# Patent

## Title
Transmitting apparatus and interleaving method thereof

## Abstract

A transmitting apparatus is provided. The transmitting apparatus includes: an encoder configured to generate a low-density parity check (LDPC) codeword by LDPC encoding based on a parity check matrix; 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 is further configured to map a bit included in a predetermined bit group from among a plurality of bit groups constituting the LDPC codeword onto a predetermined bit of the modulation symbol.

## Background
CROSS-REFERENCE TO THE RELATED APPLICATIONS
This is a continuation of U.S. patent application Ser. No. 14/625,795, filed Feb. 19, 2015, which claims priority from U.S. Provisional Application No. 61/941,708 filed on Feb. 19, 2014 and Korean Patent Application No. 10-2015-0024183 filed on Feb. 17, 2015. The entire disclosures of the prior applications are considered part of the disclosure of this continuation application, and are hereby incorporated by reference.


BACKGROUND
1. Field
Apparatuses and methods consistent with exemplary embodiments relate to a transmitting apparatus and an interleaving method thereof, and more particularly, to a transmitting apparatus which processes and transmits data, and an interleaving 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 high quality digital televisions, portable multimedia players and portable broadcasting equipment are increasingly used in recent years, there is an increasing demand for methods for supporting various receiving methods of digital broadcasting services.
In order to meet such demand, standard groups are establishing various standards and are providing a variety of services to satisfy users' needs. Therefore, there is a need for a method for providing improved services to users with high decoding and receiving performance.
SUMMARY
Exemplary embodiments of the inventive concept may overcome the above disadvantages and other disadvantages not described above. However, it is understood that the exemplary embodiment are not required to overcome the disadvantages described above, and may not overcome any of the problems described above.
The exemplary embodiments provide a transmitting apparatus which can map a bit included in a predetermined bit group from among a plurality of bit groups of a low density parity check (LDPC) codeword onto a predetermined bit of a modulation symbol, and transmit the bit, and an interleaving method thereof.
According to an aspect of an exemplary embodiment, there is provided a transmitting apparatus including: an encoder configured to generate an LDPC codeword by LDPC encoding based on a parity check matrix; 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 is further configured to map a bit included in a predetermined bit group from among a plurality of bit groups constituting the LDPC codeword onto a predetermined bit of the modulation symbol.
Each of the plurality of bit groups may be formed of M number of bits. M may be a common divisor of Nldpc and Kldpc and may be determined to satisfy Qldpc=(Nldpc−Kldpc)/M. In this case, Qldpc may be a cyclic shift parameter value regarding columns in a column group of an information word submatrix of the parity check matrix, Nldpc may be a length of the LDPC codeword, and Kldpc may be a length of information word bits of the LDPC codeword.
The interleaver may include: a parity interleaver configured to interleave parity bits of the LDPC codeword; a group interleaver configured to divide the parity-interleaved LDPC codeword by the plurality of bit groups and rearrange an order of the plurality of bit groups in bit group wise; and a block interleaver configured to interleave the plurality of bit groups the order of which is rearranged.
The group interleaver may be configured to rearrange the order of the plurality of bit groups in bit group wise by using the following equation:

Yj=Xπ(j)(0≦j<Ngroup)

where Xj is a jth bit group before the plurality of bit groups are interleaved, Yj is a jth bit group after the plurality of bit groups are interleaved, Ngroup is a total number of the plurality of bit groups, and π(j) is a parameter indicating an interleaving order.

Here, π(j) may be determined based on at least one of a length of the LDPC codeword, a modulation method, and a code rate.
When the LDPC codeword has a length of 64800, the modulation method is 16-QAM, and the code rate is 6/15, π(j) may be defined as in table 11.
When the LDPC codeword has a length of 64800, the modulation method is 16-QAM, and the code rate is 10/15, π(j) may be defined as in table 14.
When the LDPC codeword has a length of 64800, the modulation method is 16-QAM, and the code rate is 12/15, π(j) may be defined as in table 15.
When the LDPC codeword has a length of 64800, the modulation method is 64-QAM, and the code rate is 6/15, π(j) may be defined as in table 17.
When the LDPC codeword has a length of 64800, the modulation method is 64-QAM, and the code rate is 8/15, π(j) may be defined as in table 18.
When the LDPC codeword has a length of 64800, the modulation method is 64-QAM, and the code rate is 12/15, π(j) may be defined as in table 21.
The block interleaver may be configured to interleave by writing the plurality of bit groups in each of a plurality of columns in bit group wise in a column direction, and reading each row of the plurality of columns in which the plurality of bit groups are written in bit group wise in a row direction.
The block interleaver may be configured to serially write, in the plurality of columns, at least some bit groups which are writable in the plurality of columns in bit group wise from among the plurality of bit groups, and then divide and write the other bit groups in an area which remains after the at least some bit groups are written in the plurality of columns in bit group wise.
According to an aspect of another exemplary embodiment, there is provided an interleaving method of a transmitting apparatus, including: generating an LDPC codeword by LDPC encoding based on a parity check matrix; interleaving the LDPC codeword; and mapping the interleaved LDPC codeword onto a modulation symbol, wherein the mapping comprises mapping a bit included in a predetermined bit group from among a plurality of bit groups constituting the LDPC codeword onto a predetermined bit of the modulation symbol.
Each of the plurality of bit groups may be formed of M number of bits, and M may be a common divisor of Nldpc and Kldpc and may be determined to satisfy Qldpc=(Nldpc−Kldpc)/M. In this case, Qldpc may be a cyclic shift parameter value regarding columns in a column group of an information word submatrix of the parity check matrix, Nldpc may be a length of the LDPC codeword, and Kldpc may be a length of information word bits of the LDPC codeword.
The interleaving may include: interleaving parity bits of the LDPC codeword; dividing the parity-interleaved LDPC codeword by the plurality of bit groups and rearranging an order of the plurality of bit groups in bit group wise; and interleaving the plurality of bit groups the order of which is rearranged.
The rearranging in bit group wise may include rearranging the order of the plurality of bit groups in bit group wise by using the following equation:

Yj=Xπ(j)(0≦j<Ngroup),

where Xj is a jth bit group before the plurality of bit groups are interleaved, Yj is a jth bit group after the plurality of bit groups are interleaved, Ngroup is a total number of the plurality of bit groups, and π(j) is a parameter indicating an interleaving order.

