 
                 67 
                 119 
                 86 
                 157 
                 87 
                 175 
                 102 
                 15 
                 54 
                 50 
                 141 
                 163 
                 38 
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                  46 
                 47 
                 48 
                 49 
                  50 
                  51 
                  52 
                 53 
                 54 
                 55 
                 56 
                 57 
                 58 
                 59 
                 60 
                  61 
                  62 
                  63 
                 64 
                 65 
                 66 
                  67 
                 68 
               
               
                 6/15 
                 125 
                 33 
                 43 
                 48 
                 105 
                 139 
                 117 
                 75 
                 85 
                  9 
                 29 
                 60 
                 84 
                 89 
                 74 
                 100 
                 155 
                 148 
                 49 
                 61 
                 27 
                 107 
                 90 
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 69 
                  70 
                  71 
                 72 
                 73 
                 74 
                 75 
                  76 
                  77 
                  78 
                  79 
                 80 
                 81 
                 82 
                 83 
                  84 
                 85 
                  86 
                 87 
                 88 
                 89 
                  90 
                 91 
               
               
                 6/15 
                 76 
                 131 
                 116 
                  0 
                 59 
                 10 
                 12 
                 158 
                 136 
                 176 
                 161 
                 58 
                 70 
                 25 
                 73 
                 153 
                 20 
                 150 
                 80 
                 42 
                 45 
                 165 
                 79 
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 92 
                  93 
                  94 
                  95 
                 96 
                 97 
                  98 
                  99 
                 100 
                 101 
                 102 
                 103 
                 104 
                 105 
                 106 
                 107 
                 108 
                 109 
                 110 
                 111 
                 112 
                 113 
                 114 
               
               
                 6/15 
                 81 
                 134 
                 130 
                 177 
                 23 
                 55 
                 174 
                 118 
                  6 
                 94 
                 124 
                  83 
                  1 
                  56 
                  44 
                 167 
                 104 
                  35 
                 113 
                  4 
                  47 
                  66 
                  21 
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 115 
                 116 
                 117 
                 118 
                 119 
                 120 
                 121 
                 122 
                 123 
                 124 
                 125 
                 126 
                 127 
                 128 
                 129 
                 130 
                 131 
                 132 
                 133 
                 134 
                 135 
                 136 
                 137 
               
               
                 6/15 
                 166 
                  88 
                 132 
                 173 
                 133 
                  32 
                  64 
                  19 
                  72 
                 123 
                 152 
                  91 
                 122 
                  7 
                  17 
                 145 
                 171 
                  99 
                 156 
                  95 
                 160 
                  36 
                  40 
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 138 
                 139 
                 140 
                 141 
                 142 
                 143 
                 144 
                 145 
                 146 
                 147 
                 148 
                 149 
                 150 
                 151 
                 152 
                 153 
                 154 
                 155 
                 156 
                 157 
                 158 
                 159 
                 160 
               
               
                 6/15 
                 112 
                  82 
                 101 
                 146 
                 110 
                 121 
                  34 
                  69 
                  30 
                  96 
                 144 
                 103 
                  93 
                 128 
                  14 
                  52 
                 140 
                 127 
                  97 
                  77 
                  92 
                  78 
                  37 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                   
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                   
                   
                 Code Rate 
                 161 
                 162 
                 163 
                 164 
                 165 
                 166 
                 167 
                 168 
                 169 
                 170 
                 171 
                 172 
                 173 
                 174 
                 175 
                 176 
                 177 
                 178 
                 179 
               
               
                   
                   
                   
                 6/15 
                  62 
                  16 
                 142 
                 168 
                  2 
                 149 
                 111 
                  18 
                  65 
                  13 
                 162 
                 137 
                  41 
                 138 
                 169 
                  22 
                  24 
                  26 
                  31 
               
               
                   
               
            
           
         
       
     
     In the case of Table 102, Equation 13 may be expressed as Y 0 =X π(0) =X 53 , Y 2 =X π(2) =X 135 , . . . , Y 178 =X π(178) =X 26 , and Y 179 =X π(179) =X 31 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups in group units by changing the 53 rd  group to the 0 th  group, the 71 st  group to the 1 st  group, the 135 th  group to the 2 nd  group, . . . , the 26 th  group to the 178 th  group, and the 31 st  group to the 179 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 64800, the code rate is 8/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 103 presented below: 
     
       
         
           
               
             
               
                 TABLE 103 
               
               
                   
               
             
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                  0 
                  1 
                  2 
                  3 
                  4 
                  5 
                  6 
                  7 
                  8 
                  9 
                  10 
                 11 
                  12 
                 13 
                  14 
                  15 
                 16 
                 17 
                 18 
                 19 
                  20 
                 21 
                  22 
               
               
                 8/15 
                 71 
                 36 
                 38 
                 78 
                 140 
                 35 
                 175 
                 171 
                 104 
                 87 
                 110 
                 63 
                 176 
                 34 
                 145 
                 154 
                 84 
                 62 
                 76 
                 53 
                 142 
                 33 
                 127 
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                  23 
                 24 
                 25 
                 26 
                 27 
                  28 
                 29 
                 30 
                  31 
                 32 
                 33 
                 34 
                 35 
                  36 
                  37 
                  38 
                  39 
                 40 
                 41 
                 42 
                 43 
                  44 
                  45 
               
               
                 8/15 
                 122 
                 69 
                 10 
                 67 
                 49 
                 158 
                 97 
                 96 
                 128 
                 94 
                 75 
                 66 
                 28 
                 138 
                 172 
                 143 
                 107 
                 93 
                 12 
                 98 
                 23 
                 108 
                 111 
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                  46 
                  47 
                 48 
                 49 
                 50 
                 51 
                  52 
                 53 
                  54 
                  55 
                 56 
                 57 
                 58 
                 59 
                  60 
                  61 
                  62 
                  63 
                 64 
                 65 
                  66 
                 67 
                  68 
               
               
                 8/15 
                 141 
                 157 
                 74 
                 85 
                 52 
                 31 
                 166 
                 27 
                 159 
                 103 
                 89 
                 17 
                 79 
                 50 
                 149 
                 137 
                 109 
                 174 
                 57 
                 47 
                 164 
                 14 
                 144 
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 69 
                  70 
                  71 
                 72 
                 73 
                 74 
                 75 
                  76 
                  77 
                  78 
                 79 
                 80 
                 81 
                 82 
                 83 
                  84 
                 85 
                  86 
                  87 
                 88 
                 89 
                  90 
                 91 
               
               
                 8/15 
                 26 
                 101 
                 170 
                 58 
                 80 
                 46 
                 25 
                 123 
                 160 
                 135 
                  9 
                 56 
                  7 
                 90 
                 65 
                 169 
                 21 
                 153 
                 131 
                 59 
                 60 
                 120 
                 40 
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                  92 
                 93 
                  94 
                  95 
                  96 
                 97 
                 98 
                 99 
                 100 
                 101 
                 102 
                 103 
                 104 
                 105 
                 106 
                 107 
                 108 
                 109 
                 110 
                 111 
                 112 
                 113 
                 114 
               
               
                 8/15 
                 148 
                 20 
                 116 
                 125 
                 173 
                 68 
                 51 
                 30 
                 112 
                 163 
                 106 
                  3 
                  86 
                  6 
                  82 
                  19 
                 156 
                 162 
                 124 
                 118 
                 132 
                  92 
                 133 
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 115 
                 116 
                 117 
                 118 
                 119 
                 120 
                 121 
                 122 
                 123 
                 124 
                 125 
                 126 
                 127 
                 128 
                 129 
                 130 
                 131 
                 132 
                 133 
                 134 
                 135 
                 136 
                 137 
               
               
                 8/15 
                  24 
                 167 
                  32 
                 102 
                 161 
                  83 
                  43 
                  44 
                  88 
                 100 
                 134 
                 146 
                  81 
                  77 
                  13 
                  39 
                  29 
                 114 
                  22 
                 168 
                 126 
                  55 
                  70 
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 138 
                 139 
                 140 
                 141 
                 142 
                 143 
                 144 
                 145 
                 146 
                 147 
                 148 
                 149 
                 150 
                 151 
                 152 
                 153 
                 154 
                 155 
                 156 
                 157 
                 158 
                 159 
                 160 
               
               
                 8/15 
                 115 
                  95 
                 177 
                 151 
                 130 
                  0 
                  64 
                  91 
                 165 
                  73 
                 179 
                 136 
                 152 
                 150 
                  45 
                  48 
                  37 
                  2 
                 147 
                  15 
                 139 
                 129 
                  54 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                   
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                   
                   
                 Code Rate 
                 161 
                 162 
                 163 
                 164 
                 165 
                 166 
                 167 
                 168 
                 169 
                 170 
                 171 
                 172 
                 173 
                 174 
                 175 
                 176 
                 177 
                 178 
                 179 
               
               
                   
                   
                   
                 8/15 
                  61 
                 119 
                  8 
                 105 
                  42 
                  99 
                 117 
                  41 
                  1 
                 155 
                  72 
                 178 
                 121 
                 113 
                  11 
                  4 
                  5 
                  16 
                  18 
               
               
                   
               
            
           
         
       
     
     In the case of Table 103, Equation 13 may be expressed as Y 0 =X π(0) =X 71 , Y 1 =X π(1) =X 36 , Y 2 =X π(2) =X 38 , . . . , Y 178 =X π(178) =X 16 , and Y 179 =X π(179) =X 18 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups in group units by changing the 71 st  group to the 0 th  group, the 36 th  group to the 1 st  group, the 38 th  group to the 2 nd  group, . . . , the 16 th  group to the 178 th  group, and the 18 th  group to the 179 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 104 presented below. 
     
       
         
           
               
             
               
                 TABLE 104 
               
               
                   
               
             
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                  0 
                  1 
                  2 
                  3 
                  4 
                  5 
                  6 
                  7 
                  8 
                  9 
                  10 
                 11 
                 12 
                  13 
                 14 
                  15 
                 16 
                  17 
                 18 
                 19 
                 20 
                 21 
                  22 
               
               
                 10/15 
                 111 
                 39 
                 34 
                 100 
                 48 
                 155 
                 173 
                 120 
                 65 
                 101 
                 115 
                 58 
                 63 
                 148 
                  3 
                 142 
                 78 
                 105 
                 94 
                 56 
                 67 
                  1 
                 130 
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                  23 
                  24 
                 25 
                 26 
                 27 
                  28 
                  29 
                 30 
                  31 
                 32 
                 33 
                  34 
                 35 
                 36 
                 37 
                 38 
                  39 
                 40 
                 41 
                 42 
                 43 
                  44 
                  45 
               
               
                 10/15 
                 141 
                 49 
                 45 
                 60 
                 81 
                 112 
                 125 
                 12 
                 165 
                 68 
                 55 
                 104 
                 84 
                 47 
                 24 
                 15 
                 167 
                 44 
                 98 
                 19 
                  0 
                 113 
                 161 
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                  46 
                  47 
                  48 
                 49 
                  50 
                 51 
                  52 
                  53 
                  54 
                  55 
                 56 
                 57 
                 58 
                 59 
                 60 
                 61 
                  62 
                  63 
                 64 
                  65 
                  66 
                 67 
                 68 
               
               
                 10/15 
                 172 
                 170 
                 119 
                 93 
                 117 
                  2 
                 151 
                 162 
                 163 
                 164 
                 96 
                 41 
                 46 
                 21 
                 52 
                 22 
                 146 
                 126 
                 97 
                 109 
                 102 
                 80 
                 86 
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                  69 
                  70 
                  71 
                  72 
                 73 
                 74 
                 75 
                  76 
                  77 
                  78 
                  79 
                 80 
                  81 
                 82 
                 83 
                 84 
                 85 
                 86 
                  87 
                  88 
                 89 
                 90 
                 91 
               
               
                 10/15 
                 133 
                 138 
                 121 
                 108 
                 42 
                 75 
                 26 
                 154 
                 174 
                 139 
                 147 
                 69 
                 110 
                 91 
                 33 
                  6 
                 82 
                 17 
                 135 
                 114 
                 87 
                 76 
                 70 
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 92 
                  93 
                  94 
                  95 
                 96 
                 97 
                 98 
                 99 
                 100 
                 101 
                 102 
                 103 
                 104 
                 105 
                 106 
                 107 
                 108 
                 109 
                 110 
                 111 
                 112 
                 113 
                 114 
               
               
                 10/15 
                 40 
                 124 
                 143 
                 140 
                 51 
                 36 
                 50 
                 74 
                  11 
                 160 
                 159 
                 137 
                  66 
                  90 
                  5 
                  57 
                 107 
                  18 
                  25 
                 144 
                  29 
                  32 
                  79 
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 115 
                 116 
                 117 
                 118 
                 119 
                 120 
                 121 
                 122 
                 123 
                 124 
                 125 
                 126 
                 127 
                 128 
                 129 
                 130 
                 131 
                 132 
                 133 
                 134 
                 135 
                 136 
                 137 
               
               
                 10/15 
                  88 
                  31 
                 158 
                  10 
                 175 
                  62 
                 116 
                  92 
                  13 
                 177 
                 176 
                 152 
                 157 
                  73 
                  4 
                  35 
                  27 
                 132 
                 168 
                 145 
                 127 
                 106 
                  20 
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 138 
                 139 
                 140 
                 141 
                 142 
                 143 
                 144 
                 145 
                 146 
                 147 
                 148 
                 149 
                 150 
                 151 
                 152 
                 153 
                 154 
                 155 
                 156 
                 157 
                 158 
                 159 
                 160 
               
               
                 10/15 
                  95 
                  14 
                  64 
                 149 
                  59 
                  9 
                  54 
                  23 
                  99 
                  77 
                 136 
                 134 
                 153 
                 171 
                 103 
                  38 
                  53 
                  7 
                 131 
                 178 
                 179 
                 122 
                  43 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                   
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                   
                   
                 Code Rate 
                 161 
                 162 
                 163 
                 164 
                 165 
                 166 
                 167 
                 168 
                 169 
                 170 
                 171 
                 172 
                 173 
                 174 
                 175 
                 176 
                 177 
                 178 
                 179 
               
               
                   
                   
                   
                 10/15 
                  71 
                  37 
                  30 
                 150 
                 169 
                 166 
                 123 
                 89 
                  8 
                  72 
                  61 
                  16 
                 128 
                 129 
                 156 
                  28 
                  83 
                  85 
                 118 
               
               
                   
               
            
           
         
       
     
     In the case of Table 104, Equation 13 may be expressed as Y 0 =X π(0) =X 111 , Y 1 =X π(1) =X 39 , Y 2 =X π(2) =X 34 , . . . , Y 178 =X π(178) =X 85 , and Y 179 =X π(179) =X 118 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups in group units by changing the 111 th  group to the 0 th  group, the 39 th  group to the 1 st  group, the 34 th  group to the 2 nd  group, . . . , the 85 th  group to the 178 th  group, and the 118 th  group to the 179 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 105 presented below: 
     
       
         
           
               
             
               
                 TABLE 105 
               
               
                   
               
             
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                  0 
                  1 
                  2 
                  3 
                  4 
                  5 
                  6 
                  7 
                  8 
                  9 
                  10 
                 11 
                 12 
                  13 
                  14 
                  15 
                 16 
                 17 
                 18 
                 19 
                  20 
                  21 
                  22 
               
               
                 10/15 
                 89 
                 20 
                 72 
                 104 
                 85 
                 172 
                 13 
                 165 
                 64 
                 118 
                 109 
                 74 
                 99 
                 166 
                 177 
                 126 
                 50 
                 84 
                 35 
                 21 
                 145 
                 152 
                 178 
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                  23 
                 24 
                 25 
                 26 
                 27 
                  28 
                  29 
                 30 
                  31 
                 32 
                 33 
                 34 
                 35 
                  36 
                  37 
                  38 
                  39 
                 40 
                 41 
                 42 
                 43 
                  44 
                  45 
               
               
                 10/15 
                 125 
                 28 
                 95 
                 82 
                  2 
                 114 
                 127 
                 19 
                 140 
                 32 
                 81 
                 67 
                 23 
                 103 
                 169 
                 137 
                 153 
                 26 
                  7 
                 33 
                 86 
                 158 
                 159 
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 46 
                  47 
                 48 
                 49 
                 50 
                  51 
                 52 
                 53 
                  54 
                  55 
                 56 
                 57 
                 58 
                 59 
                 60 
                  61 
                  62 
                  63 
                 64 
                 65 
                 66 
                 67 
                  68 
               
               
                 10/15 
                 12 
                 175 
                 52 
                 96 
                 44 
                 105 
                 93 
                 14 
                 168 
                 176 
                 98 
                 36 
                 48 
                 53 
                 58 
                 143 
                 136 
                 131 
                 66 
                 18 
                 91 
                 38 
                 101 
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                  69 
                  70 
                  71 
                 72 
                 73 
                  74 
                 75 
                 76 
                  77 
                  78 
                 79 
                 80 
                 81 
                 82 
                  83 
                 84 
                  85 
                  86 
                  87 
                 88 
                 89 
                 90 
                 91 
               
               
                 10/15 
                 139 
                 160 
                 122 
                 31 
                  3 
                 112 
                 62 
                 34 
                 146 
                 170 
                 10 
                 90 
                 65 
                 49 
                 110 
                 77 
                 161 
                 161 
                 155 
                 59 
                  1 
                 78 
                  4 
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 92 
                  93 
                  94 
                  95 
                 96 
                  97 
                 98 
                 99 
                 100 
                 101 
                 102 
                 103 
                 104 
                 105 
                 106 
                 107 
                 108 
                 109 
                 110 
                 111 
                 112 
                 113 
                 114 
               
               
                 10/15 
                 61 
                 130 
                 150 
                 154 
                 70 
                 116 
                 55 
                 83 
                 164 
                 129 
                 124 
                 174 
                  17 
                  97 
                 106 
                  15 
                 173 
                 173 
                 144 
                 162 
                  76 
                 119 
                  46 
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 115 
                 116 
                 117 
                 118 
                 119 
                 120 
                 121 
                 122 
                 123 
                 124 
                 125 
                 126 
                 127 
                 128 
                 129 
                 130 
                 131 
                 132 
                 133 
                 134 
                 135 
                 136 
                 137 
               
               
                 10/15 
                  87 
                 132 
                 179 
                 156 
                  80 
                 117 
                  94 
                 108 
                  73 
                  39 
                 157 
                 167 
                 133 
                  54 
                 100 
                  51 
                  79 
                  79 
                 148 
                 123 
                  16 
                  68 
                 107 
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 138 
                 139 
                 140 
                 141 
                 142 
                 143 
                 144 
                 145 
                 146 
                 147 
                 148 
                 149 
                 150 
                 151 
                 152 
                 153 
                 154 
                 155 
                 156 
                 157 
                 158 
                 159 
                 160 
               
               
                 10/15 
                 113 
                 115 
                  88 
                  9 
                 149 
                  22 
                  11 
                  75 
                 102 
                  6 
                  60 
                 138 
                 134 
                 128 
                  43 
                  69 
                  71 
                  71 
                  41 
                 147 
                 142 
                 163 
                  57 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                   
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                   
                   
                 Code Rate 
                 161 
                 162 
                 163 
                 164 
                 165 
                 166 
                 167 
                 168 
                 169 
                 170 
                 171 
                 172 
                 173 
                 174 
                 175 
                 176 
                 177 
                 178 
                 179 
               
               
                   
                   
                   
                 10/15 
                  63 
                  40 
                  42 
                  37 
                  0 
                 121 
                 120 
                  92 
                  30 
                 111 
                  47 
                  45 
                 135 
                 141 
                  8 
                  24 
                  25 
                  25 
                  29 
               
               
                   
               
            
           
         
       
     
     In the case of Table 105, Equation 13 may be expressed as Y 0 =X π(0) =X 89 , Y 1 =X π(1) =X 20 , Y 2 =X π(2) =X 72 , . . . , Y 178 =X π(178) =X 27 , and Y 179 =X π(179) =X 29 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups in group units by changing the 89 th  group to the 0 th  group, the 20 th  group to the 1 st  group, the 72 nd  group to the 2 nd  group, . . . , the 27 th  group to the 178 th  group, and the 29 th  group to the 179 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 64800, the code rate is 12/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 106 presented below: 
     
       
         
           
               
             
               
                 TABLE 106 
               
               
                   
               
             
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                  0 
                 1 
                  2 
                  3 
                  4 
                  5 
                  6 
                  7 
                  8 
                  9 
                 10 
                  11 
                  12 
                 13 
                  14 
                  15 
                 16 
                 17 
                  18 
                 19 
                 20 
                  21 
                  22 
               
               
                 12/15 
                 51 
                 6 
                 75 
                 108 
                 93 
                 47 
                 168 
                 15 
                 122 
                 14 
                 42 
                 113 
                 136 
                 69 
                 147 
                 159 
                 91 
                  3 
                 129 
                 58 
                 68 
                 125 
                 161 
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 23 
                  24 
                 25 
                  26 
                 27 
                 28 
                 29 
                  30 
                  31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                  38 
                  39 
                  40 
                  41 
                 42 
                  43 
                 44 
                 45 
               
               
                 12/15 
                 11 
                 111 
                 21 
                 107 
                 97 
                 62 
                 31 
                 165 
                 176 
                 95 
                 71 
                 30 
                 38 
                 54 
                 83 
                 175 
                 152 
                 100 
                 134 
                 45 
                 124 
                 40 
                 36 
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                  46 
                  47 
                  48 
                 49 
                  50 
                 51 
                 52 
                 53 
                  54 
                  55 
                  56 
                 57 
                  58 
                 59 
                  60 
                 61 
                  62 
                  63 
                 64 
                  65 
                 66 
                 67 
                  68 
               
               
                 12/15 
                 162 
                 156 
                 119 
                  2 
                 137 
                 86 
                 81 
                 59 
                 164 
                 144 
                 130 
                  0 
                 114 
                 33 
                 103 
                 90 
                 158 
                 148 
                 78 
                 140 
                 37 
                 74 
                 121 
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 69 
                  70 
                  71 
                 72 
                  73 
                 74 
                 75 
                 76 
                 77 
                  78 
                  79 
                 80 
                 81 
                 82 
                 83 
                 84 
                  85 
                  86 
                 87 
                 88 
                  89 
                 90 
                  91 
               
               
                 12/15 
                 79 
                 157 
                 172 
                 57 
                 106 
                 87 
                 32 
                 76 
                 52 
                 160 
                 178 
                 65 
                  7 
                 53 
                 29 
                 44 
                 133 
                 150 
                 24 
                 26 
                 118 
                 85 
                 128 
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 92 
                 93 
                  94 
                 95 
                 96 
                 97 
                  98 
                 99 
                 100 
                 101 
                 102 
                 103 
                 104 
                 105 
                 106 
                 107 
                 108 
                 109 
                 110 
                 111 
                 112 
                 113 
                 114 
               
               
                 12/15 
                 84 
                 60 
                 171 
                 22 
                 61 
                 23 
                 101 
                 67 
                  96 
                  92 
                 167 
                 179 
                 126 
                  35 
                 141 
                 104 
                 123 
                 139 
                 145 
                  4 
                 105 
                  20 
                 120 
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 115 
                 116 
                 117 
                 118 
                 119 
                 120 
                 121 
                 122 
                 123 
                 124 
                 125 
                 126 
                 127 
                 128 
                 129 
                 130 
                 131 
                 132 
                 133 
                 134 
                 135 
                 136 
                 137 
               
               
                 12/15 
                  80 
                 154 
                 110 
                 151 
                 163 
                 143 
                  17 
                  99 
                 127 
                  98 
                  27 
                 153 
                 174 
                  70 
                  50 
                  88 
                  56 
                  82 
                  73 
                  9 
                 173 
                 132 
                  48 
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 138 
                 139 
                 140 
                 141 
                 142 
                 143 
                 144 
                 145 
                 146 
                 147 
                 148 
                 149 
                 150 
                 151 
                 152 
                 153 
                 154 
                 155 
                 156 
                 157 
                 158 
                 159 
                 160 
               
               
                 12/15 
                 117 
                  34 
                 142 
                  43 
                 155 
                  19 
                  39 
                 112 
                  64 
                  89 
                  46 
                  77 
                 170 
                  10 
                 102 
                  13 
                  28 
                  94 
                 169 
                 109 
                 146 
                 177 
                 115 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                   
                   
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                   
                   
                 Code Rate 
                 161 
                 162 
                 163 
                 164 
                 165 
                 166 
                 167 
                 168 
                 169 
                 170 
                 171 
                 172 
                 173 
                 174 
                 175 
                 176 
                 177 
                 178 
                 179 
               
               
                   
                   
                   
                 12/15 
                  66 
                 135 
                  49 
                 131 
                  63 
                 166 
                  12 
                 116 
                  5 
                 138 
                  55 
                  72 
                  41 
                 149 
                  16 
                  1 
                  8 
                  18 
                  25 
               
               
                   
               
            
           
         
       
     
     In the case of Table 106, Equation 13 may be expressed as Y 0 =X π(0) =X 51 , Y 1 =X π(1) =X 6 , Y 2 =X π(2) =X 75 , . . . , Y 178 =X π(178) =X 18 , and Y 179 =X π(179) =X 25 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups in group units by changing the 51 st  group to the 0 th  group, the 6 th  group to the 1 st  group, the 75′ group to the 2 nd  group, . . . , the 18 th  group to the 178 th  group, and the 25 th  group to the 179 th  group. 
     As described above, the group interleaver  122  may rearrange the order of the plurality of groups in group units by using Equation 13 and Tables 92 to 106. 
     On the other hand, since the order of the groups constituting the LDPC codeword is rearranged in group units by the group interleaver  122 , and then, the groups are block-interleaved by the block interleaver  124 , which will be described below, “Order of bits groups to be block interleaved” is set forth in Tables 19 to 106 in relation to π(j). 
     In addition, the group interleaver  122  may interleave the LDPC codeword in group units by using Equation 14 presented below: 
       Y π(j) =X j (0≤j&lt;N group )   (14),
 
     where X j  is the jth group before group interleaving, and Y j  is the jth group after group interleaving. 
     In addition, π(j) is a parameter indicating an interleaving order and is determined by at least one of a length of an LDPC codeword, a code rate and a modulation method. 
     According to an exemplary embodiment, an example of π(j) may be defined as in Tables 107 to 121 presented below. 
     For example, when the length N ldpc  of the LDPC codeword is 16200, the code rate is 10/15, 11/15, 12/15 and 13/15, and the modulation method is 16-QAM, π(j) may be defined as in Table 107 or 108 presented below: 
     
       
         
           
               
             
               
                 TABLE 107 
               
               
                   
               
             
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                  0 
                  1 
                  2 
                  3 
                  4 
                  5 
                  6 
                 7 
                  8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                 10/15, 11/15, 
                 11 
                 38 
                 27 
                 33 
                 30 
                 37 
                 15 
                 0 
                 36 
                 9 
                 20 
                 19 
                 25 
                 43 
                 41 
                 35 
                 14 
                  4 
                  3 
                 10 
                  5 
                 34 
                 21 
               
               
                 12/15, 13/15  
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
               
               
                 10/15, 11/15, 
                 42 
                 40 
                 26 
                 16 
                 18 
                 32 
                 31 
                 39 
                 12 
                 24 
                  8 
                 23 
                 13 
                  7 
                  2 
                 29 
                 22 
                  6 
                 28 
                  1 
                 17 
                 44 
               
               
                 12/15, 13/15  
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 108 
               
               
                   