Here, π(j) may be determined based on at least one of a length of the LDPC codeword, a modulation method, and a code rate.
When the LDPC codeword has a length of 64800, the modulation method is 16-QAM, and the code rate is 6/15, π(j) may be defined as in table 11.
When the LDPC codeword has a length of 64800, the modulation method is 16-QAM, and the code rate is 10/15, π(j) may be defined as in table 14.
When the LDPC codeword has a length of 64800, the modulation method is 16-QAM, and the code rate is 12/15, π(j) may be defined as in table 15.
When the LDPC codeword has a length of 64800, the modulation method is 64-QAM, and the code rate is 6/15, π(j) may be defined as in table 17.
When the LDPC codeword has a length of 64800, the modulation method is 64-QAM, and the code rate is 8/15, π(j) may be defined as in table 18.
When the LDPC codeword has a length of 64800, the modulation method is 64-QAM, and the code rate is 12/15, π(j) may be defined as in table 21.
The interleaving the plurality of bit groups may include interleaving by writing the plurality of bit groups in each of a plurality of columns in bit group wise in a column direction, and reading each row of the plurality of columns in which the plurality of bit groups are written in bit group wise in a row direction.
The interleaving the plurality of bit groups may include serially writing, in the plurality of columns, at least some bit groups which are writable in the plurality of columns in bit group wise from among the plurality of bit groups, and then dividing and writing the other bit groups in an area which remains after the at least some bit groups are written in the plurality of columns in bit group wise.
According to various exemplary embodiments, improved decoding and receiving performance can be 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 transmitting apparatus, according to an exemplary embodiment;
FIGS. 2 to 4 are views to illustrate a configuration of a parity check matrix, according to exemplary embodiments;
FIG. 5 is a block diagram to illustrate a configuration of an interleaver, according to an exemplary embodiment;
FIGS. 6 to 8 are views to illustrate an interleaving method, according to exemplary embodiments;
FIGS. 9 to 14 are views to illustrate an interleaving method of a block interleaver, according to exemplary embodiments;
FIG. 15 is a view to illustrate an operation of a demultiplexer, according to an exemplary embodiment;
FIGS. 16 and 17 are views to illustrate a method for designing an interleaving pattern, according to exemplary embodiments;
FIG. 18 is a block diagram to illustrate a configuration of a receiving apparatus according to an exemplary embodiment;
FIG. 19 is a block diagram to illustrate a configuration of a deinterleaver, according to an exemplary embodiment;
FIG. 20 is a view to illustrate a deinterleaving method of a block deinterleaver, according to an exemplary embodiment; and
FIG. 21 is a flowchart to illustrate an interleaving method, 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 transmitting apparatus according to an exemplary embodiment. Referring to FIG. 1, the transmitting 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 based on a parity check matrix. To achieve this, the encoder 110 may include an LDPC encoder (not shown) to perform the LDPC encoding.
Specifically, the encoder 110 LDPC-encodes information word (or information) bits to generate the LDPC codeword which is formed of information word bits and parity bits (that is, LDPC parity bits). Here, bits input to the encoder 110 may be used as the information word bits. Also, since an LDPC code 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 Nldpc number of bits, and includes Kldpc number of information word bits and Nparity=Nldpc−Kldpc number of parity bits.
In this case, the encoder 110 may generate the LDPC codeword by performing the LDPC encoding based on the parity check matrix. That is, since the LDPC encoding is a process for generating an LDPC codeword to satisfy H−CT=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 transmitting apparatus 100 may include a memory and may pre-store parity check matrices of various formats.
For example, the transmitting 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 transmitting apparatus 100 may pre-store parity check matrices of other formats in addition to these parity check matrices.
Hereinafter, a parity check matrix according to various exemplary embodiments will be explained in detail with reference to the drawings. In the parity check matrix, elements other than elements having 1 have 0.
For example, the parity check matrix according to an exemplary embodiment may have a configuration of FIG. 2.
Referring to FIG. 2, a parity check matrix 200 is formed of an information word submatrix (or an information submatrix) 210 corresponding to information word bits, and a parity submatrix 220 corresponding to parity bits.
The information word submatrix 210 includes Kldpc number of columns and the parity submatrix 220 includes Nparity=Nldpc−Kldpc 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, Nparity=Nldpc−Kldpc.
In addition, in the parity check matrix 200, Nldpc is a length of an LDPC codeword, Kldpc is a length of information word bits, and Nparity=Nldpc−Kldpc 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 word 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 Kldpc number of columns (that is, 0th column to (Kldpc−1)th column), and follows the following rules:
First, M number of columns from among Kldpc number of columns of the information word submatrix 210 belong to the same group, and Kldpc number of columns is divided into Kldpc/M number of column groups. In each column group, a column is cyclic-shifted from an immediately previous column by Qldpc. That is, Qldpc may be a cyclic shift parameter value regarding columns in a column group of the information word submatrix 210 of the parity check matrix 200.
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 Qldpc 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. Also, M is a common divisor of Nldpc and Kldpc and is determined to satisfy Qldpc=(Nldpc−Kldpc)/M. Here, M and Qldpc are integers and Kldpc/M is also an integer. M and Qldpc may have various values according to a length of the LDPC codeword and a code rate (CR) (or, coding rate).
For example, when M=360 and the length of the LDPC codeword, Nldpc, is 64800, Qldpc may be defined as in table 1 presented below, and, when M=360 and the length Nldpc of the LDPC codeword is 16200, Qldpc may be defined as in table 2 presented below.












TABLE 1







Code Rate
Nldpc
M
Qldpc





















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
Nldpc
M
Qldpc





















5/15
16200
360
30



6/15
16200
360
27



7/15
16200
360
24



8/15
16200
360
21



9/15
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 0th column of the ith column group (i=0, 1, . . . , Kldpc/M−1) is Di (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 0th column of the ith column group is Ri,0(0), Ri,0(1), . . . , Ri,0(D−1), an index Ri,j(k) of a row where kth 1 is located in the jth column in the ith column group is determined by following Equation 1:

Ri,j(k)=Ri(j−1)(k)+Qldpc mod(Nldpc−Kldpc)  (1),

where k=0, 1, 2, . . . Di−1; i=0, 1, . . . , Kldpc/M−1; and j=1, 2, . . . , M−1.

Equation 1 can be expressed as following Equation 2:

Ri,j(k)={Ri,0(k)+(j mod M)×Qldpc} mod(Nldpc−Kldpc)  (2),

where k=0, 1, 2, . . . Di−1; i=0, 1, . . . , Kldpc/M−1; and j=1, 2, . . . , M−1. Since j=1, 2, . . . , M−1, (j mod M) of Equation 2 may be regarded as j.

In the above equations, Ri,j(k) is an index of a row where kth 1 is located in the jth column in the ith column group, Nldpc is a length of an LDPC codeword, Kldpc is a length of information word bits, Di is a degree of columns belonging to the ith column group, M is the number of columns belonging to a single column group, and Qldpc is a size by which each column in the column group is cyclic-shifted.
As a result, referring to these equations, when only Ri,0(k) is known, the index Ri,0(k) of the row where the kth 1 is located in the jth column in the ith column group can be known. Therefore, when the index value of the row where the kth 1 is located in the 0th column of each column group is stored, a position of column and row where 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 ith column group have the same degree Di. 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 Nldpc is 30, Kldpc is 15, and Qldpc is 3, position information of the row where 1 is located in the 0th 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”.

R1,0(1)=1,R1,0(2)=2,R1,0(3)=8,R1,0(4)=10,

R2,0(1)=0,R2,0(2)=9,R2,0(3)=13,

R3,0(1)=0,R3,0(2)=14.  (3)

where Ri,j(k) is an index of a row where kth 1 is located in the jth column in the ith column group.

The weight−1 position sequence like Equation 3 which expresses an index of a row where 1 is located in the 0th 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 value 1 in the parity check matrix, and the ith weight−1 position sequence is expressed by indexes of rows where 1 is located in the 0th column belonging to the ith 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 8 presented below, based on the above descriptions.
Specifically, Tables 4 to 8 show indexes of rows where 1 is located in the 0th column of the ith 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 0th column of each of the plurality of column groups may be defined by Tables 4 to 8.
Herein, the indexes of the rows where 1 is located in the 0th column of the ith 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 Nldpc of the LDPC codeword is 64800, the code rate is 6/15, and M is 360, the indexes of the rows where 1 is located in the 0th column of the ith 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
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 25962



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 Nldpc of the LDPC codeword is 64800, the code rate is 8/15, and M is 360, the indexes of the rows where 1 is located in the 0th column of the ith 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
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 28348 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
2352 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 Nldpc of the LDPC codeword is 64800, the code rate is 10/15, and M is 360, the indexes of rows where 1 exists in the 0th column of the ith column group of the information word submatrix 210 are defined as shown in Table 6 below.








TABLE 6





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









In another example, when the length Nldpc of the LDPC codeword is 64800, the code rate is 10/15, and M is 360, the indexes of rows where 1 exists in the 0th column of the ith column group of the information word submatrix 210 are defined as shown in Table 7 below.








TABLE 7





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 12288 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 Nldpc of the LDPC codeword is 64800, the code rate is 12/15, and M is 360, the indexes of rows where 1 exists in the 0th column of the ith column group of the information word submatrix 210 are defined as shown in Table 8 below.








TABLE 8





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









In the above-described examples, the length of the LDPC codeword is 64800 and the code rate is 6/15, 8/15, 10/15, and 12/15. However, this is merely an example and the position of 1 in the information word submatrix 210 may be defined variously when the length of the LDPC codeword is 16200 or the code rate has different values.
According to an exemplary embodiment, even when the order of numbers in a sequence corresponding to the ith column group of the parity check matrix 200 as shown in the above-described Tables 4 to 8 is changed, the changed parity check matrix is a parity check matrix used for the same code. Therefore, a case in which the order of numbers in the sequence corresponding to the ith column group in Tables 4 to 8 is changed is covered by the inventive concept.
According to an exemplary embodiment, even when the arrangement order of sequences corresponding to each column group is changed in Tables 4 to 8, cycle characteristics on a graph of a 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 8 is changed is also covered by the inventive concept.
In addition, even when a multiple of Qldpc is equally added to all sequences corresponding to a certain column group in Tables 4 to 8, the cycle characteristics on the graph of the code or the algebraic characteristics such as degree distribution are not changed. Therefore, a result of equally adding a multiple of Qldpc to the sequences shown in Tables 4 to 8 is also covered by the inventive concept. However, it should be noted that, when the resulting value obtained by adding the multiple of Qldpc to a given sequence is greater than or equal to (Nldpc−Kldpc), a value obtained by applying a modulo operation for (Nldpc−Kldpc) to the resulting value should be applied instead.
Once positions of the rows where 1 exists in the 0th column of the ith group of the information word submatrix 210 are defined as shown in Tables 4 to 8, 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 0th column are cyclic-shifted by Qldpc in the next column.
For example, in the case of Table 4, in the 0th column of the 0th column group of the information word submatrix 210, 1 exists in the 1606th row, 3402nd row, 4961st row, . . . .
In this case, since Qldpc=(Nldpc−Kldpc)/M=(64800−25920)/360=108, the indexes of the rows where 1 is located in the 1st column of the 0th column group may be 1714(=1606+108), 3510(=3402+108), 5069(=4961+108), . . . , and the indexes of the rows where 1 is located in the 2nd column of the 0th column group may be 1822(=1714+108), 3618(=3510+108), 5177(=5069+108), . . . .
In the above-described method, the indexes of the rows where 1 is located in all rows of each column group may be defined.
The parity submatrix 220 of the parity check matrix 200 shown in FIG. 2 may be defined as follows:
The parity submatrix 220 includes Nldpc−Kldpc number of columns (that is, Kldpcth column to (Nldpc−1)th column), and has a dual diagonal or staircase configuration. Accordingly, the degree of columns except the last column (that is, (Nldpc−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 8, and the parity submatrix 220 of the parity check matrix 200 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.

Qldpc·i+jM·j+i(0≦i<M,0≦j<Qldpc)  (4)

Kldpc+Qldpc·k+lKldpc+M·l+k(0≦k<M,0≦l<Qldpc)  (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 Xth row, i and j satisfying X=Qldpc×i+j are calculated and the Xth row is permutated by assigning the calculated i and j to M×j+i. For example, regarding the 7th row, i and j satisfying 7=2×i+j are 3 and 1, respectively. Therefore, the 7th row is permutated to the 13th 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 Nqc_column=Nldpc/M number of column blocks and Nqc_row=Nparity/M number of row blocks.
Hereinafter, the submatrix of M×M will be explained.
First, the (Nqc_column−1) column block of the 0th 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 0th row and the (M−1)th column are all “0”, and, regarding 0≦i≦(M−2), the (i+1)th row of the ith column is “1” and the other values are “0”.
Second, regarding 0≦i≦(Nldpc−Kldpc)/M−1 in the parity submatrix 320, the ith row block of the (Kldpc/M+i)th column block is configured by a unit matrix IM×M 340. In addition, regarding 0≦i≦(Nldpc−Kldpc)/M−2, the (i+1)th row block of the (Kldpc/M+i)th column block is configured by a unit matrix IM×M 340.
Third, a block 350 constituting the information word submatrix 310 may have a cyclic-shifted format of a cyclic matrix P, Paij, or an added format of the cyclic-shifted matrix Paij 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 aij is 0, the cyclic matrix P, that is, P0 indicates a unit matrix IM×M, and when aij is ∞, P∞ is a zero matrix.
A submatrix existing where the ith row block and the jth column block intersect in the parity check matrix 300 of FIG. 3 may be Paij. 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 Nldpc=M×Nqc_column, and the total number of rows is Nparity=M×Nqc_row. That is, the parity check matrix 300 is formed of Nqc_column number of “column blocks” and Nqc_row number of “row blocks”.
Hereinafter, a method for performing LDPC encoding based on the parity check matrix 200 as shown in FIG. 2 will be explained. An LDPC encoding process when the parity check matrix 200 is defined as shown in Table 4 by way of an example will be explained for the convenience of explanation.
First, when information word bits having a length of Kldpc are [i0, i1, i2, . . . , ikldpc−1], and parity bits having a length of Nldpc−Kldpc are [p0, p1, p2, . . . pNldpc−Kldpc−1], the LDPC encoding is performed by the following process.
Step 1) Parity bits are initialized as ‘0’. That is, p0=p1=p2= . . . =pNldpc−Kldpc−1=0.
Step 2) The 0th information word bit i0 is accumulated in a parity bit having the address of the parity bit defined in the first row (that is, the row of i=0) of table 4 as the index of the parity bit. This may be expressed by Equation 8 presented below:

P1606=P1606⊕i0 

P3402=P3402⊕i0 

P4961=P4961⊕i0 

P6751=P6751⊕i0 

P7132=P7132⊕i0 

P11516=P11516⊕i0 

P12300=P12300⊕i0 

P12482=P12482⊕i0 

P12592=P12592⊕i0 

P13342=P13342⊕i0 

P13764=P13764⊕i0 

P14123=P14123⊕i0 

P21576=P21576⊕i0 

P23946=P23946⊕i0 

P24533=P24533⊕i0 

P25376=P25676⊕i0 

P25667=P25667⊕i0 

P26836=P26836⊕i0 

P31799=P31799⊕i0 

P34173=P34173⊕i0 

P35462=P35462⊕i0 

P36153=P36153⊕i0 

P36740=P36740⊕i0 

P37085=P37085⊕i0 

P37152=P37152⊕i0 

P37468=P37468⊕i0 

P37658=P37658⊕i0  (8)

Herein, i0 is a 0th information word bit, pi is an ith parity bit, and ⊕ is a binary operation. According to the binary operation, 1⊕1 equals 0, 1⊕0 equals 1, 0⊕1 equals 1, 0⊕0 equals 0.
Step 3) The other 359 information word bits im (m=1, 2, . . . , 359) are accumulated in the parity bit. The other information word bits may belong to the same column group as that of i0. In this case, the address of the parity bit may be determined based on Equation 9 presented below:

(x+(m mod 360)×Qldpc)mod(Nldpc−Kldpc)  (9)

Herein, x is an address of a parity bit accumulator corresponding to the information word bit i0, and Qldpc is a size by which each column is cyclic-shifted in the information word submatrix, and may be 108 in the case of table 4. In addition, since m=1, 2, . . . , 359, (m mod 360) in Equation 9 may be regarded as m.
As a result, information word bits im (m=1, 2, . . . , 359) are accumulated in the parity bits having the address of the parity bit calculated based on Equation 9 as the index. For example, an operation as shown in Equation 10 presented below may be performed for the information word bit i1:

P1714=P1714⊕i1 

P3510=P3510⊕i1 

P5069=P5069⊕i1 

P6859=P6859⊕i1 

P7240=P7240⊕i1 

P11624=P11624⊕i1 

P12408=P12408⊕i1 

P12590=P12590⊕i1 

P12700=P12700⊕i1 

P13450=P13450⊕i1 

P13872=P13872⊕i1 

P14231=P14231⊕i1 

P21684=P21684⊕i1 

P24054=P24054⊕i1 

P24641=P24641⊕i1 

P25484=P25484⊕i1 

P25775=P25775⊕i1 

P26944=P26944⊕i1 

P31907=P31907⊕i1 

P34281=P34281⊕i1 

P35570=P35570⊕i1 

P32261=P32261⊕i1 

P36848=P36848⊕i1 

P37193=P37193⊕i1 

P37260=P37260⊕i1 

P37576=P37576⊕i1 

P37766=P37766⊕i1  (10)

Herein, i1 is a 1st information word bit, pi is an ith parity bit, and ⊕ is a binary operation. According to the binary operation, 1⊕1 equals 0, 1⊕0 equals 1, 0⊕1 equals 1, 0⊕0 equals 0.
Step 4) The 360th information word bits i360 is accumulated in a parity bit having the address of the parity bit defined in the 2nd row (that is, the row of i=1) of table 4 as the index of the parity bit.
Step 5) The other 359 information word bits belonging to the same group as that of the information word bit i360 are accumulated in the parity bit. In this case, the address of the parity bit may be determined based on Equation 9. However, in this case, x is the address of the parity bit accumulator corresponding to the information word bit i360.
Step 6) Steps 4 and 5 described above are repeated for all of the column groups of table 4.
Step 7) As a result, a parity bit pi is calculated based on Equation 11 presented below. In this case, i is initialized as 1.

pi=pi⊕pi−1i=1,2, . . . ,Nldpc−Kldpc−1  (11)

In Equation 11, pi is an ith parity bit, Nldpc is a length of an LDPC codeword, Kldpc is a length of an information word of the LDPC codeword, and ⊕ is a binary operation.
As a result, the encoder 110 may calculate the parity bits according to the above-described method.
In another example, a parity check matrix according to an exemplary embodiment may have a configuration as shown in FIG. 4.
Referring to FIG. 4, the parity check matrix 400 may be formed of 5 matrices A, B, C, Z, and D. Hereinafter, the configuration of each matrix will be explained to explain the configuration of the parity check matrix 400.
First, M1, M2, Q1, and Q2, which are parameter values related to the parity check matrix 400 as shown in FIG. 4, may be defined as shown in table 9 presented below according to the length and the code rate of the LDPC codeword.