               
             
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                 10/15, 11/15, 
                 7 
                 31 
                 36 
                 33 
                 3 
                 19 
                 0 
                 5 
                 20 
                 24 
                 40 
                 8 
                 16 
                 17 
                 9 
                 1 
                 41 
                 25 
                 29 
                 37 
                 11 
                 12 
                 32 
               
               
                 12/15, 13/15  
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
               
               
                 10/15, 11/15, 
                 28 
                 6 
                 2 
                 39 
                 43 
                 35 
                 44 
                 13 
                 15 
                 21 
                 23 
                 4 
                 27 
                 22 
                 26 
                 18 
                 30 
                 14 
                 38 
                 42 
                 10 
                 34 
               
               
                 12/15, 13/15  
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                   
               
            
           
         
       
     
     In the case of Table 107, Equation 14 may be expressed as X 0 =Y π(0) =Y 11 , X 1 =Y π(1) =Y 38 , X 2 =Y π(2) =Y 27 , . . . , X 43 =Y π(43) =Y 17 , and X 44 =Y π(44) =Y 44 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups in group units by changing the 0 th  group to the 11 th  group, the 1 st  group to the 38 th  group, the 2 nd  group to the 27 th  group, . . . , the 43 rd  group to the 17 th  group, and the 44 th  group to the 44 th  group. 
     In the case of Table 108, Equation 14 may be expressed as X 0 =Y π(0) =Y 7 , X 1 =Y π(1) =Y 31 , X 2 =Y π(2) =Y 36 , . . . , X 43 =Y π(43) =Y 10 , and X 44 =Y π(44) =Y 34 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups in group units by changing the 0 th  group to the 7 th  group, the 1 st  group to the 31 th  group, the 2 nd  group to the 36 th  group, . . . , the 43 rd  group to the 10 th  group, and the 44 th  group to the 44 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 16200, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 64-QAM, π(j) may be defined as in Table 109 or 110 presented below: 
     
       
         
           
               
             
               
                 TABLE 109 
               
               
                   
               
             
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                 6/15, 7/15, 
                 26 
                 22 
                 41 
                 5 
                 6 
                 7 
                 8 
                 35 
                 2 
                 34 
                 33 
                 29 
                 16 
                 37 
                 21 
                 32 
                 36 
                 27 
                 31 
                 17 
                 11 
                 38 
                 13 
               
            
           
           
               
               
               
            
               
                 8/15, 9/15  
                   
                   
               
               
                   
               
            
           
           
               
            
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
               
               
                 6/15, 7/15, 
                 12 
                 30 
                 4 
                 15 
                 18 
                 10 
                 28 
                 9 
                 39 
                 0 
                 19 
                 20 
                 24 
                 23 
                 14 
                 3 
                 1 
                 25 
                 40 
                 42 
                 43 
                 44 
               
               
                 8/15, 9/15  
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 110 
               
               
                   
               
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                   
               
               
                 6/15, 7/15, 
                 18 
                 31 
                 41 
                 35 
                 1 
                 8 
                 15 
                 40 
                 14 
                 33 
                 26 
                 39 
                 30 
                 13 
                 24 
                 19 
                 6 
                 25 
                 12 
                 37 
                 36 
                 20 
                 9 
               
               
                 8/15, 9/15  
                 2 
                 5 
                 28 
                 23 
                 3 
                 29 
                 32 
                 22 
                 27 
                 0 
                 10 
                 17 
                 4 
                 38 
                 16 
                 21 
                 7 
                 11 
                 34 
                 42 
                 43 
                 44 
               
               
                   
               
            
           
         
       
     
     In the case of Table 109, Equation 14 may be expressed as X 0 =Y π(0) =Y 26 , X 1 =Y π(1) =Y 22 , X 2 =Y π(2) =Y 41 , . . . , X 43 =Y π(43) =Y 43 , and X 44 =Y π(44) =Y 44 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups in group units by changing the 0 th  group to the 26 th  group, the 1 st  group to the 22 nd  group, the 2 nd  group to the 41 th  group, . . . , the 43 rd  group to the 43 rd  group, and the 44 th  group to the 44 th  group. 
     In the case of Table 110, Equation 14 may be expressed as X 0 =Y π(0) =Y 18 , X 1 =Y π(1) =Y 31 , X 2 =Y π(2) =Y 41 , . . . , X 43 =Y π(43) =Y 43 , and X 44 =Y π(44) =Y 44 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups in group units by changing the 0 th  group to the 18 th  group, the 1 st  group to the 31 st  group, the 2 nd  group to the 41′ group, . . . , the 43 rd  group to the 43 rd  group, and the 44 th  group to the 44 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 16200, the code rate is 10/15, 11/15, 12/15 and 13/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 111 or 112 presented below: 
     
       
         
           
               
             
               
                 TABLE 111 
               
               
                   
               
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                   
               
               
                 10/15, 11/15, 
                 32 
                 26 
                 14 
                 23 
                 22 
                 29 
                 8 
                 2 
                 24 
                 12 
                 27 
                 19 
                 10 
                 11 
                 7 
                 16 
                 37 
                 5 
                 35 
                 30 
                 15 
                 25 
                 1 
               
               
                 12/15, 13/15  
                 38 
                 36 
                 21 
                 33 
                 18 
                 0 
                 13 
                 6 
                 31 
                 34 
                 3 
                 4 
                 17 
                 39 
                 9 
                 28 
                 20 
                 40 
                 41 
                 42 
                 43 
                 44 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 112 
               
               
                   
               
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                   
               
               
                 10/15, 11/15, 
                 24 
                 9 
                 35 
                 15 
                 39 
                 21 
                 19 
                 28 
                 8 
                 1 
                 34 
                 10 
                 18 
                 2 
                 26 
                 27 
                 11 
                 3 
                 12 
                 29 
                 32 
                 0 
                 17 
               
               
                 12/15, 13/15  
                 25 
                 33 
                 40 
                 41 
                 42 
                 43 
                 44 
                 16 
                 20 
                 31 
                 4 
                 36 
                 23 
                 37 
                 13 
                 5 
                 14 
                 38 
                 22 
                 7 
                 30 
                 6 
               
               
                   
               
            
           
         
       
     
     In the case of Table 111, Equation 14 may be expressed as X 0 =Y π(0) =Y 32 , X 1 =Y π(1) =Y 26 , X 2 =Y π(2) =Y 14 , . . . , X 43 =Y π(43) =Y 43 , X 44 =Y π(44) =Y 44 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups in group units by changing the 0 th  group to the 32 nd  group, the 1 st  group to the 26 th  group, the 2 nd  group to the 14 th  group, . . . , the 43 rd  group to the 43 rd  group, and the 44 th  group to the 44 th  group. 
     In the case of Table 112, Equation 14 may be expressed as X 0 =Y π(0) =Y 24 , X 1 =Y π(1) =Y 9 , X 2 =Y π(2) =Y 35 , . . . , X 43 =Y π(43) =Y 30 , and X 44 =Y π(44) =Y 6 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups in group units by changing the 0 th  group to the 24 th  group, the 1 st  group to the 9 th  group, the 2 nd  group to the 3 5 th  group, . . . , the 43 rd  group to the 30 th  group, and the 44 th  group to the 6 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 16200, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 1024-QAM, π(j) may be defined as in Table 113 or 114 presented below: 
     
       
         
           
               
             
               
                 TABLE 113 
               
               
                   
               
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                   
               
               
                 6/15, 7/15, 
                 22 
                 20 
                 7 
                 18 
                 21 
                 6 
                 16 
                 37 
                 23 
                 33 
                 25 
                 14 
                 5 
                 10 
                 27 
                 15 
                 0 
                 32 
                 13 
                 8 
                 35 
                 28 
                 3 
               
               
                 8/15, 9/15  
                 38 
                 1 
                 30 
                 17 
                 4 
                 29 
                 31 
                 12 
                 9 
                 2 
                 11 
                 19 
                 34 
                 26 
                 24 
                 36 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 114 
               
               
                   
               
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 45) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code Rate 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                   
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                   
               
               
                 6/15, 7/15, 
                 8 
                 4 
                 40 
                 41 
                 22 
                 33 
                 32 
                 3 
                 2 
                 23 
                 15 
                 12 
                 10 
                 11 
                 20 
                 21 
                 0 
                 31 
                 24 
                 30 
                 35 
                 14 
                 29 
               
               
                 8/15, 9/15  
                 18 
                 6 
                 19 
                 27 
                 16 
                 25 
                 38 
                 7 
                 34 
                 36 
                 9 
                 1 
                 28 
                 37 
                 42 
                 43 
                 44 
                 5 
                 26 
                 17 
                 39 
                 13 
               
               
                   
               
            
           
         
       
     
     In the case of Table 113, Equation 14 may be expressed as X 0 =Y π(0) =Y 22 , X 1 =Y π(1) =Y 20 , X 2 =Y π(2) =Y 7 , . . . , X 43 =Y π(43) =Y 43 , and X 44 =Y π(44) =Y 44 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups in group units by changing the 0 th  group to the 22 nd  group, the 1 st  group to the 20 th  group, the 2 nd  group to the 7 th  group, . . . , the 43 rd  group to the 43 rd  group, and the 44 th  group to the 44 th  group. 
     In the case of Table 114, Equation 14 may be expressed as X 0 =Y π(0) =Y 8 , X 1 =Y π(1) =Y 4 , X 2 =Y π(2) =Y 40 , . . . , X 43 =Y π(43) =Y 39 , and X 44 =Y π(44) =Y 13 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups in group units by changing the 0 th  group to the 8 th  group, the 1 st  group to the 4 th  group, the 2 nd  group to the 40 th  group, . . . , the 43 rd  group to the 39 th  group, and the 44 th  group to the 13 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 64800, the code rate is 6/15, 7/15, 8/15 and 9/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 115 or 116 presented below: 
     
       
         
           
               
             
               
                 TABLE 115 
               
               
                   
               
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                 Rate 
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                 45 
               
               
                   
                 46 
                 47 
                 48 
                 49 
                 50 
                 51 
                 52 
                 53 
                 54 
                 55 
                 56 
                 57 
                 58 
                 59 
                 60 
                 61 
                 62 
                 63 
                 64 
                 65 
                 66 
                 67 
                 68 
               
               
                   
                 69 
                 70 
                 71 
                 72 
                 73 
                 74 
                 75 
                 76 
                 77 
                 78 
                 79 
                 80 
                 81 
                 82 
                 83 
                 84 
                 85 
                 86 
                 87 
                 88 
                 89 
                 90 
                 91 
               
               
                   
                 92 
                 93 
                 94 
                 95 
                 96 
                 97 
                 98 
                 99 
                 100 
                 101 
                 102 
                 103 
                 104 
                 105 
                 106 
                 107 
                 108 
                 109 
                 110 
                 111 
                 112 
                 113 
                 114 
               
               
                   
                 115 
                 116 
                 117 
                 118 
                 119 
                 120 
                 121 
                 122 
                 123 
                 124 
                 125 
                 126 
                 127 
                 128 
                 129 
                 130 
                 131 
                 132 
                 133 
                 134 
                 135 
                 136 
                 137 
               
               
                   
                 138 
                 139 
                 140 
                 141 
                 142 
                 143 
                 144 
                 145 
                 146 
                 147 
                 148 
                 149 
                 150 
                 151 
                 152 
                 153 
                 154 
                 155 
                 156 
                 157 
                 158 
                 159 
                 160 
               
               
                   
                 161 
                 162 
                 163 
                 164 
                 165 
                 166 
                 167 
                 168 
                 169 
                 170 
                 171 
                 172 
                 173 
                 174 
                 175 
                 176 
                 177 
                 178 
                 179 
                   
                   
                   
                   
               
               
                 6/15, 
                 72 
                 48 
                 55 
                 99 
                 8 
                 105 
                 116 
                 132 
                 163 
                 110 
                 13 
                 114 
                 103 
                 63 
                 36 
                 16 
                 117 
                 67 
                 61 
                 152 
                 119 
                 59 
                 101 
               
               
                 7/15, 
                 81 
                 62 
                 161 
                 145 
                 140 
                 100 
                 102 
                 45 
                 7 
                 38 
                 76 
                 15 
                 17 
                 153 
                 54 
                 149 
                 12 
                 50 
                 115 
                 42 
                 33 
                 162 
                 75 
               
               
                 8/15, 
                 127 
                 118 
                 0 
                 89 
                 84 
                 51 
                 122 
                 85 
                 159 
                 68 
                 169 
                 157 
                 34 
                 80 
                 126 
                 64 
                 25 
                 98 
                 139 
                 128 
                 11 
                 37 
                 21 
               
               
                 9/15  
                 20 
                 166 
                 88 
                 167 
                 57 
                 5 
                 94 
                 40 
                 129 
                 155 
                 35 
                 26 
                 14 
                 52 
                 74 
                 92 
                 71 
                 41 
                 135 
                 79 
                 106 
                 173 
                 97 
               
               
                   
                 156 
                 3 
                 143 
                 165 
                 170 
                 24 
                 136 
                 121 
                 93 
                 144 
                 29 
                 58 
                 174 
                 108 
                 123 
                 109 
                 32 
                 168 
                 18 
                 90 
                 160 
                 4 
                 120 
               
               
                   
                 164 
                 95 
                 39 
                 171 
                 46 
                 96 
                 141 
                 19 
                 27 
                 131 
                 47 
                 83 
                 82 
                 31 
                 77 
                 70 
                 44 
                 148 
                 146 
                 60 
                 87 
                 78 
                 150 
               
               
                   
                 9 
                 151 
                 28 
                 43 
                 138 
                 133 
                 130 
                 124 
                 142 
                 147 
                 69 
                 137 
                 91 
                 53 
                 1 
                 49 
                 154 
                 10 
                 2 
                 158 
                 22 
                 66 
                 175 
               
               
                   
                 86 
                 134 
                 111 
                 172 
                 73 
                 23 
                 112 
                 107 
                 113 
                 125 
                 30 
                 6 
                 65 
                 56 
                 104 
                 176 
                 177 
                 178 
                 179 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 116 
               
               
                   
               
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                 Rate 
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                 45 
               
               
                   
                 46 
                 47 
                 48 
                 49 
                 50 
                 51 
                 52 
                 53 
                 54 
                 55 
                 56 
                 57 
                 58 
                 59 
                 60 
                 61 
                 62 
                 63 
                 64 
                 65 
                 66 
                 67 
                 68 
               
               
                   
                 69 
                 70 
                 71 
                 72 
                 73 
                 74 
                 75 
                 76 
                 77 
                 78 
                 79 
                 80 
                 81 
                 82 
                 83 
                 84 
                 85 
                 86 
                 87 
                 88 
                 89 
                 90 
                 91 
               
               
                   
                 92 
                 93 
                 94 
                 95 
                 96 
                 97 
                 98 
                 99 
                 100 
                 101 
                 102 
                 103 
                 104 
                 105 
                 106 
                 107 
                 108 
                 109 
                 110 
                 111 
                 112 
                 113 
                 114 
               
               
                   
                 115 
                 116 
                 117 
                 118 
                 119 
                 120 
                 121 
                 122 
                 123 
                 124 
                 125 
                 126 
                 127 
                 128 
                 129 
                 130 
                 131 
                 132 
                 133 
                 134 
                 135 
                 136 
                 137 
               
               
                   
                 138 
                 139 
                 140 
                 141 
                 142 
                 143 
                 144 
                 145 
                 146 
                 147 
                 148 
                 149 
                 150 
                 151 
                 152 
                 153 
                 154 
                 155 
                 156 
                 157 
                 158 
                 159 
                 160 
               
               
                   
                 161 
                 162 
                 163 
                 164 
                 165 
                 166 
                 167 
                 168 
                 169 
                 170 
                 171 
                 172 
                 173 
                 174 
                 175 
                 176 
                 177 
                 178 
                 179 
                   
                   
                   
                   
               
               
                 6/15, 
                 9 
                 6 
                 160 
                 78 
                 1 
                 35 
                 102 
                 104 
                 86 
                 145 
                 111 
                 58 
                 166 
                 161 
                 92 
                 2 
                 124 
                 74 
                 117 
                 19 
                 168 
                 73 
                 122 
               
               
                 7/15, 
                 32 
                 139 
                 42 
                 40 
                 105 
                 100 
                 144 
                 115 
                 154 
                 136 
                 97 
                 155 
                 24 
                 41 
                 138 
                 128 
                 89 
                 50 
                 80 
                 49 
                 26 
                 64 
                 75 
               
               
                 8/15, 
                 169 
                 146 
                 0 
                 33 
                 98 
                 72 
                 59 
                 120 
                 173 
                 96 
                 43 
                 129 
                 48 
                 10 
                 147 
                 8 
                 25 
                 56 
                 83 
                 16 
                 67 
                 114 
                 112 
               
               
                 9/15  
                 90 
                 152 
                 11 
                 174 
                 29 
                 110 
                 143 
                 5 
                 38 
                 85 
                 70 
                 47 
                 133 
                 94 
                 53 
                 99 
                 162 
                 27 
                 170 
                 163 
                 57 
                 131 
                 34 
               
               
                   
                 107 
                 66 
                 171 
                 130 
                 65 
                 3 
                 17 
                 37 
                 121 
                 18 
                 113 
                 51 
                 153 
                 101 
                 81 
                 123 
                 4 
                 21 
                 46 
                 55 
                 20 
                 88 
                 15 
               
               
                   
                 108 
                 165 
                 158 
                 87 
                 137 
                 12 
                 127 
                 68 
                 69 
                 82 
                 159 
                 76 
                 54 
                 157 
                 119 
                 140 
                 93 
                 106 
                 62 
                 95 
                 164 
                 141 
                 150 
               
               
                   
                 23 
                 172 
                 91 
                 71 
                 61 
                 126 
                 60 
                 103 
                 149 
                 84 
                 118 
                 39 
                 77 
                 116 
                 22 
                 28 
                 63 
                 45 
                 44 
                 151 
                 134 
                 52 
                 175 
               
               
                   
                 142 
                 148 
                 167 
                 109 
                 31 
                 156 
                 14 
                 79 
                 36 
                 125 
                 135 
                 132 
                 30 
                 7 
                 13 
                 176 
                 177 
                 178 
                 179 
               
               
                   
               
            
           
         
       
     
     In the case of Table 115, Equation 14 may be expressed as X 0 =Y π(0) =Y 72 , X 1 =Y π(1) =Y 48 , X 2 =Y π(2) =Y 55 , . . . , X 178 =Y π(178) =Y 178 , and X 179 =Y π(179) =Y 179 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups in group units by changing the 0 th  group to the 72 nd  group, the 1 st  group to the 48 th  group, the 2 nd  group to the 55 th  group, . . . , the 178 th  group to the 178 th  group, and the 179 th  group to the 179 th  group. 
     In the case of Table 116, Equation 14 may be expressed as X 0 =Y π(0) =Y 9 , X 1 =Y π(1) =Y 6 , X 2 =Y π(2) =Y 160 , . . . , X 178 =Y π(178) =Y 178 , and X 179 =Y π(179) =Y 179 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups in group units by changing the 0 th  group to the 9 th  group, the 1 st  group to the 6 th  group, the 2 nd  group to the 160 th  group, . . . , the 178 th  group to the 178 th  group, and the 179 th  group to the 179 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 64800, the code rate is 6/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 117 presented below: 
     
       
         
           
               
             
               
                 TABLE 117 
               
               
                   
               
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                 Rate 
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                 45 
               
               
                   
                 46 
                 47 
                 48 
                 49 
                 50 
                 51 
                 52 
                 53 
                 54 
                 55 
                 56 
                 57 
                 58 
                 59 
                 60 
                 61 
                 62 
                 63 
                 64 
                 65 
                 66 
                 67 
                 68 
               
               
                   
                 69 
                 70 
                 71 
                 72 
                 73 
                 74 
                 75 
                 76 
                 77 
                 78 
                 79 
                 80 
                 81 
                 82 
                 83 
                 84 
                 85 
                 86 
                 87 
                 88 
                 89 
                 90 
                 91 
               
               
                   
                 92 
                 93 
                 94 
                 95 
                 96 
                 97 
                 98 
                 99 
                 100 
                 101 
                 102 
                 103 
                 104 
                 105 
                 106 
                 107 
                 108 
                 109 
                 110 
                 111 
                 112 
                 113 
                 114 
               
               
                   
                 115 
                 116 
                 117 
                 118 
                 119 
                 120 
                 121 
                 122 
                 123 
                 124 
                 125 
                 126 
                 127 
                 128 
                 129 
                 130 
                 131 
                 132 
                 133 
                 134 
                 135 
                 136 
                 137 
               
               
                   
                 138 
                 139 
                 140 
                 141 
                 142 
                 143 
                 144 
                 145 
                 146 
                 147 
                 148 
                 149 
                 150 
                 151 
                 152 
                 153 
                 154 
                 155 
                 156 
                 157 
                 158 
                 159 
                 160 
               
               
                   
                 161 
                 162 
                 163 
                 164 
                 165 
                 166 
                 167 
                 168 
                 169 
                 170 
                 171 
                 172 
                 173 
                 174 
                 175 
                 176 
                 177 
                 178 
                 179 
                   
                   
                   
                   
               
               
                 6/15 
                 72 
                 104 
                 165 
                 8 
                 111 
                 28 
                 100 
                 128 
                 5 
                 55 
                 74 
                 21 
                 75 
                 170 
                 152 
                 40 
                 162 
                 129 
                 168 
                 122 
                 85 
                 114 
                 176 
               
               
                   
                 96 
                 177 
                 82 
                 178 
                 66 
                 16 
                 56 
                 146 
                 179 
                 120 
                 47 
                 144 
                 109 
                 136 
                 160 
                 45 
                 29 
                 137 
                 173 
                 88 
                 48 
                 106 
                 89 
               
               
                   
                 24 
                 112 
                 49 
                 64 
                 42 
                 17 
                 153 
                 0 
                 41 
                 97 
                 105 
                 25 
                 80 
                 73 
                 57 
                 65 
                 161 
                 9 
                 121 
                 169 
                 113 
                 33 
                 32 
               
               
                   
                 145 
                 81 
                 1 
                 123 
                 83 
                 60 
                 53 
                 69 
                 157 
                 159 
                 91 
                 87 
                 92 
                 139 
                 103 
                 58 
                 54 
                 35 
                 37 
                 116 
                 59 
                 68 
                 126 
               
               
                   
                 158 
                 150 
                 101 
                 134 
                 147 
                 156 
                 13 
                 132 
                 61 
                 140 
                 39 
                 149 
                 108 
                 50 
                 10 
                 67 
                 22 
                 30 
                 142 
                 167 
                 138 
                 110 
                 6 
               
               
                   
                 19 
                 71 
                 52 
                 99 
                 34 
                 15 
                 143 
                 127 
                 124 
                 102 
                 46 
                 7 
                 155 
                 151 
                 31 
                 94 
                 70 
                 117 
                 119 
                 93 
                 2 
                 77 
                 172 
               
               
                   
                 174 
                 51 
                 154 
                 43 
                 163 
                 14 
                 148 
                 130 
                 141 
                 23 
                 63 
                 166 
                 86 
                 18 
                 125 
                 84 
                 11 
                 62 
                 133 
                 36 
                 76 
                 12 
                 135 
               
               
                   
                 79 
                 171 
                 44 
                 4 
                 90 
                 115 
                 107 
                 164 
                 175 
                 27 
                 131 
                 3 
                 118 
                 98 
                 38 
                 78 
                 95 
                 26 
                 20 
               
               
                   
               
            
           
         
       
     
     In the case of Table 117, Equation 14 may be expressed as X 0 =Y π(0) =Y 72 , X 1 =Y π(1) =Y 104 , X 2 =Y π(2) =Y 165 , . . . , X 178 =Y π(178) =Y 26 , and X 179 =Y π(179) =Y 20 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups in group units by changing the 0 th  group to the 72 nd  group, the 1 st  group to the 104 th  group, the 2 nd  group to the 165 th  group, . . . , the 178 th  group to the 26 th  group, and the 179 th  group to the 20 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 64800, the code rate is 8/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 118 presented below: 
     
       
         
           
               
             
               
                 TABLE 118 
               
               
                   
               
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                 Rate 
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                 45 
               
               
                   
                 46 
                 47 
                 48 
                 49 
                 50 
                 51 
                 52 
                 53 
                 54 
                 55 
                 56 
                 57 
                 58 
                 59 
                 60 
                 61 
                 62 
                 63 
                 64 
                 65 
                 66 
                 67 
                 68 
               
               
                   
                 69 
                 70 
                 71 
                 72 
                 73 
                 74 
                 75 
                 76 
                 77 
                 78 
                 79 
                 80 
                 81 
                 82 
                 83 
                 84 
                 85 
                 86 
                 87 
                 88 
                 89 
                 90 
                 91 
               
               
                   
                 92 
                 93 
                 94 
                 95 
                 96 
                 97 
                 98 
                 99 
                 100 
                 101 
                 102 
                 103 
                 104 
                 105 
                 106 
                 107 
                 108 
                 109 
                 110 
                 111 
                 112 
                 113 
                 114 
               
               
                   
                 115 
                 116 
                 117 
                 118 
                 119 
                 120 
                 121 
                 122 
                 123 
                 124 
                 125 
                 126 
                 127 
                 128 
                 129 
                 130 
                 131 
                 132 
                 133 
                 134 
                 135 
                 136 
                 137 
               
               
                   
                 138 
                 139 
                 140 
                 141 
                 142 
                 143 
                 144 
                 145 
                 146 
                 147 
                 148 
                 149 
                 150 
                 151 
                 152 
                 153 
                 154 
                 155 
                 156 
                 157 
                 158 
                 159 
                 160 
               
               
                   
                 161 
                 162 
                 163 
                 164 
                 165 
                 166 
                 167 
                 168 
                 169 
                 170 
                 171 
                 172 
                 173 
                 174 
                 175 
                 176 
                 177 
                 178 
                 179 
                   
                   
                   
                   
               
               
                 8/15 
                 143 
                 169 
                 155 
                 103 
                 176 
                 177 
                 105 
                 81 
                 163 
                 79 
                 25 
                 175 
                 41 
                 129 
                 67 
                 157 
                 178 
                 57 
                 179 
                 107 
                 93 
                 85 
                 133 
               
               
                   
                 43 
                 115 
                 75 
                 69 
                 53 
                 35 
                 131 
                 99 
                 51 
                 117 
                 21 
                 13 
                 5 
                 1 
                 154 
                 2 
                 130 
                 91 
                 168 
                 165 
                 121 
                 122 
                 152 
               
               
                   
                 74 
                 65 
                 153 
                 27 
                 59 
                 98 
                 50 
                 19 
                 160 
                 136 
                 80 
                 64 
                 72 
                 88 
                 89 
                 161 
                 17 
                 11 
                 144 
                 83 
                 34 
                 26 
                 97 
               
               
                   
                 24 
                 137 
                 0 
                 171 
                 147 
                 48 
                 33 
                 18 
                 128 
                 3 
                 58 
                 73 
                 127 
                 106 
                 120 
                 16 
                 49 
                 104 
                 9 
                 123 
                 56 
                 82 
                 145 
               
               
                   
                 113 
                 40 
                 32 
                 139 
                 30 
                 29 
                 42 
                 166 
                 124 
                 70 
                 118 
                 55 
                 8 
                 164 
                 102 
                 39 
                 44 
                 62 
                 10 
                 45 
                 100 
                 174 
                 132 
               