TABLE 9









Sizes















Rate
Length
M1
M2
Q1
Q2


















1/15
16200
2520
12600
7
35




64800
1080
59400
3
165



2/15
16200
3240
10800
9
30




64800
1800
54360
5
151



3/15
16200
1080
11880
3
33




64800
1800
50040
5
139



4/15
16200
1080
10800
3
30




64800
1800
45720
5
127



5/15
16200
720
10080
2
28




64800
1440
41760
4
116



6/15
16200
1080
8640
3
24




64800
1080
37800
3
105










The matrix A is formed of K number of columns and g number of rows, and the matrix C is formed of K+g number of columns and N−K−g number of rows. Herein, K is a length of information word bits, and N is a length of the LDPC codeword.
Indexes of rows where 1 is located in the 0th column of the ith column group in the matrix A and the matrix C may be defined based on table 10 according to the length and the code rate of the LDPC codeword. In this case, an interval at which a pattern of a column is repeated in each of the matrix A and the matrix C, that is, the number of columns belonging to the same group, may be 360.
For example, when the length N of the LDPC codeword is 64800 and the code rate is 6/15, the indexes of rows where 1 is located in the 0th column of the ith column group in the matrix A and the matrix C are defined as shown in table 10 presented below:








TABLE 10






Index of row where 1 is located in the


i
0th column of the ith column group
















0
71 276 856 6867 12964 17373 18159 26420 28460 28477


1
257 322 672 2533 5316 6578 9087 10231 13845 36497


2
233 765 904 1366 3875 13145 15409 18620 23910 30825


3
100 224 405 12776 13688 14787 16781 23886 29099 31419


4
23 496 891 2512 12589 14074 19392 20339 27658 26634


5
473 712 759 1283 4374 9898 12551 13814 24247 32728


6
511 567 815 11823 17106 17900 19338 22315 24596 26448


7
45 733 836 1923 3727 17468 25746 33806 35995 36657


8
17 487 675 2670 3922 5145 18009 23993 31073 36624


9
72 751 773 1937 17324 28512 30666 30934 31016 31849


10
257 343 594 14041 19141 24914 25864 28809 32055 34753


11
99 241 491 2650 9670 17433 17785 18988 22236 30742


12
198 299 655 6737 8304 10917 16092 19387 20755 37690


13
351 916 926 18151 21708 23216 30321 33578 34052 37949


14
54 332 373 2010 3382 5628 16801 34337 36451 37861


15
139 257 1068 11090 20289 29694 29732 32640 35133 36404


16
45 885 968 2115 4956 5422 5949 17570 26673 32387


17
137 570 619 5006 6099 7979 14429 16650 25443 32789


18
46 282 287 10258 18383 20258 27186 27494 28429 38266


19
445 486 1058 1868 9976 11294 20364 23695 30826 35330


20
134 900 931 12518 14544 17715 19623 21111 33868 34570


21
62 65 586 8020 20270 23831 31041 31965 32224 35189


22
174 290 784 6740 14673 17642 26286 27382 33447 34679


23
332 675 1033 1838 12004 15439 20765 31721 34225 38863


24
527 558 832 3867 6318 8317 10883 13466 18427 25377


25
431 780 1021 1112 2873 7675 13059 17793 20570 20771


26
339 536 1015 5725 6916 10846 14487 21156 28123 32614


27
456 830 1078 7511 11801 12362 12705 17401 28867 34032


28
222 538 989 5593 6022 8302 14008 23445 25127 29022


29
37 393 788 3025 7768 11367 22276 22761 28232 30394


30
234 257 1045 1307 2908 6337 26530 28142 34129 35997


31
35 46 978 9912 9978 12567 17843 24194 34887 35206


32
59 959 967 5027 10847 14657 18859 28075 28214 36325


33
275 477 823 11376 18073 28997 30521 31661 31941 32116


34
185 580 966 11733 12013 12760 13358 19372 32534 35504


35
760 891 1046 11150 20358 21638 29930 31014 33050 34840


36
360 389 1057 5316 5938 14186 16404 32445 34021 35722


37
306 344 679 5224 6674 10305 18753 25583 30585 36943


38
103 171 1016 8780 11741 12144 19470 20955 22495 27377


39
818 832 894 3883 14279 14497 22505 28129 28719 31246


40
215 411 760 5885 25612 28556 32213 32704 35901 36130


41
229 489 1067 2385 8587 20565 23431 28102 30147 32859


42
288 664 980 8138 8531 21676 23787 26708 28798 34490


43
89 552 847 6656 9889 23949 26226 27080 31236 35825


44
66 142 443 3339 3813 7977 14944 15464 19186 25983


45
605 876 931 16682 17669 25800 28220 33432 35738 37382


46
346 423 806 5669 7668 8789 9928 19724 24039 27893


47
48 460 1055 3512 7389 7549 20216 22180 28221 35437


48
187 636 824 1678 4508 13588 19683 21750 30311 33480


49
25 768 935 2856 8187 9052 21850 29941 33217 34293


50
349 624 716 2698 6395 6435 8974 10649 15932 17378


51
336 410 871 3582 9830 10885 13892 18027 19203 36659


52
176 849 1078 17302 19379 27964 28164 28720 32557 35495


53
234 690 1075 9431 9605 9700 10113 11332 12679 24268


54
516 638 733 8851 19871 22740 25791 30152 32659 35568


55
253 830 879 2036 16885 22952 23765 25389 34656 37293


56
94 954 998 2003 3389 6870 7321 29856 31373 34838


57
79 350 983 4853 6252 11932 12058 21631 24552 24876


58
246 647 778 4036 10391 10656 13194 32335 32360 34179


59
149 339 436 6971 8356 8715 11577 22376 28684 31249


60
36 149 220 6936 18408 19192 19288 23063 28411 35311


61
273 683 1042 6327 10011 18041 21704 29097 30791 31425


62
46 138 722 2701 10984 13002 19930 26625 28458 28965


63
12 1009 1040 1990 2930 5302 21215 22625 23011 29288


64
125 241 819 2245 3199 8415 21133 26788 27226 38838


65
45 476 1075 7393 15141 20414 31244 33336 35004 38391


66
432 578 667 1343 10456 11314 11507 23314 27720 34465


67
248 291 556 1971 3989 8992 18000 19998 23932 34652


68
68 694 837 2246 7472 7873 11078 12868 20937 35591


69
272 924 949 2030 4360 6203 9737 19705 19902 38039


70
21 314 979 2311 2632 4109 19527 21920 31413 34277


71
197 253 804 1249 4315 10021 14358 20559 27099 30525


72
9802 16164 17499 22378 22408 22704 26742 29908


73
9064 10904 12305 14057 16156 26000 32613 34536


74
5178 6319 10239 19343 25628 30577 31110 32291









In the above-described example, the length of the LDPC codeword is 64800 and the code rate 6/15. However, this is merely an example and the indexes of rows where 1 is located in the 0th column of the ith column group in the matrix A and the matrix C may be defined variously when the length of the LDPC codeword is 16200 or the code rate has different values.
Hereinafter, positions of rows where 1 exists in the matrix A and the matrix C will be explained with reference to table 10 by way of an example.
Since the length N of the LDPC codeword is 64800 and the code rate is 6/15 in table 10, M1=1080, M2=37800, Q1=3, and Q2=105 in the parity check matrix 400 defined by table 10 with reference to table 9.
Herein, Q1 is a size by which columns of the same column group are cyclic-shifted in the matrix A, and Q2 is a size by which columns of the same column group are cyclic-shifted in the matrix C.
In addition, Q1=M1/L, Q2=M2/L, M1=g, and M2=N−K−g, and L is an interval at which a pattern of a column is repeated in the matrix A and the matrix C, and for example, may be 360.
The index of the row where 1 is located in the matrix A and the matrix C may be determined based on the M1 value.
For example, since M1=1080 in the case of table 10, the positions of the rows where 1 exists in the 0th column of the ith column group in the matrix A may be determined based on values smaller than 1080 from among the index values of table 10, and the positions of the rows where 1 exists in the 0th column of the ith column group in the matrix C may be determined based on values greater than or equal to 1080 from among the index values of table 10.
Specifically, in table 10, the sequence corresponding to the 0th column group is “71, 276, 856, 6867, 12964, 17373, 18159, 26420, 28460, 28477”. Accordingly, in the case of the 0th column of the 0th column group of the matrix A, 1 may be located in the 71st row, 276th row, and 856th row, and, in the case of the 0th column of the 0th column group of the matrix C, 1 may be located in the 6867th row, 12964th row, 17373rd row, 18159th row, 26420th row, 28460th row, and 28477th row.
Once positions of 1 in the 0th column of each column group of the matrix A are defined, positions of rows where 1 exists in another column of each column group may be defined by cyclic-shifting from the previous column by Q1. Once positions of 1 in the 0th column of each column group of the matrix C are defined, position of rows where 1 exists in another column of each column group may be defined by cyclic-shifting from the previous column by Q2.