               
                   
                 138 
                 94 
                 167 
                 111 
                 162 
                 90 
                 173 
                 23 
                 76 
                 110 
                 95 
                 135 
                 22 
                 31 
                 159 
                 142 
                 87 
                 112 
                 114 
                 125 
                 78 
                 149 
                 61 
               
               
                   
                 36 
                 158 
                 4 
                 46 
                 20 
                 38 
                 68 
                 14 
                 126 
                 156 
                 92 
                 60 
                 151 
                 141 
                 150 
                 86 
                 15 
                 170 
                 108 
                 47 
                 28 
                 54 
                 77 
               
               
                   
                 119 
                 109 
                 101 
                 66 
                 146 
                 52 
                 116 
                 134 
                 84 
                 72 
                 7 
                 37 
                 96 
                 63 
                 6 
                 12 
                 140 
                 172 
                 148 
               
               
                   
               
            
           
         
       
     
     In the case of Table 118, Equation 14 may be expressed as X 0 =Y π(0) =Y 143 , X 1 =Y π(1) =Y 169 , X 2 =Y π(2) =Y 155 , . . . , X 178 =Y π(178) =Y 172 , and X 179 =Y π(179) =Y 148 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups in group units by changing the 0 th  group to the 143 rd  group, the 1 st  group to the 169 th  group, the 2 nd  group to the 155 th  group, . . . , the 178 th  group to the 172 nd  group, and the 179 th  group to the 148 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 119 presented below: 
     
       
         
           
               
             
               
                 TABLE 119 
               
               
                   
               
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                 Rate 
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                 45 
               
               
                   
                 46 
                 47 
                 48 
                 49 
                 50 
                 51 
                 52 
                 53 
                 54 
                 55 
                 56 
                 57 
                 58 
                 59 
                 60 
                 61 
                 62 
                 63 
                 64 
                 65 
                 66 
                 67 
                 68 
               
               
                   
                 69 
                 70 
                 71 
                 72 
                 73 
                 74 
                 75 
                 76 
                 77 
                 78 
                 79 
                 80 
                 81 
                 82 
                 83 
                 84 
                 85 
                 86 
                 87 
                 88 
                 89 
                 90 
                 91 
               
               
                   
                 92 
                 93 
                 94 
                 95 
                 96 
                 97 
                 98 
                 99 
                 100 
                 101 
                 102 
                 103 
                 104 
                 105 
                 106 
                 107 
                 108 
                 109 
                 110 
                 111 
                 112 
                 113 
                 114 
               
               
                   
                 115 
                 116 
                 117 
                 118 
                 119 
                 120 
                 121 
                 122 
                 123 
                 124 
                 125 
                 126 
                 127 
                 128 
                 129 
                 130 
                 131 
                 132 
                 133 
                 134 
                 135 
                 136 
                 137 
               
               
                   
                 138 
                 139 
                 140 
                 141 
                 142 
                 143 
                 144 
                 145 
                 146 
                 147 
                 148 
                 149 
                 150 
                 151 
                 152 
                 153 
                 154 
                 155 
                 156 
                 157 
                 158 
                 159 
                 160 
               
               
                   
                 161 
                 162 
                 163 
                 164 
                 165 
                 166 
                 167 
                 168 
                 169 
                 170 
                 171 
                 172 
                 173 
                 174 
                 175 
                 176 
                 177 
                 178 
                 179 
                   
                   
                   
                   
               
               
                 10/15 
                 43 
                 21 
                 51 
                 14 
                 129 
                 106 
                 84 
                 155 
                 169 
                 143 
                 118 
                 100 
                 30 
                 123 
                 139 
                 38 
                 172 
                 86 
                 109 
                 42 
                 137 
                 59 
                 61 
               
               
                   
                 145 
                 37 
                 110 
                 75 
                 131 
                 176 
                 112 
                 163 
                 116 
                 113 
                 83 
                 2 
                 130 
                 97 
                 162 
                 153 
                 1 
                 92 
                 57 
                 73 
                 160 
                 40 
                 25 
               
               
                   
                 58 
                 36 
                 4 
                 24 
                 98 
                 96 
                 60 
                 154 
                 144 
                 33 
                 19 
                 107 
                 11 
                 142 
                 26 
                 171 
                 120 
                 12 
                 140 
                 8 
                 104 
                 20 
                 32 
               
               
                   
                 80 
                 91 
                 161 
                 170 
                 128 
                 99 
                 74 
                 90 
                 147 
                 16 
                 114 
                 67 
                 27 
                 85 
                 177 
                 35 
                 178 
                 68 
                 89 
                 115 
                 168 
                 105 
                 82 
               
               
                   
                 122 
                 49 
                 18 
                 138 
                 56 
                 64 
                 41 
                 146 
                 3 
                 9 
                 66 
                 152 
                 34 
                 17 
                 136 
                 108 
                 72 
                 65 
                 81 
                 0 
                 28 
                 44 
                 88 
               
               
                   
                 10 
                 121 
                 50 
                 179 
                 48 
                 7 
                 71 
                 159 
                 167 
                 93 
                 29 
                 63 
                 135 
                 173 
                 174 
                 22 
                 156 
                 132 
                 69 
                 149 
                 87 
                 148 
                 103 
               
               
                   
                 70 
                 78 
                 95 
                 23 
                 15 
                 94 
                 111 
                 134 
                 62 
                 79 
                 13 
                 141 
                 164 
                 52 
                 126 
                 150 
                 76 
                 5 
                 175 
                 127 
                 117 
                 102 
                 101 
               
               
                   
                 45 
                 53 
                 54 
                 55 
                 31 
                 166 
                 39 
                 133 
                 165 
                 47 
                 151 
                 46 
                 6 
                 77 
                 119 
                 125 
                 124 
                 157 
                 158 
               
               
                   
               
            
           
         
       
     
     In the case of Table 119, Equation 14 may be expressed as X 0 =Y π(0) =Y 43 , X 1 =Y π(1) =Y 21 , X 2 =Y π(2) =Y 51 , . . . , X 178 =Y π(178) =Y 157 , and X 179 =Y π(179) =Y 158 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups in group units by changing the 0 th  group to the 43 rd  group, the 1 st  group to the 21 th  group, the 2 nd  group to the 51 st  group, . . . , the 178 th  group to the 157 th  group, and the 179 th  group to the 158 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 120 presented below: 
     
       
         
           
               
             
               
                 TABLE 120 
               
               
                   
               
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                 Rate 
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                 45 
               
               
                   
                 46 
                 47 
                 48 
                 49 
                 50 
                 51 
                 52 
                 53 
                 54 
                 55 
                 56 
                 57 
                 58 
                 59 
                 60 
                 61 
                 62 
                 63 
                 64 
                 65 
                 66 
                 67 
                 68 
               
               
                   
                 69 
                 70 
                 71 
                 72 
                 73 
                 74 
                 75 
                 76 
                 77 
                 78 
                 79 
                 80 
                 81 
                 82 
                 83 
                 84 
                 85 
                 86 
                 87 
                 88 
                 89 
                 90 
                 91 
               
               
                   
                 92 
                 93 
                 94 
                 95 
                 96 
                 97 
                 98 
                 99 
                 100 
                 101 
                 102 
                 103 
                 104 
                 105 
                 106 
                 107 
                 108 
                 109 
                 110 
                 111 
                 112 
                 113 
                 114 
               
               
                   
                 115 
                 116 
                 117 
                 118 
                 119 
                 120 
                 121 
                 122 
                 123 
                 124 
                 125 
                 126 
                 127 
                 128 
                 129 
                 130 
                 131 
                 132 
                 133 
                 134 
                 135 
                 136 
                 137 
               
               
                   
                 138 
                 139 
                 140 
                 141 
                 142 
                 143 
                 144 
                 145 
                 146 
                 147 
                 148 
                 149 
                 150 
                 151 
                 152 
                 153 
                 154 
                 155 
                 156 
                 157 
                 158 
                 159 
                 160 
               
               
                   
                 161 
                 162 
                 163 
                 164 
                 165 
                 166 
                 167 
                 168 
                 169 
                 170 
                 171 
                 172 
                 173 
                 174 
                 175 
                 176 
                 177 
                 178 
                 179 
                   
                   
                   
                   
               
               
                 10/15 
                 165 
                 89 
                 27 
                 73 
                 91 
                 86 
                 147 
                 41 
                 175 
                 141 
                 79 
                 144 
                 46 
                 6 
                 53 
                 107 
                 135 
                 104 
                 65 
                 30 
                 1 
                 19 
                 143 
               
               
                   
                 35 
                 176 
                 177 
                 40 
                 178 
                 24 
                 179 
                 169 
                 72 
                 32 
                 42 
                 76 
                 18 
                 57 
                 164 
                 67 
                 124 
                 162 
                 156 
                 163 
                 152 
                 50 
                 172 
               
               
                   
                 114 
                 171 
                 58 
                 82 
                 16 
                 130 
                 48 
                 59 
                 128 
                 98 
                 155 
                 160 
                 60 
                 88 
                 148 
                 92 
                 75 
                 161 
                 8 
                 81 
                 64 
                 34 
                 136 
               
               
                   
                 153 
                 96 
                 154 
                 2 
                 123 
                 11 
                 145 
                 112 
                 84 
                 90 
                 131 
                 119 
                 33 
                 26 
                 99 
                 17 
                 4 
                 43 
                 115 
                 140 
                 0 
                 80 
                 66 
               
               
                   
                 168 
                 52 
                 121 
                 25 
                 49 
                 105 
                 56 
                 12 
                 129 
                 68 
                 146 
                 36 
                 3 
                 51 
                 106 
                 137 
                 122 
                 10 
                 83 
                 170 
                 74 
                 138 
                 28 
               
               
                   
                 139 
                 97 
                 120 
                 9 
                 113 
                 167 
                 166 
                 71 
                 134 
                 102 
                 23 
                 15 
                 29 
                 151 
                 101 
                 93 
                 63 
                 116 
                 127 
                 150 
                 173 
                 62 
                 38 
               
               
                   
                 149 
                 69 
                 31 
                 174 
                 158 
                 61 
                 110 
                 20 
                 77 
                 157 
                 133 
                 142 
                 94 
                 132 
                 21 
                 39 
                 95 
                 87 
                 118 
                 125 
                 44 
                 45 
                 70 
               
               
                   
                 85 
                 111 
                 159 
                 100 
                 7 
                 13 
                 126 
                 54 
                 37 
                 78 
                 109 
                 5 
                 108 
                 103 
                 47 
                 55 
                 14 
                 22 
                 117 
               
               
                   
               
            
           
         
       
     
     In the case of Table 120, Equation 14 may be expressed as X 0 =Y π(0) =Y 165 , X 1 =Y π(1) =Y 89 , X 2 =Y π(2) =Y 27 , . . . , X 178 =Y π(178) =Y 22 , and X 179 =Y π(179) =Y 117 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups in group units by changing the 0 th  group to the 165 th  group, the 1 st  group to the 89 th  group, the 2 nd  group to the 27 th  group, . . . , the 178 th  group to the 22 nd  group, and the 179 th  group to the 117 th  group. 
     In another example, when the length N ldpc  of the LDPC codeword is 64800, the code rate is 12/15, and the modulation method is 256-QAM, π(j) may be defined as in Table 121 presented below: 
     
       
         
           
               
             
               
                 TABLE 121 
               
               
                   
               
               
                 Order of bits group to be block interleaved π(j) (0 ≤ j &lt; 180) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Code 
                 0 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
                 15 
                 16 
                 17 
                 18 
                 19 
                 20 
                 21 
                 22 
               
               
                 Rate 
                 23 
                 24 
                 25 
                 26 
                 27 
                 28 
                 29 
                 30 
                 31 
                 32 
                 33 
                 34 
                 35 
                 36 
                 37 
                 38 
                 39 
                 40 
                 41 
                 42 
                 43 
                 44 
                 45 
               
               
                   
                 46 
                 47 
                 48 
                 49 
                 50 
                 51 
                 52 
                 53 
                 54 
                 55 
                 56 
                 57 
                 58 
                 59 
                 60 
                 61 
                 62 
                 63 
                 64 
                 65 
                 66 
                 67 
                 68 
               
               
                   
                 69 
                 70 
                 71 
                 72 
                 73 
                 74 
                 75 
                 76 
                 77 
                 78 
                 79 
                 80 
                 81 
                 82 
                 83 
                 84 
                 85 
                 86 
                 87 
                 88 
                 89 
                 90 
                 91 
               
               
                   
                 92 
                 93 
                 94 
                 95 
                 96 
                 97 
                 98 
                 99 
                 100 
                 101 
                 102 
                 103 
                 104 
                 105 
                 106 
                 107 
                 108 
                 109 
                 110 
                 111 
                 112 
                 113 
                 114 
               
               
                   
                 115 
                 116 
                 117 
                 118 
                 119 
                 120 
                 121 
                 122 
                 123 
                 124 
                 125 
                 126 
                 127 
                 128 
                 129 
                 130 
                 131 
                 132 
                 133 
                 134 
                 135 
                 136 
                 137 
               
               
                   
                 138 
                 139 
                 140 
                 141 
                 142 
                 143 
                 144 
                 145 
                 146 
                 147 
                 148 
                 149 
                 150 
                 151 
                 152 
                 153 
                 154 
                 155 
                 156 
                 157 
                 158 
                 159 
                 160 
               
               
                   
                 161 
                 162 
                 163 
                 164 
                 165 
                 166 
                 167 
                 168 
                 169 
                 170 
                 171 
                 172 
                 173 
                 174 
                 175 
                 176 
                 177 
                 178 
                 179 
                   
                   
                   
                   
               
               
                 12/15 
                 57 
                 176 
                 49 
                 17 
                 111 
                 169 
                 1 
                 81 
                 177 
                 134 
                 151 
                 23 
                 167 
                 153 
                 9 
                 7 
                 175 
                 121 
                 178 
                 143 
                 113 
                 25 
                 95 
               
               
                   
                 97 
                 87 
                 179 
                 88 
                 125 
                 154 
                 83 
                 34 
                 29 
                 75 
                 59 
                 139 
                 105 
                 45 
                 66 
                 35 
                 144 
                 44 
                 173 
                 10 
                 141 
                 84 
                 42 
               
               
                   
                 148 
                 5 
                 137 
                 163 
                 129 
                 0 
                 77 
                 82 
                 36 
                 171 
                 131 
                 72 
                 19 
                 53 
                 93 
                 96 
                 28 
                 165 
                 146 
                 80 
                 161 
                 99 
                 20 
               
               
                   
                 13 
                 128 
                 33 
                 172 
                 133 
                 67 
                 2 
                 76 
                 149 
                 64 
                 69 
                 115 
                 52 
                 132 
                 37 
                 92 
                 90 
                 51 
                 74 
                 130 
                 147 
                 61 
                 16 
               
               
                   
                 101 
                 4 
                 155 
                 32 
                 100 
                 27 
                 124 
                 122 
                 40 
                 98 
                 152 
                 60 
                 107 
                 112 
                 73 
                 26 
                 3 
                 157 
                 117 
                 24 
                 145 
                 11 
                 58 
               
               
                   
                 160 
                 168 
                 138 
                 89 
                 48 
                 114 
                 68 
                 8 
                 108 
                 43 
                 21 
                 104 
                 123 
                 91 
                 18 
                 56 
                 164 
                 136 
                 85 
                 41 
                 162 
                 12 
                 50 
               
               
                   
                 170 
                 109 
                 65 
                 106 
                 140 
                 120 
                 55 
                 110 
                 158 
                 14 
                 63 
                 174 
                 86 
                 118 
                 39 
                 126 
                 116 
                 142 
                 47 
                 70 
                 62 
                 15 
                 78 
               
               
                   
                 22 
                 46 
                 119 
                 54 
                 30 
                 166 
                 102 
                 6 
                 156 
                 150 
                 94 
                 71 
                 135 
                 127 
                 38 
                 31 
                 159 
                 79 
                 103 
               
               
                   
               
            
           
         
       
     
     In the case of Table  121 , Equation 14 may be expressed as X 0 =Y π(0) =Y 57 , X 1 =Y π(1) =Y 176 , X 2 =Y π(2) =Y 49 , . . . , X 178 =Y π(178) =Y 79 , and X 179 =Y π(179) =Y 103 . Accordingly, the group interleaver  122  may rearrange the order of the plurality of groups in group units by changing the 0 th  group to the 57 th  group, the 1 st  group to the 176 th  group, the 2 nd  group to the 49 th  group, . . . , the 178 th  group to the 79 th  group, and the 179 th  group to the 103 rd  group. 
     As described above, the group interleaver  122  may rearrange the order of the plurality of groups in group units by using Equation 14 and Tables 107 to 121. 
     On the other hand, since the order of the groups constituting the LDPC codeword is rearranged in group units by the group interleaver  122 , and then the groups are block-interleaved by the block interleaver  124 , which will be described below, “Order of bits groups to be block interleaved” is set forth in Tables 107 to 121 in relation to π(j). 
     When the group interleaving is performed in the above-described method, the order of the groups constituting the group-interleaved LDPC codeword is different from that of exemplary embodiment 1. 
     This is because the block-row interleaver  125  is used in the present exemplary embodiment instead of the block interleaver  124  in  FIG.  4   . That is, since the interleaving method used in the block interleaver  124  and the interleaving method used in the block-row interleaver  125  are different from each other, the group interleaver  122  of the present exemplary embodiment rearranges the order of the plurality of groups constituting the LDPC codeword in a method different from that of exemplary embodiment 1. 
     Specifically, the group interleaver  122  may rearrange the order of the plurality of groups in such that that an arrangement unit, in which at least one group including bits to be mapped onto the same modulation symbol is serially arranged in group units, is repeated. 
     That is, the group interleaver  122  may serially arrange one of a plurality of first groups including bits to be mapped onto a first specific location of each modulation symbol, one of a plurality of second groups including bits to be mapped onto a second specific location of each modulation symbol, . . . , one of a plurality of n th  groups including bits to be mapped onto an n th  specific location of each modulation symbol, and may arrange the other groups repeatedly in the same method. 
     The block-row interleaver  125  interleaves the plurality of groups the order of which has been rearranged. In this case, the block-row interleaver  125  may interleave the plurality of groups the order of which has been rearranged in group units by using at least one row including a plurality of columns. This will be explained in detail below with reference to  FIGS.  24  to  26   . 
       FIGS.  24  to  26    are views to illustrate a configuration of a block-row interleaver and an interleaving method according to an exemplary embodiment. 
     First, when N group /m is an integer, the block-row interleaver  125  includes an interleaver  125 - 1  including m number of rows each including M number of columns as shown in  FIG.  24   , and the block-row interleaver  125  may interleave by using N group /m number of interleavers  125 - 1  having the configuration of  FIG.  24   . 
     Herein, N group  is the total number of groups constituting an LDPC codeword. In addition, M is the number of bits included in a single group and may be 360, for example. m may be identical to the number of bits constituting a modulation symbol or may be ½ of the number of bits constituting a modulation symbol. For example, when a non-uniform QAM is used, performance of the bits constituting a modulation symbol is different, and thus, by setting m to be identical to the number of bits constituting a modulation symbol, a single group can be mapped onto a single bit of the modulation symbol. 
     Specifically, the block-row interleaver  125  may interleave by writing each of a plurality of groups constituting an LDPC codeword in each row in the row direction in group units, and reading each column of the plurality of rows in which the plurality of groups are written in group units in the column direction. 
     For example, as shown in  FIG.  24   , the block-row interleaver  125  writes m number of continuous groups from among the plurality of groups in each of the m number of rows of the interleaver  125 - 1  in the row direction, and reads each column of m number of rows in which bits are written in the column direction. In this case, as many interleavers  125 - 1  as the number of groups divided by the number of rows, that is, N group /m, may be used. 
     As described above, when the number of groups constituting an LDPC codeword is an integer multiple of the number of rows, the block-row interleaver  125  may interleave by writing as many groups as the number of rows from among a plurality of groups constituting the LDPC codeword serially. 
     On the other hand, when the number of groups constituting an LDPC codeword is not an integer multiple of the number of rows, the block-row interleaver  125  interleaves by using N number of interleavers (N is an integer greater than or equal to 2) including different number of columns. 
     For example, as shown in  FIGS.  25  and  26   , the block-row interleaver  125  may interleave by using a first interleaver  125 - 2  including m number of rows each including M number of columns, and a second interleaver  125 - 3  including m number of rows each including a×M/m number of columns. Herein, a is N group −└N group /m┘×m, and └N group /m┘ is the largest integer below N group /m. 
     In this case, the first interleaver  125 - 2  may be used as many as └N group /m┘ and one second interleaver  125 - 3  may be used. 
     Specifically, the block-row interleaver  125  may interleave a plurality of groups constituting an LDPC codeword by writing each of └N group /m┘×m number of groups from among the plurality of groups constituting the LDPC codeword in each row in the row direction in group units, and reading each column of the plurality of rows in which └N group /m┘×m number of groups are written in group units in the column direction. 
     For example, as shown in  FIGS.  25  and  26   , the block-row interleaver  125  may write the same m number of continuous groups as the number of rows from among └N group /m┘×m number of groups in each row of the first interleaver  125 - 2  in the row direction, and may read each column of the plurality of rows of the first interleaver  125 - 2  in which m number of groups are written in the column direction. In this case, the first interleaver  125 - 2  having the configuration  FIGS.  25  and  26    may be used as many as └N group /m┘. 
     In addition, in a system where a plurality of antennas are used, m may be the number of bits constituting a modulation method multiplied by the number of antennas. 
     Thereafter, the block-row interleaver  125  may divide bits included in the other groups except the groups written in the first interleaver  125 - 2 , and may write these bits in each row of the second interleaver  125 - 3  in the row direction. In this case, the same number of bits are written in each row of the second interleaver  125 - 3 . In other words, a single bit group may be input in a plurality of columns of the second interleaver  125 - 3 . 
     For example, as shown in  FIG.  25   , the block-row interleaver  125  may write a×M/m number of bits from among the bits included in the other groups except the groups written in the first interleaver  125 - 2  in each of m number of rows of the second interleaver  125 - 3  in the row direction, and may read each column of m number of rows of the second interleaver  125 - 3  in which the bits are written in the column direction. In this case, one second interleaver  125 - 3  having the configuration of  FIG.  25    may be used. 
     However, according to another exemplary embodiment, as shown in  FIG.  26   , the block-row interleaver  125  may write the bits in the first interleaver  125 - 2  in the same method as explained in  FIG.  25   , but may write the bits in the second interleaver  125 - 3  in a method different from that of  FIG.  25   . 
     That is, the block-row interleaver  125  may write the bits in the second interleaver  125 - 3  in the column direction. 
     For example, as shown in  FIG.  26   , the block-row interleaver  125  may write the bits included in the other groups except the groups written in the first interleaver  125 - 2  in each column of m number of rows each including axMlm number of columns of the second interleaver  125 - 3  in the column direction, and may read each column of m number of rows of the second interleaver  125 - 3  in which the bits are written in the column direction. In this case, one second interleaver  125 - 3  having the configuration of  FIG.  26    may be used. 
     In the method shown in  FIG.  26   , the block-row interleaver  125  interleaves by reading in the column direction after writing the bits in the second interleaver in the column direction. Accordingly, the bits included in the groups interleaved by the second interleaver are read in the order they were written and output to the modulator  130 . Accordingly, the bits included in the groups belonging to the second interleaver are not rearranged by the block-row interleaver  125  and may be mapped onto the modulation symbols serially. 
     As described above, the block-row interleaver  125  may interleave the plurality of groups of the LDPC codeword by using the methods described above with reference to  FIGS.  24  to  26   . 
     According to the above-described method, the output of the block-row interleaver  125  may be the same as the output of the block interleaver  124 . Specifically, when the block-row interleaver  125  interleaves as shown in  FIG.  24   , the block-row interleaver  125  may output the same value as that of the block interleaver  124  which interleaves as shown in  FIG.  8   . In addition, when the block-row interleaver  125  interleaves as shown in  FIG.  25   , the block-row interleaver  125  may output the same value as that of the block interleaver  124  which interleaves as shown in  FIG.  9   . In addition, when the block-row interleaver  125  interleaves as shown in  FIG.  26   , the block-row interleaver  125  may output the same value as that of the block interleaver  124  which interleaves as shown in  FIG.  10   . 
     Specifically, when the group interleaver  122  is used based on Equation 11 and the block interleaver  124  is used, and the output groups of the group interleaver  122  are Y i (0≤i&lt;N group ) and when the group interleaver  122  is used based on Equation 13 and the block-row interleaver  125  is used, and the output groups of the group interleaver  122  are Z i (0≤i&lt;N group ), a relationship between the output groups Z i  and Y i  after group interleaving may be expressed as in Equations 15 and 16, and as a result, the same value may be output from the block interleaver  124 : 
       Z i+m×j =Y α×i+j (0≤i&lt;m,0≤j&lt;α)   (15)
 