In the above-described example, in the case of the 0th column of the 0th column group of the matrix A, 1 exists in the 71st row, 276th row, and 856th row. In this case, since Q1=3, the indexes of rows where 1 exists in the 1st column of the 0th column group are 74(=71+3), 279(=276+3), and 859(=856+3), and the index of rows where 1 exists in the 2nd column of the 0th column group are 77(=74+3), 282 (=279+3), and 862(=859+3).
In the case of the 0th column of the 0th column group of the matrix C, 1 exists in the 6867th row, 12964th row, 17373rd row, 18159th row, 26420th row, 28460th row, and 28477th row. In this case, since Q2=105, the index of rows where 1 exists in the 1st column of the 0th column group are 6972(=6867+105), 13069(=12964+105), 17478(=17373+105), 18264(=18159+105), 26525(=26420+105), 28565(=28460+105), 28582(=28477+105), and the indexes of rows where 1 exists in the 2nd column of the 0th column group are 7077(=6972+105), 13174(=13069+105), 17583(=17478+105), 18369(=18264+105), 26630(=26525+105), 28670(=28565+105), 28687(=28582+105).
In this method, the positions of rows where 1 exists in all column groups of the matrix A and the matrix C are defined.
The matrix B may have a dual diagonal configuration, the matrix D may have a diagonal configuration (that is, the matrix D is an identity matrix), and the matrix Z may be a zero matrix.
As a result, the parity check matrix 400 shown in FIG. 4 may be defined by the matrices A, B, C, D, and Z having the above-described configurations.
Hereinafter, a method for performing LDPC encoding based on the parity check matrix 400 shown in FIG. 4 will be explained. An LDPC encoding process when the parity check matrix 400 is defined as shown in Table 10 by way of an example will be explained for the convenience of explanation.
For example, when an information word block S=(s0, s1, . . . , SK−1) is LDPC-encoded, an LDPC codeword Λ=(λ0, λ1, . . . , λN−1)=(s0, s1, . . . , SK−1, p0, p1, . . . , PM1+M2−1) including a parity bit P=(p0, p1, . . . , PM1+M2−1) may be generated.
M1 and M2 indicate the size of the matrix B having the dual diagonal configuration and the size of the matrix C having the diagonal configuration, respectively, and M1=g, M2=N−K−g.
A process of calculating a parity bit is as follows. In the following explanation, the parity check matrix 400 is defined as shown in table 10 by way of an example, for the convenience of explanation.
Step 1) λ and p are initialized as λi=si (i=0, 1, . . . , K−1), pj=0 (j=0, 1, . . . , M1+M2−1).
Step 2) The 0th information word bit λ0 is accumulated in the address of the parity bit defined in the first row (that is, the row of i=0) of table 10. This may be expressed by Equation 12 presented below:

P71=P71⊕λ0 

P276=P276⊕λ0 

P856=P856⊕λ0 

P6867=P6867⊕λ0 

P12964=P12964⊕λ0 

P17373=P17373⊕λ0 

P18159=P18159⊕λ0 

P26420=P26420⊕λ0 

P28460=P28460⊕λ0 

P28477=P28477⊕λ0  (12)

Step 3) Regarding the next L−1 number of information word bits λm (m=1, 2, . . . , L−1), λm is accumulated in the parity bit address calculated based on Equation 13 presented below:

(χ+m×Q1)modM1(if χ<M1)

M1+{(χ−M1+m×Q2)modM2}(if χ≧M1)  (13)

Herein, x is an address of a parity bit accumulator corresponding to the 0th information word bit λ0.
In addition, Q1=M1/L and Q2=M2/L. In addition, since the length N of the LDPC codeword is 64800 and the code rate is 6/15 in table 10, M1=1080, M2=37800, Q1=3, Q2=105, and L=360 with reference to table 9.
Accordingly, an operation as shown in Equation 14 presented below may be performed for the 1st information word bit λ1:

P74=P74⊕λ1 

P279=P279⊕λ1 

P859=P859⊕λ1 

P6972=P6972⊕λ1 

P13069=P13069⊕λ1 

P17478=P17478⊕λ1 

P18264=P18264⊕λ1 

P26525=P26525⊕λ1 

P28565=P28565⊕λ1 

P28582=P28582⊕λ1  (14)

Step 4) Since the same address of the parity bit as in the second row (that is the row of i=1) of table 10 is given to the Lth information word bit λL, in a similar method to the above-described method, the address of the parity bit regarding the next L−1 number of information word bits λm (m=L+1, L+2, . . . , 2L−1) is calculated based on Equation 13. In this case, x is the address of the parity bit accumulator corresponding to the information word bit λL, and may be obtained based on the second row of table 10.
Step 5) The above-described processes are repeated for L number of new information word bits of each group by considering new rows of table 10 as the address of the parity bit accumulator.
Step 6) After the above-described processes are repeated for the codeword bits λ0 to λK−1, values regarding Equation 15 presented below are calculated in sequence from i=1:

Pi=Pi⊕Pi−1(i=1,2, . . . ,M1−1)  (15)

Step 7) Parity bits λK to λK+M1−1 corresponding to the matrix B having the dual diagonal configuration are calculated based on Equation 16 presented below:

λK+L×t+s=pQ1×S+t(0≦s<L,0≦t<Q1)  (16)

Step 8) The address of the parity bit accumulator regarding L number of new codeword bits λK to λK+M1−1 of each group is calculated based on table 10 and Equation 13.
Step 9) After the codeword bits λK to λK+M1−1 are calculated, parity bits λK+M1 to λK+M1+M2−1 corresponding to the matrix C having the diagonal configuration are calculated based on Equation 17 presented below:

λK+M1+L×t+s=pM1+Q2×S+t(0≦s<L,0≦t<Q2)  (17)

As a result, the parity bits may be calculated in the above-described method.
Referring back to FIG. 1, the encoder 110 may perform the LDPC encoding by using various code rates such as 3/15, 4/15, 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, and the parity check matrix is configured as shown in FIGS. 2 to 4.
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 information word bits including the input bits and the BCH parity 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 bit group from among a plurality of bit groups constituting the LDPC codeword (that is, a plurality of groups or a plurality of blocks) is mapped onto a predetermined bit of a modulation symbol. Accordingly, the modulator 130 may map a bit included in a predetermined group from among the plurality of groups of the LDPC codeword onto a predetermined bit of the modulation symbol.
To achieve this, as shown in FIG. 5, the interleaver 120 may include 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 the 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 17 presented below:

ui=ci for 0≦i<Kldpc, and

uKldpc+M·t+s=cKldpc+Qldpc·s+t for 0≦s<M,0≦t<Qldpc  (18)

where M is an interval at which a pattern of a column group is repeated in the information word submatrix 210, that is, the number of columns included in a column group (for example, M=360), and Qldpc 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=(c0, c1, . . . , cNldpc−1), and outputs U=(u0, u1, . . . , uNldpc−1).

The LDPC codeword parity-interleaved in the above-described method may be configured such 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 210 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 ith LDPC codeword bit, ci(i=0, 1, . . . , Nldpc−1) and the ith column of the parity check matrix should be a “0” vector. Accordingly, the ith LDPC codeword bit may be regarded as corresponding to the ith column of the parity check matrix.
In the case of the parity check matrix 200 of FIG. 2, M number of columns in the information word submatrix 210 belong to the same group and the information word submatrix 210 has the same characteristics on the basis of a column group (for example, the columns belonging to the same column group have the same degree distribution and the same cycle characteristic).
In this case, since M number of continuous bits in the information word bits correspond to the same column group of the information word submatrix 210, the information word bits may be formed of M number of continuous bits having 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 M number of continuous bits having the same codeword characteristics.
However, regarding the LDPC codeword encoded based on the parity check matrix 300 of FIG. 3 and the parity check matrix 400 of FIG. 4, parity interleaving may not be performed. In this case, the parity interleaver 121 may be omitted.
The group interleaver 122 may divide the parity-interleaved LDPC codeword into a plurality of bit groups and rearrange the order of the plurality of bit groups in bit group wise (or bit group unit). That is, the group interleaver 122 may interleave the plurality of bit groups in bit group wise.
To achieve this, the group interleaver 122 divides the parity-interleaved LDPC codeword into a plurality of bit groups by using Equation 19 or Equation 20 presented below.