       Z i =Y i (α×m≤i&lt;N group )   (16),
 
     where α is └N group /m┘ and is the number of groups written in a single column of the first part when the block interleaver  124  is used, and └N group /m┘ is the largest integer below N group /M. Here, m is identical to the number of bits constituting a modulation symbol or half of the bits constituting a modulation symbol. In addition, m is the number of columns of the block interleaver  124  and m is the number of rows of the block-row interleaver  125 . 
     Accordingly, a case in which the group interleaving is performed by the group interleaver  122  based on Equation 11 and then the block interleaving is performed by the block interleaver  124 , and a case in which the group interleaving is performed by the group interleaver  122  based on Equation 12 and then the block interleaving is performed by the block interleaver  124  may have an inverse relationship. 
     In addition, a case in which the group interleaving is performed by the group interleaver  122  based on Equation 13 and then the block-row interleaving is performed by the block-row interleaver  125 , and a case in which the group interleaving is performed by the group interleaver  122  based on Equation 14 and then the block-row interleaving is performed by the block-row interleaver  125  may have an inverse relationship. 
     Accordingly, the modulator  130  may map the bits output from the block-row interleaver  125  onto a modulation symbol in the same method as when the block interleaver  124  is used. 
     The bit interleaving method suggested in the exemplary embodiments is performed by the parity interleaver  121 , the group interleaver  122 , the group twist interleaver  123 , and the block interleaver  124  as shown in  FIG.  4    (the parity interleaver  121  or the group twist interleaver  123  may be omitted according to circumstances). However, this is merely an example and the bit interleaving method is not limited to three modules or four modules described above. 
     For example, when the block interleaver is used and the group interleaving method expressed as in Equation 11 is used, regarding the bit groups X j (0≤j&lt;N group ) defined as in Equation 9 and Equation 10, bits belonging to m number of bit groups, for example, {X π(i) , X π(α+i) , . . . , X π((m-1)×α+i }(0≤i&lt;α), may constitute a single modulation symbol. 
     Herein, α is the number of bit groups constituting the first part of the block interleaver, and α=└N group /m┘. In addition, m is the number of columns of the block interleaver and may be equal to the number of bits constituting the modulation symbol or half of the number of bits constituting the modulation symbol. 
     Therefore, for example, regarding parity-interleaved bits u i , {u π(i)+j , u π(α+i)+j , . . . , u π((m-1)×α+i)+j } (0&lt;i≤m, 0&lt;j≤M) may constitute a single modulation symbol. As described above, there are various methods for constituting a single modulation symbol. 
     In addition, the bit interleaving method suggested in the exemplary embodiments is performed by the parity interleaver  121 , the group interleaver  122 , the group twist interleaver  123 , and the block-row interleaver  125  as shown in  FIG.  23    (the group twist interleaver  123  may be omitted according to circumstances). However, this is merely an example and the bit interleaving method is not limited to three modules or four modules described above. 
     For example, when the block-row interleaver is used and the group interleaving method expressed as in Equation 13 is used, regarding the bit groups X j (0≤j&lt;N group ) defined as in Equation 9 and Equation 10, bits belonging to m number of bit groups, for example, {X π(m×i) , X π(m×i+1) , . . . ,X π(m×i+(m-1)) } (0≤i&lt;α), may constitute a single modulation symbol. 
     Herein, α is the number of bit groups constituting the first part of the block interleaver, and α=└N group /m┘. In addition, m is the number of columns of the block interleaver and may be equal to the number of bits constituting the modulation symbol or half of the number of bits constituting the modulation symbol. 
     Therefore, for example, regarding parity-interleaved bits u i , {u π(m×i)+j , u π(m×i+l)+j , . . . ,u π(m×i+(m-1))+j } (0&lt;i≤m, 0&lt;j≤M) may constitute a single modulation symbol. As described above, there are various methods for constituting a single modulation symbol. 
     Hereinafter, a method for determining π(j) which is a parameter used for group interleaving according to various exemplary embodiments will be explained. 
     Hereinafter, a method for designing the group interleaver  122  of  FIG.  4  or  23    will be explained. 
     Criteria to be considered first are as follows: 
     Criteria 1) A different interleaving method is determined according to a modulation method and a code rate. 
     Criteria 2) A performance characteristic of LDPC codeword bits for each group and a performance characteristic of bits constituting a modulation signal should be considered simultaneously. For example, in the case of an LDPC codeword, the leftmost bits may have high performance, and the leftmost bits constituting the modulation symbol may have high performance. That is, regarding six (6) bits y 0 , y 1 , y 2 , y 3 , y 4 , y 5  constituting the non-uniform 64-QAM, performance P(y i ) for each bit may have a relationship of P(y 0 )&gt;P(y 1 )&gt;P(y 2 )&gt;P(y 3 )&gt;P(y 4 )&gt;P(y 5 ). 
     Therefore, when a code of 64800 is used and the non-uniform 64-QAM (hereinafter, referred to as 64-NUQ) is used, it is determined which bit from among the six (6) bits of 64-NUQ is mapped with 180 LDPC groups, considering characteristics of the LDPC code and the modulation method simultaneously, and a case of the highest estimated performance is determined by using a desnity evolution method. 
     That is, many cases in which 180 groups can be mapped onto the six (6) bits are considered, and a theoretically estimated threshold value for each case is calculated by the density evolution method. Herein, the threshold is an SNR value and an error probability is “0” in an SNR region higher than the threshold value when the LDPC codeword is transmitted. Therefore, when the LDPC codeword is transmitted in a method of the case in which the threshold value is small from among many cases for mapping, high performance can be guaranteed. Designing an interleaver based on the density evolution is a theoretical approach. Therefore, an interleaver should be designed by verifying code performance based on an actually designed parity check matrix and based on cycle distribution, as well as the theoretical approach of the density evolution. 
     Herein, considering the many cases in which 180 groups can be mapped onto the six (6) bits refers to re-grouping the groups into groups related to the rows of the same degree of the parity check matrix and considering how many groups will be mapped onto the six (6) 64 QAM bits. 
     Hereinafter, a case where 256-QAM is used will be described in detail. 
     In case of a LDPC codeword, leftmost bits have superior performance, and the performace of the bits forming a modulation symbol and leftmost bits may be superior. In other words, as for eight bits constituting non-uniform 256-QAM, y 0 , y 1 , y 2 , y 3 , y 4 , y 5 , y 6 , y 7 , the performance of each bit P(y i ) becomes P(y 0 )&gt;P(y 1 )&gt;P(y 2 )&gt;P(y 3 )&gt;P(y 4 )&gt;P(y 5 )&gt;P(y 6 )&gt;P(y 7 ). In addition, if a code rate is 12/15, there are 26 bit groups corresponding to the column group of which degree is 14 in the parity check matrix, 118 bit groups corresponding to the column group of which degree is 3 in the partity check matrix, and 36 bit groups corresponding to the column group of which degree is 2 in the partity check column, among 180 LDPC codeword bit groups. 
     As a result of using a density evolution method, there are 26 bit groups corresponding to the column group of which degree is 14 in the parity check matrix, as for the bit groups X j (0≤j&lt;25) which are defined as shown in Equations 9 and 10, there are 12 groups mapping onto y 1 , 1 group mapped onto y 6 , and 9 groups mapped onto y 7 . 
     In addition, there are 118 bit groups corresponding to the column group of which degree is 3 in the parity check matrix, as for the bit groups X j (26≤j&lt;143) which are defined as shown in Equations 9 and 10, there are 22 groups mapping onto y 0 , 10 groups mapped onto y 1 , 22 groups mapped onto y 2 , 22 groups mapped onto y 3 , 20 groups mapped onto y 4 , and 22 groups mapped onto y 5    
     Further, there are 36 bit groups corresponding to the column group of which degree is 2 in the parity check matrix, as for the bit groups X j (144≤j&lt;180) which are defined as shown in Equations 9 and 10, there are 2 groups mapped onto y 4 , 21 groups mapped onto y 6 , and 13 groups mapped onto y 7 . 
     In this case, the LDPC codeword bit groups which are input and mapped onto the second part of the block interleaver  124  or the second interleaver  125 - 3  of the block-row interlaver  125  may gurantee the most superior performance when there are four bit groups among the bit groups corresponding to the column group of which degree is 14 in the partiy check matrix. 
     The summary of the above-mentioned contents may be represented as shown in the following table 122. 
     
       
         
           
               
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 122 
               
               
                   
               
               
                   
                 y 0   
                 y 1   
                 y 2   
                 y 3   
                 y 4   
                 y 5   
                 y 6   
                 y 7   
                 Sum 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 Degree 14(a) 
                 0 
                 12 
                 0 
                 0 
                 0 
                 0 
                 1 
                 9 
                 22 
               
               
                 Degree 3(b) 
                 22 
                 10 
                 22 
                 22 
                 20 
                 22 
                 0 
                 0 
                 118 
               
               
                 Degree 2(c) 
                 0 
                 0 
                 0 
                 0 
                 2 
                 0 
                 21 
                 13 
                 36 
               
               
                 Sum (a + b + c) 
                 22 
                 22 
                 22 
                 22 
                 22 
                 22 
                 22 
                 22 
               
               
                   
               
            
           
         
       
     