  
    
      
        
          
        
        ⁢
        
          
            X
            j
          
          =
          
            
              
                {
                
                  
                    
                      
                        u
                        k
                      
                      ❘
                      j
                    
                    =
                    
                      ⌊
                      
                        k
                        360
                      
                      ⌋
                    
                  
                  ,
                  
                    0
                    ≤
                    k
                    <
                    
                      N
                      ldpc
                    
                  
                
                }
              
              ⁢
              for
              ⁢
              
                
              
              ⁢
              0
            
            ≤
            j
            <
            
              N
              group
            
          
        
      
    
    
      
        (
        19
        )
      
    
  
  
    
      
        
          X
          j
        
        =
        
          
            
              {
              
                
                  
                    u
                    k
                  
                  ❘
                  
                    
                      360
                      ×
                      j
                    
                    ≤
                    k
                    <
                    
                      360
                      ×
                      
                        (
                        
                          j
                          +
                          1
                        
                        )
                      
                    
                  
                
                ,
                
                  0
                  ≤
                  k
                  <
                  
                    N
                    ldpc
                  
                
              
              }
            
            ⁢
            for
            ⁢
            
              
            
            ⁢
            0
          
          ≤
          j
          <
          
            N
            group
          
        
      
    
    
      
        (
        20
        )
      
    
  




where Ngroup is the total number of bit groups, Xj is the jth bit group, and uk is the kth LDPC codeword bit input to the group interleaver 122. In addition,





  ⌊
  
    k
    360
  
  ⌋




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 bit groups may be as shown in FIG. 6.
Referring to FIG. 6, the LDPC codeword is divided into the plurality of bit groups and each bit group is formed of M number of continuous bits. When M is 360, each of the plurality of bit groups may be formed of 360 bits. Accordingly, the bit groups may be formed of bits corresponding to the column groups of the parity check matrix.
Specifically, since the LDPC codeword is divided by M number of continuous bits, Kldpc number of information word bits are divided into (Kldpc/M) number of bit groups and Nldpc−Kldpc number of parity bits are divided into (Nldpc−Kldpc)/M number of bit groups. Accordingly, the LDPC codeword may be divided into (Nldpc/M) number of bit groups in total.
For example, when M=360 and the length Nldpc of the LDPC codeword is 16200, the number of groups Ngroups constituting the LDPC codeword is 45(=16200/360), and, when M=360 and the length Nldpc of the LDPC codeword is 64800, the number of bit groups Ngroup constituting the LDPC codeword is 180(=64800/360).
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.
In the above-described example, the number of bits constituting each bit group is M. However, this is merely an example and the number of bits constituting each bit group is variable.
For example, the number of bits constituting each bit group may be an aliquot part of M. That is, the number of bits constituting each bit group may be an aliquot part of the number of columns constituting a column group of the information word submatrix of the parity check matrix. In this case, each bit group may be formed of aliquot part of M number of bits. For example, when the number of columns constituting a column group of the information word submatrix is 360, that is, M=360, the group interleaver 122 may divide the LDPC codeword into a plurality of bit groups such that the number of bits constituting each bit group is one of the aliquot parts of 360.
In the following explanation, the number of bits constituting a bit group is M by way of an example, for the convenience of explanation.
Thereafter, the group interleaver 122 interleaves the LDPC codeword in bit group wise. Specifically, the group interleaver 122 may group the LDPC codeword into the plurality of bit groups and rearrange the plurality of bit groups in bit group wise. That is, the group interleaver 122 changes positions of the plurality of bit groups constituting the LDPC codeword and rearranges the order of the plurality of bit groups constituting the LDPC codeword in bit group wise.
Herein, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise such that bit groups including bits mapped onto the same modulation symbol from among the plurality of bit groups are spaced apart from one another at predetermined intervals.
In this case, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by considering at least one of the number of rows and columns of the block interleaver 124, the number of bit groups of the LDPC codeword, and the number of bits included in each bit group, such that bit groups including bits mapped onto the same modulation symbol are spaced apart from one another at predetermined intervals.
To achieve this, the group interleaver 122 may rearrange the order of the plurality of groups in bit group wise by using Equation 21 presented below:

Yj=Xπ(j)(0≦j<Ngroup)  (21)

where Xj is the jth bit group before group interleaving, and Yj is the jth bit 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 modulation method, and a code rate. That is, π(j) denotes a permutation order for group wise interleaving.

Accordingly, Xπ(j) in a π(j)th group before group interleaving, and Equation 21 means that the pre-interleaving π(j)th bit group is interleaved into the jth bit group.
According to an exemplary embodiment, an example of π(j) may be defined as in Tables 11 to 22 presented below.
In this case, π(j) is defined according to a length of an LPDC codeword and a code rate, and a parity check matrix is also defined according to a length of an LDPC codeword and a code rate. Accordingly, when LDPC encoding is performed based on a specific parity check matrix according to a length of an LDPC codeword and a code rate, the LDPC codeword may be interleaved in bit group wise based on π(j) satisfying the corresponding length of the LDPC codeword and code rate.
For example, when the encoder 110 performs LDPC encoding at a code rate of 6/15 to generate an LDPC codeword of a length of 64800, the group interleaver 122 may perform interleaving by using π(j) which is defined according to the length of the LDPC codeword of 16200 and the code rate of 6/15 in tables 11 to 22 presented below.
For example, when the length of the LDPC codeword is 64800, the code rate is 6/15, and the modulation method (or modulation format) is 16-Quadrature Amplitude Modulation (QAM), π(j) may be defined as in table 11 presented below. In particular, table 11 may be applied when LDPC encoding is performed based on the parity check matrix defined by table 4.









TABLE 11









Order of bit groups to be block interleaved



π(j) (0 ≦ j < 180)























j-th block
0
1
2
3
4
5
6
7
8
9
10
11


of
23
24
25
26
27
28
29
30
31
32
33
34


group-
46
47
48
49
50
51
52
53
54
55
56
57


wise
69
70
71
72
73
74
75
76
77
78
79
80


interleaver
92
93
94
95
96
97
98
99
100
101
102
103


output
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


π(j)-th
55
146
83
52
62
176
160
68
53
56
81
97


block of
144
57
67
116
59
70
156
172
65
149
155
82


group-
14
37
54
44
63
43
18
47
7
25
34
29


wise
27
38
48
33
22
49
51
60
46
21
4
3


interleaver
127
101
94
115
105
31
19
177
74
10
145
162


input
78
171
8
142
178
154
85
107
75
12
9
151



150
110
175
166
131
119
103
139
148
157
114
147



11
92
165
84
168
124
169
2
130
167
153
137












Order of bit groups to be block interleaved



π(j) (0 ≦ j < 180)
























j-th block
12
13
14
15
16
17
18
19
20
21
22



of
35
36
37
38
39
40
41
42
43
44
45



group-
58
59
60
61
62
63
64
65
66
67
68



wise
81
82
83
84
85
86
87
88
89
90
91



interleaver
104
105
106
107
108
109
110
111
112
113
114



output
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



π(j)-th
79
113
163
61
58
69
133
108
66
71
86



block of
138
136
141
111
96
170
90
140
64
159
15



group-
30
26
39
16
41
45
36
0
23
32
28



wise
20
13
50
35
24
40
17
42
6
112
93



interleaver
102
120
126
95
73
152
129
174
125
72
128



input
77
117
109
80
106
134
98
1
122
173
161




87
158
121
164
104
89
179
123
118
99
88




143
91
100
5
76
132
135










In the case of Table 11, Equation 21 may be expressed as Y0=Xπ(0)=X55, Y1=Xπ(1)=X146, Y2=Xπ(2)=X83, . . . , Y178=Xπ(178)=X132, and Y179=Xπ(179)=X135. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 55th bit group to the 0th bit group, the 146th bit group to the 1st bit group, the 83rd bit group to the 2nd bit group, . . . , the 132nd bit group to the 178th bit group, and the 135th bit group to the 179th bit group.
In another example, when the length of the LDPC codeword is 64800, the code rate is 8/15, and the modulation method is 16-QAM, π(j) may be defined as in table 12 presented below. In particular, table 12 may be applied when LDPC encoding is performed based on the parity check matrix defined by table 5.









TABLE 12









Order of bit groups to be block interleaved



π(j) (0 ≦ j < 180)























j-th block of
0
1
2
3
4
5
6
7
8
9
10
11


group-wise
23
24
25
26
27
28
29
30
31
32
33
34


interleaver
46
47
48
49
50
51
52
53
54
55
56
57


output
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


π(j)-th block
58
55
111
73
150
87
110
71
172
45
41
113


of
118
38
89
99
85
79
75
83
68
63
40
77


group-wise
92
17
65
60
25
29
23
28
61
59
74
57


interleaver
33
24
91
47
10
52
50
20
31
48
0
39


input
7
5
11
136
35
165
8
3
106
159
138
19



100
142
96
34
161
170
134
156
12
154
174
2



116
130
177
160
129
108
125
147
97
148
162
173



105
126
109
119
101
121
107
131
152
164
175
151












Order of bit groups to be block interleaved



π(j) (0 ≦ j < 180)
























j-th block of
12
13
14
15
16
17
18
19
20
21
22



group-wise
35
36
37
38
39
40
41
42
43
44
45



interleaver
58
59
60
61
62
63
64
65
66
67
68



output
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



π(j)-th block
115
69
120
95
88
178
123
80
66
53
82



of
117
70
81
112
43
94
37
72
46
67
51



group-wise
49
62
78
86
30
93
42
44
90
22
26



interleaver
27
54
15
32
76
21
36
56
84
18
169



input
4
128
168
166
144
149
1
179
141
6
13




9
145
146
14
124
16
102
133
176
132
135




163
122
104
64
143
167
103
140
158
139
98




127
114
137
157
153
171
155










In the case of Table 12, Equation 21 may be expressed as Y0=Xπ(0)=X58, Y1=Xπ(1)=X55, Y2=Xπ(2)=X111, . . . , Y178=Xπ(178)=X171, and Y179=Xπ(179)=X155. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 58th bit group to the 0th bit group, the 55th bit group to the 1st bit group, the 111th bit group to the 2nd bit group, . . . , the 171st bit group to the 178th bit group, and the 155th bit group to the 179th bit group.
In another example, when the length of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 16-QAM, π(j) may be defined as in table 13 presented below. In particular, table 13 may be applied when LDPC encoding is performed based on the parity check matrix defined by table 6.









TABLE 13









Order of bit groups to be block interleaved



π(j) (0 ≦ j < 180)























j-th block of
0
1
2
3
4
5
6
7
8
9
10
11


group-wise
23
24
25
26
27
28
29
30
31
32
33
34


interleaver
46
47
48
49
50
51
52
53
54
55
56
57


output
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


π(j)-th block
74
53
84
109
28
103
99
1
65
41
50
12


of
34
77
81
58
113
44
49
45
33
40
91
17


group-wise
107
86
38
72
31
83
76
61
54
73
102
42


interleaver
56
105
4
119
39
32
70
7
101
114
52
47


input
160
78
18
59
23
64
19
79
134
63
24
20



147
11
161
162
123
138
173
177
100
22
87
137



146
144
139
176
164
155
175
170
125
171
152
154



165
149
136
145
130
120
150
167
126
178
140
133












Order of bit groups to be block interleaved



π(j) (0 ≦ j < 180)
























j-th block of
12
13
14
15
16
17
18
19
20
21
22



group-wise
35
36
37
38
39
40
41
42
43
44
45



interleaver
58
59
60
61
62
63
64
65
66
67
68



output
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



π(j)-th block
95
115
29
48
25
35
89
62
80
71
8



of
94
82
16
46
93
104
36
92
111
57
116



group-wise
108
85
110
97
14
30
60
27
66
118
69



interleaver
15
117
13
55
37
96
88
112
68
106
5



input
156
3
90
2
10
75
21
98
26
9
128




132
6
169
158
0
43
51
67
168
143
131




157
127
124
129
142
135
172
151
153
122
166




121
174
141
148
179
159
163










In the case of Table 13, Equation 21 may be expressed as Y0=Xπ(0)=X74, Y1=Xπ(1)=X53, Y2=Xπ(2)=X84, . . . , Y178=Xπ(178)=X159, and Y179=Xπ(179)=X163. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 74th bit group to the 0th bit group, the 53rd bit group to the 1st bit group, the 84th bit group to the 2nd bit group, . . . , the 159th bit group to the 178th bit group, and the 163rd bit group to the 179th bit group.
In another example, when the length of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 16-QAM, π(j) may be defined as in table 14 presented below. In particular, table 14 may be applied when LDPC encoding is performed based on the parity check matrix defined by table 7.









TABLE 14









Order of bit groups to be block interleaved



π(j) (0 ≦ j < 180)























j-th block of
0
1
2
3
4
5
6
7
8
9
10
11


group-wise
23
24
25
26
27
28
29
30
31
32
33
34


interleaver
46
47
48
49
50
51
52
53
54
55
56
57


output
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


π(j)-th block
68
71
54
19
25
21
102
32
105
29
16
79


of
57
28
76
31
26
96
65
119
114
109
9
125


group-wise
38
77
115
56
87
113
100
75
72
60
47
92


interleaver
104
8
34
0
84
111
35
30
64
55
80
40


input
50
33
7
175
51
131
106
134
88
140
117
132



41
158
5
120
12
52
99
146
144
78
155
128



11
27
160
178
133
142
121
168
173
123
13
15



152
177
137
149
167
1
14
169
124
148
164
130












Order of bit groups to be block interleaved



π(j) (0 ≦ j < 180)
























j-th block of
12
13
14
15
16
17
18
19
20
21
22



group-wise
35
36
37
38
39
40
41
42
43
44
45



interleaver
58
59
60
61
62
63
64
65
66
67
68



output
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



π(j)-th block
53
82
107
91
67
94
85
48
83
58
42



of
81
43
103
93
70
46
89
112
61
45
66



group-wise
36
98
4
59
6
44
20
86
3
73
95



interleaver
97
101
2
69
63
74
62
118
110
159
18



input
147
153
116
161
10
39
126
136
90
37
174




165
141
179
150
157
171
143
108
170
22
49




154
127
139
151
163
172
138
176
145
129
162




17
156
122
23
166
135
24










In the case of Table 14, Equation 21 may be expressed as Y0=Xπ(0)=X68, Y1=Xπ(1)=X71, Y2=Xπ(2)=X54, . . . , Y178=Xπ(178)=X135, and Y179=Xπ(179)=X24. Acordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 68th bit group to the 0th bit group, the 71st bit group to the 1st bit group, the 54th bit group to the 2nd bit group, . . . , the 135th bit group to the 178th bit group, and the 24th bit group to the 179th bit group.
In another example, when the length of the LDPC codeword is 64800, the code rate is 12/15, and the modulation method is 16-QAM, π(j) may be defined as in table 15 presented below. In particular, table 15 may be applied when LDPC encoding is performed based on the parity check matrix defined by table 8.









TABLE 15









Order of bit groups to be block interleaved



π(j) (0 ≦ j < 180)























j-th block of
0
1
2
3
4
5
6
7
8
9
10
11


group-wise
23
24
25
26
27
28
29
30
31
32
33
34


interleaver
46
47
48
49
50
51
52
53
54
55
56
57


output
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


π(j)-th block
120
32
38
113
71
31
65
109
36
106
134
66


of
125
107
44
99
75
64
78
51
95
88
49
60


group-wise
67
92
98
42
77
28
121
87
18
21
93
72


interleaver
85
104
124
52
20
118
34
5
94
41
68
80


input
173
165
175
166
169
174
159
148
158
155
145
178



163
152
146
177
103
160
147
76
172
144
150
132



119
114
117
115
84
57
62
13
47
24
0
7



102
15
55
23
25
11
56
45
58
128
43
135












Order of bit groups to be block interleaved



π(j) (0 ≦ j < 180)
























j-th block of
12
13
14
15
16
17
18
19
20
21
22



group-wise
35
36
37
38
39
40
41
42
43
44
45



interleaver
58
59
60
61
62
63
64
65
66
67
68



output
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



π(j)-th block
29
86
136
108
83
70
79
81
105
48
30



of
54
122
140
137
89
74
129
82
164
59
3



group-wise
2
142
112
9
50
8
90
139
14
97
63



interleaver
110
12
133
131
53
116
123
96
61
111
33



input
126
100
154
156
179
157
46
149
171
37
153




176
168
167
162
170
138
151
161
40
26
130




10
69
19
127
17
16
27
91
4
73
35




1
143
141
6
22
101
39










In the case of Table 15, Equation 21 may be expressed as Y0=Xπ(0)=X120, Y1=Xπ(1)=X32, Y2=Xπ(2)=X38, . . . , Y178=Xπ(178)=X101, and Y179=Xπ(179)=X39. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 120th bit group to the 0th bit group, the 32nd bit group to the 1st bit group, the 38th bit group to the 2nd bit group, . . . , the 101st bit group to the 178th bit group, and the 39th bit group to the 179th bit group.
In another example, when the length of the LDPC codeword is 64800, the code rate is 6/15, and the modulation method is 16-QAM, π(j) may be defined as in table 16 presented below. In particular, table 16 may be applied when LDPC encoding is performed based on the parity check matrix defined by table 10.