     In other words, in table 41, 22 bit groups {51, 122, 91, 111, 95, 100, 119, 130, 78, 57, 65, 26, 61, 126, 105, 143, 70, 132, 39, 102, 115, 116} are mapped onto y 0 , and 22 bit groups are selected from the bit groups corresponding to the column group of which degree is 3 in the parity check matrix. The selected bit groups optimize actual BER/FER performance. 
     In addition, 22 bit groups {6, 14, 3, 21, 71, 134, 2, 0, 140, 106, 7, 118, 23, 35, 20, 17, 50, 48, 112, 13, 66, 5 } are mapped onto y 1 , and 12 bit groups are selected from the bit groups corresponding to the column group of which degree is 14, and 10 bit groups are selected from the bit groups corresponding to the column group of which degree is 3. 
     Further, 22 bit groups { 75, 42, 129, 107, 30, 45, 137, 114, 37, 87, 53, 85, 101, 141, 120, 99, 88, 117, 64, 28, 135, 138 } are mapped onto y2, and 22 bit groups are selected from the bit groups corresponding to the column group of which degree is 3. 
     In addition, 22 bit groups { 108, 113, 58, 97, 38, 124, 86, 33, 74, 32, 29, 128, 67, 104, 80, 127, 56, 34, 89, 94, 49, 55 } are mapped onto y 3 , and 22 bit groups are selected from the bit groups corresponding to the column group of which degree is 3. 
     Further, 22 bit groups { 93, 136, 68, 62, 54, 40, 81, 103, 121, 76, 44, 84, 96, 123, 154, 98, 82, 142, 46, 169, 131, 72 } are mapped onto y 4 , and 20 bit groups are selected from the bit groups corresponding to the column group of which degree is 3, and 2 bit groups are selected from the bit groups corresponding to the column group of which degree is 2. 
     In addition, 22 bit groups { 47, 69, 125, 31, 83, 36, 59, 90, 79, 52, 133, 60, 92, 139, 110, 27, 73, 43, 77, 109, 63, 41 } are mapped onto y 5 , and 22 bit groups are selected from the bit groups corresponding to the column group of which degree is 3. 
     Further, 22 bit groups { 168, 147, 161, 165, 175, 162, 164, 158, 157, 160, 150, 171, 167, 145, 151, 153, 9, 155, 170, 146, 166, 149 } are mapped onto y 6 , and one bit group is selected from the bit groups corresponding to the column group of which degree is 14, and 21 bit groups are selected from the bit groups corresponding to the column group of which degree is 2. 
     In addition, 22 bit groups { 15, 159, 11, 176, 152, 156, 144, 148, 172, 178, 24, 22, 179, 4, 163, 174, 173, 19, 10, 177, 12, 16 } are mapped onto y 7 , and 9 bit groups are selected from the bit groups corresponding to the column group of which degree is 14, and 13 bit groups are selected from the bit groups corresponding to the column group of which degree is 2. 
     Further, 4 bit groups { 1, 8, 18, 25 } are selected from the bit groups corresponding to the column group of which degree is 14, and the bit groups are input to the second part of the block interleaver or the second interleaver of the block-row interleaver. The bit group X 1  is mapped onto y 0  or y 1 , the bit group X 8  is mapped onto y 2  or y 3 , the bit group X 18  is mapped onto y 4  or y 5 , and the bit group X 25  is mapped onto y6 or y7. 
     In the above-described method, the group interleaver  122  of  FIG.  4  or  23    may be designed. 
       FIG.  27    is a block diagram to illustrate a configuration of a receiver apparatus according to an exemplary embodiment. Referring to  FIG.  27   , the receiver apparatus  2700  includes a demodulator  2710 , a multiplexer  2720 , a deinterleaver  2730  and a decoder  2740 . 
     The demodulator  2710  receives and demodulates a signal transmitted from the transmitter apparatus  100 . Specifically, the demodulator  2710  generates a value corresponding to an LDPC codeword by demodulating the received signal, and outputs the value to the multiplexer  2720 . In this case, the demodulator  2710  may use a demodulation method corresponding to a modulation method used in the transmitter apparatus  100 . 
     The value corresponding to the LDPC codeword may be expressed as a channel value for the received signal. There are various methods for determining the channel value, and for example, a method for determining a Log Likelihood Ratio (LLR) value may be the method for determining the channel value. 
     The LLR value is a log value for a ratio of the probability that a bit transmitted from the transmitter apparatus  100  is 0 and the probability that the bit is 1. In addition, the LLR value may be a bit value which is determined by a hard decision, or may be a representative value which is determined according to a section to which the probability that the bit transmitted from the transmitter apparatus  100  is 0 or 1 belongs. 
     The multiplexer  2720  multiplexes the output value of the demodulator  2710  nd outputs the value to the deinterleaver  2730 . 
     Specifically, the multiplexer  2720  is an element corresponding to a demultiplexer such as the demultiplexer shown in  FIG.  12  or  13    provided in the transmitter apparatus  100 , and performs an operation corresponding to the demultiplexer. Accordingly, when the demultiplexer is omitted from the transmitter apparatus  100 , the multiplexer  2720  may be omitted from the receiver apparatus  2700 . 
     That is, the multiplexer  2720  converts the output value of the demodulator  2710  into cell-to-bit and outputs an LLR value on a bit basis. 
     In this case, when the demultiplexer does not change the order of the LDPC codeword bits as shown in  FIG.  13   , the multiplexer  2720  may output the LLR values serially on the bit basis without changing the order of the LLR values corresponding to the bits of the cell. Alternatively, the multiplexer  2720  may rearrange the order of the LLR values corresponding to the bits of the cell to perform an inverse operation to the demultiplexing operation of the demultiplexer based on Table 50. 
     The deinterleaver  2730  deinterleaves the output value of the multiplexer  2720  and outputs the values to the decoder  2740 . 
     Specifically, the deinterleaver  2730  is an element corresponding to the interleaver  120  of the transmitter apparatus  100  and performs an operation corresponding to the interleaver  120 . That is, the deinterleaver  2730  deinterleaves the LLR value by performing the interleaving operation of the interleaver  120  inversely. 
     In this case, the deinterleaver  2730  may include elements as shown in  FIG.  28  or  29   . 
     First, as shown in  FIG.  28   , the deinterleaver  2730  includes a block deinterleaver  2731 , a group twist deinterleaver  2732 , a group deinterleaver  2733 , and a parity deinterleaver  2734 , according to an exemplary embodiment. 
     The block deinterleaver  2731  deinterleaves the output of the multiplexer  2720  and outputs a value to the group twist deinterleaver  2732 . 
     Specifically, the block deinterleaver  2731  is an element corresponding to the block interleaver  124  provided in the transmitter apparatus  100  and performs the interleaving operation of the block interleaver  124  inversely. 
     That is, the block deinterleaver  2731  deinterleaves by using at least one row formed of a plurality of columns, that is, by writing the LLR value output from the multiplexer  2720  in each row in the row direction and reading each column of the plurality of rows in which the LLR value is written in the column direction. 
     In this case, when the block interleaver  124  interleaves by dividing a column into two parts, the block deinterleaver  2731  may deinterleave by dividing a row into two parts. 
     In addition, when the block interleaver  124  performs writing and reading with respect to a group which does not belong to the first part in the row direction, the block deinterleaver  2731  may deinterleave by writing and reading a value corresponding to the group which does not belong to the first part in the row direction. 
     Hereinafter, the block deinterleaver  2731  will be described with reference to  FIG.  31   . However, this is only an example, and the block deinterleaver  2731  may be realized in other methods. 
     Input LLR v i (0≤i&lt;N ldpc ) is written in row r i , column c i  of the block deinterleaver  2731 . Herein, c i =(i mod N c ), r i =└i/N c ┘. 
     Meanwhile, output LLR q i (0≤i&lt;N c ×N r1 ) is led from row c i , column r i  of the first part of the block deinterleaver  2731 . Herein, r i =(i mod N r1 ), c i =└i/N r1 ┘. 
     In addition, output LLR q i (N c ×N r1 ≤i&lt;N ldpc ) is led from row c i , column r i  of the second part of the block deinterleaver  2731 . Herein, r i =N r1 +{(i-N c ×N r1 ) mod N r2 }, c i =└(1-N c ×N r1 )/N r2 ┘. 
     The group twist deinterleaver  2732  deinterleaves the output value of the block deinterleaver  2731  and outputs the value to the group deinterleaver  2733 . 
     Specifically, the group twist deinterleaver  2732  is an element corresponding to the group twist interleaver  123  provided in the transmitter apparatus  100 , and may perform the interleaving operation of the group twist interleaver  123  inversely. 
     That is, the group twist deinterleaver  2732  may rearrange the LLR values of the same group by changing the order of the LLR values existing in the same group. When the group twist operation is not performed in the transmitter apparatus  100 , the group twist deinterleaver  2732  may be omitted. 
     The group deinterleaver  2733  (or the group-wise deinterleaver) deinterleaves an output value of the group twist deinterleaver  2732  and outputs a value to the parity deinterleaver  2734 . 
     Specifically, the group deinterleaver  2733  is an element corresponding to the group interleaver  122  provided in the transmitter apparatus  100  and may perform the interleaving operation of the group interleaver  122  inversely. 
     That is, the group deinterleaver  2733  may rearrange the order of the plurality of groups in group units. In this case, the group deinterleaver  2733  may rearrange the order of the plurality of groups in group units by applying the interleaving method of Tables 27 to 56 inversely according to a length of the LDPC codeword, a modulation method and a code rate. 
     As described above, it is possible to rearrange the order of column groups in the parity check matrix having the shape of  FIGS.  2  and  3   , and a column group corresponds to a bit group. Accordingly, if the order of column groups is changed in the partiy check matrix, the order of bit groups may also be changed and the group deinterleaver  2733  may rearrange the order of the plurality of groups in group units accordingly. 
     The parity deinterleaver  2734  performs parity deinterleaving with respect to an output value of the group deinterleaver  2733  and outputs a value to the decoder  2740 . 
     Specifically, the parity deinterleaver  2734  is an element corresponding to the parity interleaver  121  provided in the transmitter apparatus  100  and may perform the interleaving operation of the parity interleaver  121  inversely. That is, the parity deinterleaver  2734  may deinterleave the LLR values corresponding to the parity bits from among the LLR values output from the group deinterleaver  2733 . In this case, the parity deinterleaver  2734  may deinterleave the LLR values corresponding to the parity bits in an inverse method of the parity interleaving method of Equation 8. 
     However, the parity deinterleaving is performed only when the transmitter apparatus  100  generates the LDPC codeword using the parity check matrix  200  as shown in  FIG.  2   . The parity deinterleaver  2734  may be omitted when the LDPC codeword is encoded based on the parity check matrix  300  as shown in  FIG.  3   . However, even when the LDPC codeword is generated using the parity check matrix  200  of  FIG.  2   , LDPC decoding may be performed based on the parity check matrix  300  of  FIG.  3   , and in this case, the parity deinterleaver  2734  may be omitted. 
     Although the deinterleaver  2730  of  FIG.  27    includes three (3) or four (4) elements as shown in  FIG.  28   , operations of the elements may be performed by a single element. For example, when bits each of which belongs to each of bit groups Xa, Xb, Xc, and Xd constitute a single modulation symbol, the deinterleaver may deinterleave these bits to locations corresponding to their bit groups based on the received single modulation symbol. 
     For example, if the code rate is 12/15, and the modulation method is 256-QAM, the group deinterleaver  2733  may perform deinterleaving based on Table 41, and in this case, one bit from each of the bit groups X 51 , X 6 , X 75 , X 108 , X 93 , X 47 , X 168 , X 15  constitutes a single modulation symbol. Therefore, the deinterleaver  2730  may perform mapping with the decoded initial value corresponding to the bit groups X 51 , X 6 , X 75 , X 108 , X 93 , X 47 , X 168 , X 15  based on the received modulation symbol. 
     The deinterleaver  2730  may include a block-row deinterleaver  2735 , a group twist deinterleaver  2732 , a group deinterleaver  2733  and a parity deinterleaver  2734 , as shown in  FIG.  29   . In this case, the group twist deinterleaver  2732  and the parity deinterleaver  2734  perform the same functions as in  FIG.  27   , and thus, a redundant explanation is omitted. 
     The block-row deinterleaver  2735  deinterleaves an output value of the multiplexer  2720  and outputs a value to the group twist deinterleaver  2732 . 
     Specifically, the block-row deinterleaver  2735  is an element corresponding to the block-row interleaver  125  provided in the transmitter apparatus  100  and may perform the interleaving operation of the block-row interleaver  125  inversely. 
     That is, the block-row deinterleaver  2735  may deinterleave by using at least one column formed of a plurality of rows, that is, by writing the LLR values output from the multiplexer  2720  in each column in the column direction and reading each row of the plurality of columns in which the LLR value is written in the column direction. 
     However, when the block-row interleaver  125  performs writing and reading with respect to a group which does not belong to the first part in the column direction, the block-row deinterleaver  2735  may deinterleave by writing and reading a value corresponding to the group which does not belong to the first part in the column direction. 
     The group deinterleaver  2733  deinterleaves the output value of the group twist deinterleaver  2732  and outputs the value to the parity deinterleaver  2734 . 
     Specifically, the group deinterleaver  2733  is an element corresponding to the group interleaver  122  provided in the transmitter apparatus  100  and may perform the interleaving operation of the group interleaver  122  inversely. 
     That is, the group deinterleaver  2733  may rearrange the order of the plurality of groups in group units. In this case, the group deinterleaver  2733  may rearrange the order of the plurality of groups in group units by applying the interleaving method of Tables 92 to 121 inversely according to a length of the LDPC codeword, a modulation method and a code rate. 
     Meanwhile, the deinterleaver  2730  of  FIG.  27    may consiste of 3 or 4 elements as shown in  FIG.  29   , but the operation of elements may be performed as one element. For example, if one bit which belongs to each of bit groups Xa, Xb, Xc, Xd consists of a single modulation symboe, the deinterleaver  2730  may perform deinterleaving at a location corresponding to the bit groups based on the received modulation symbol. 
     In addition, when transmission is performed from a transmitter based on a block interleaver, a receiver may operate by determining the deinterleaving order in the deinterleaver  2835  based on Equations 15 and 16. In addition, when transmission is performed based on a block-row interleaver from a transmitter, the receiver may operate by determining the interleaving order in the block deinterleaver  2731  based on Equations 15 and 16. 
     The decoder  2740  may perform LDPC decoding by using the output value of the deinterleaver  2730 . To achieve this, the decoder  2740  may include a separate LDPC decoder (not shown) to perform the LDPC decoding. 
     Specifically, the decoder  2740  is an element corresponding to the encoder  110  of the transmitter apparatus  200  and may correct an error by performing the LDPC decoding by using the LLR value output from the deinterleaver  2730 . 
     For example, the decoder  2740  may perform the LDPC decoding in an iterative decoding method based on a sum-product algorithm. The sum-product algorithm is one example of a message passing algorithm, and the message passing algorithm refers to an algorithm which exchanges messages (e.g., LLR value) through an edge on a bipartite graph, calculates an output message from messages input to variable nodes or check nodes, and updates. 
     The decoder  2740  may use a parity check matrix when performing the LDPC decoding. In this case, an information word submatrix in the parity check matrix is defined as in Tables 4 to 26 according to a code rate and a length of the LDPC codeword, and a parity submatrix may have a dual diagonal configuration. 
     In addition, information on the parity check matrix and information on the code rate, etc. which are used in the LDPC decoding may be pre-stored in the receiver apparatus  2700  or may be provided by the transmitter apparatus  100 . 
       FIG.  30    is a flowchart to illustrate a signal processing method of a transmitter apparatus according to an exemplary embodiment. 
     First, an LDPC codeword is generated by performing LDPC encoding (S 3010 ). In this case, when the LDPC encoding is performed, a parity check matrix including an information word submatrix defined by Tables 4 to 26 and a parity submatrix having a dual diagonal configuration (that is, the parity check matrix as shown in  FIG.  2   ) may be used, or a parity check matrix which is obtained by row and column permutating the parity check matrix of  FIG.  2    based on Equation 4 and Equation 5 (that is, the parity check matrix as shown in  FIG.  3   ). 
     Thereafter, the LDPC codeword is interleaved (S 3020 ). 
     The interleaved LDPC codeword is mapped onto a modulation symbol (S 3030 ). In this case, a bit included in a predetermined group from among a plurality of groups of the LDPC codeword may be mapped onto a predetermined bit of the modulation symbol. 
     Herein, each of the plurality of groups may be formed of 360 bits. 
     In operation S 3020 , parity bits of the LDPC codeword may be interleaved, the parity-interleaved LDPC codeword may be divided into a plurality of groups, the order of the plurality of groups may be rearranged in group units, and the plurality of groups the order of which has been rearranged may be interleaved. 
     Specifically, the order of the plurality of groups may be rearranged in group units based on Equation 11 described above. In this case, π(j) of Equation 11 may be determined based on at least one of a length of the LDPC codeword, a modulation method and a code rate. 
     For example, π(j) may be defined as in Table 37 described above when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 6/15. 
     In another example, π(j) may be defined as in Table 38 described above when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 8/15. 
     In another example, π(j) may be defined as in Table 39 described above when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 10/15. 
     In another example, π(j) may be defined as in Table 40 described above when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 10/15. 
     In another example, π(j) may be defined as in Table 41 described above when the length of the LDPC codeword is 64800, the modulation method is 256-QAM, and the code rate is 12/15. 
     However, these are merely examples. π(j) may be defined as in Tables 27 to 36 according to the length of the LDPC codeword, the modulation method and the code rate. 
     In addition, Equation 12 may be used in rearranging the order of the plurality of groups in group units. In this case, π(j) may be defined as in Tables 42 to 56 described above. 
     The plurality of groups the order of which has been rearranged may be interleaved by writing the plurality of groups in each of the plurality of columns in the column direction in group units, and reading each row of the plurality of columns in which the plurality of groups are written in group units in the row direction. 
     In this case, from among the plurality of groups, at least some group which can be written in each of the plurality of columns in group units is written in each of the plurality of columns serially, and then, the other groups are divided and written in the other areas which remain in each of the plurality of columns after the at least some group has been written in group units. 
     In addition, the order of the plurality of groups is rearranged in group units such that groups including bits to be mapped onto the same location of different modulation symbols are serially arranged to be adjacent to one another, and the predetermined group is written in a predetermined column. 
     In this case, in operation S 3030 , a modulation symbol may be generated by mapping bits output from the predetermined column onto a predetermined bit of each modulation symbol. 
     In operation S 3020 , the interleaving may be performed in other methods in addition to the above-described method. 
     Specifically, the interleaving may be performed by using Equation 13 and Tables 92 to 106 described above, or may be performed by using Equation 14 and Tables 107 to 121 described above. 
     In these cases, the order of the plurality of groups may be rearranged in group units such that an arrangement unit, in which groups including bits to be mapped onto the same modulation symbol are serially arranged in group units, is repeated. 
     When a plurality of groups are interleaved, this interleaving may be performed by writing in each row at least one group including bits to be mapped onto a same modulation symbol from among the plurality of groups the order of which has been rearranged in the row direction, and reading each column of the row in which the at least one group is written in the column direction. 
     A non-transitory computer readable medium, which stores a program for performing the above signal processing methods according to various exemplary embodiments in sequence, may be provided. 
     The non-transitory computer readable medium refers to a medium that stores data semi-permanently rather than storing data for a very short time, such as a register, a cache, and a memory, and is readable by an apparatus. Specifically, the above-described various applications or programs may be stored in a non-transitory computer readable medium such as a compact disc (CD), a digital versatile disk (DVD), a hard disk, a Blu-ray disk, a universal serial bus (USB), a memory card, and a read only memory (ROM), and may be provided. 
     Components, elements or units represented by a block as illustrated in  FIGS.  1 ,  4 ,  12 ,  13 ,  23  and  27 - 29    may be embodied as the various numbers of hardware, software and/or firmware structures that execute respective functions described above, according to exemplary embodiments. For example, these components, elements or units may use a direct circuit structure, such as a memory, processing, logic, a look-up table, etc. that may execute the respective functions through controls of one or more microprocessors or other control apparatuses. These components, elements or units may be specifically embodied by a module, a program, or a part of code, which contains one or more executable instructions for performing specified logic functions. Also, at least one of the above components, elements or units may further include a processor such as a central processing unit (CPU) that performs the respective functions, a microprocessor, or the like. 
     Although a bus is not illustrated in the block diagrams of the transmitter apparatus and the receiver apparatus, communication may be performed between each element of each apparatus via the bus. In addition, each apparatus may further include a processor such as a Central Processing Unit (CPU) or a microprocessor to perform the above-described various operations. 
     The foregoing exemplary embodiments and advantages are merely exemplary and are not to be construed as limiting the present inventive concept. The exemplary embodiments can be readily applied to other types of apparatuses. Also, the description of the exemplary embodiments is intended to be illustrative, and not to limit the scope of the inventive concept, and many alternatives, modifications, and variations will be apparent to those skilled in the art.