TABLE 16






Order of bit groups to be block interleaved π(j) (0 ≦ j < 180)

































j-th block of
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17


group-wise
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35


interleaver
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53


output
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


π(j)-th block of
163
160
138
143
85
108
128
121
91
147
140
142
131
79
109
126
111
162


group-wise
144
75
110
118
97
81
168
157
167
90
103
80
150
125
105
129
146
141


interleaver
152
164
130
114
123
134
107
96
173
20
44
64
19
6
8
113
45
116


input
11
5
63
66
84
39
10
69
88
135
25
55
54
58
61
33
57
59



3
16
18
155
21
56
36
29
48
62
154
43
51
34
0
27
12
24



17
42
145
1
38
2
28
112
31
60
179
13
30
50
95
14
15
9



26
71
132
40
104
89
106
46
4
166
47
161
174
49
23
41
139
68



52
99
146
115
101
127
22
158
7
169
153
122
117
159
93
100
82
151



171
67
94
136
72
73
74
70
86
76
137
35
37
32
177
87
170
178



77
175
120
165
53
172
133
176
65
83
124
92
78
119
102
156
148
98









In the case of Table 16, Equation 21 may be expressed as Y0=Xπ(0)=X163, Y1=Xπ(1)=X160, Y2=Xπ(2)=X138, . . . , Y178=Xπ(178)=X148, and Y179=Xπ(179)=X98. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 163rd bit group to the 0th bit group, the 160th bit group to the 1st bit group, the 138th bit group to the 2nd bit group, . . . , the 148th bit group to the 178th bit group, and the 98th bit group to the 179th bit group.
In another example, when the length of the LDPC codeword is 64800, the code rate is 6/15, and the modulation method is 64-QAM, π(j) may be defined as in table 17 presented below. In particular, table 17 may be applied when LDPC encoding is performed based on the parity check matrix defined by table 4.








TABLE 17






Order of bit groups to be block interleaved π(j) (0 ≦ j < 180)

































j-th block of
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17


group-wise
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35


interleaver
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53


output
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


π(j)-th block of
29
17
38
37
27
43
31
35
16
46
44
9
23
1
34
45
14
18


group-wise
156
19
22
40
50
24
56
49
26
42
69
47
59
61
66
52
64
65


interleaver
67
54
170
68
132
51
70
41
21
5
160
7
13
55
62
53
63
58


input
3
167
71
57
151
60
36
25
74
39
32
72
85
86
107
113
48
88



2
129
137
20
73
166
75
77
142
174
15
149
28
145
92
169
30
133



163
119
82
176
152
134
139
148
164
99
173
104
83
106
112
135
153
0



128
144
98
171
94
97
143
110
118
127
84
79
108
126
131
93
111
91



4
125
162
157
158
109
140
123
154
150
80
11
12
146
96
81
165
8



89
138
105
141
103
6
100
161
172
78
101
115
179
147
116
136
122
87



33
130
124
175
120
90
102
10
114
159
76
177
178
121
168
95
117
155









In the case of Table 17, Equation 21 may be expressed as Y0=Xπ(0)=X29, Y1=Xπ(1)=X17, Y2=Xπ(2)=X38, . . . , Y178=Xπ(178)=X117, and Y179πXπ(179)=X155. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 29th bit group to the 0th bit group, the 17th bit group to the 1st bit group, the 38th bit group to the 2nd bit group, . . . , the 117th bit group to the 178th bit group, and the 155th bit group to the 179th bit group.
In another example, when the length of the LDPC codeword is 64800, the code rate is 8/15, and the modulation method is 64-QAM, π(j) may be defined as in table 18 presented below. In particular, table 18 may be applied when LDPC encoding is performed based on the parity check matrix defined by table 5.








TABLE 18






Order of bit groups to be block interleaved π(j) (0 ≦ j < 180)

































j-th block of
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17


group-wise
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35


interleaver
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53


output
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


π(j)-th block of
86
71
51
48
89
94
46
81
67
49
80
37
55
61
36
57
52
92


group-wise
60
82
76
72
44
42
91
62
50
90
40
78
53
58
47
85
70
4


interleaver
69
43
54
84
93
38
8
64
6
18
77
95
66
59
83
73
17
87


input
3
75
65
88
79
14
151
117
32
22
123
30
33
162
144
9
121
108



139
142
24
34
20
157
159
138
143
29
140
163
150
175
114
31
12
35



145
28
27
26
16
98
102
103
133
161
21
25
107
153
45
156
23
125



141
56
166
5
1
170
119
68
134
41
74
179
2
129
169
101
99
109



127
168
176
11
0
122
110
113
146
132
165
19
13
39
7
164
106
172



154
149
10
173
131
167
63
147
155
100
171
158
160
15
178
148
152
104



124
177
97
130
118
137
111
126
120
105
115
136
112
96
135
116
174
128









In the case of Table 18, Equation 21 may be expressed as Y0=Xπ(0)=X86, Y1=Xπ(1)=X71, Y2=Xπ(2)=X51, . . . , Y178=Xπ(178)=X174, and Y179=Xπ(179)=X128. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 86th bit group to the 0th bit group, the 71st bit group to the 1st bit group, the 51st bit group to the 2nd bit group, . . . , the 174th bit group to the 178th bit group, and the 128th bit group to the 179th bit group.
In another example, when the length of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 64-QAM, π(j) may be defined as in table 19 presented below. In particular, table 19 may be applied when LDPC encoding is performed based on the parity check matrix defined by table 6.








TABLE 19






Order of bit groups to be block interleaved π(j) (0 ≦ j < 180)

































j-th block of
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17


group-wise
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35


interleaver
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53


output
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


π(j)-th block of
73
36
21
53
37
78
102
119
82
75
40
77
104
59
58
41
18
46


group-wise
45
93
30
49
114
79
1
97
66
33
115
112
99
107
26
39
23
70


interleaver
89
116
62
55
50
96
108
57
51
86
28
88
52
69
74
113
84
109


input
65
101
8
111
61
44
105
83
35
130
27
106
90
92
6
54
7
87



38
31
85
63
117
67
110
72
94
32
118
47
48
68
76
60
91
64



17
142
156
24
12
42
56
4
170
172
5
16
34
152
29
11
20
136



158
134
43
98
141
160
95
0
154
81
169
71
171
162
139
175
129
25



167
9
131
123
165
140
124
178
10
14
145
164
3
15
143
173
176
22



161
153
2
19
151
150
174
144
157
163
122
147
132
137
128
159
155
127



138
103
100
120
146
168
166
148
13
125
177
133
126
121
179
80
149
135









In the case of Table 19, Equation 21 may be expressed as Y0=Xπ(0)=X73, Y1=Xπ(1)=X36, Y2=Xπ(2)=X21, . . . , Y178=Xπ(178)=X149, and Y179=Xπ(179)=X135. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 73rd bit group to the 0th bit group, the 36th bit group to the 1st bit group, the 21st bit group to the 2nd bit group, . . . , the 149th bit group to the 178th bit group, and the 135th bit group to the 179th bit group.
In another example, when the length of the LDPC codeword is 64800, the code rate is 10/15, and the modulation method is 64-QAM, π(j) may be defined as in table 20 presented below. In particular, table 20 may be applied when LDPC encoding is performed based on the parity check matrix defined by table 7.








TABLE 20






Order of bit groups to be block interleaved π(j) (0 ≦ j < 180)

































j-th block of
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17


group-wise
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35


interleaver
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53


output
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


π(j)-th block of
113
115
47
111
35
84
34
83
31
88
109
86
46
177
103
57
77
73


group-wise
95
150
52
107
98
43
66
55
56
49
72
118
78
27
39
97
40
6


interleaver
75
79
68
93
59
119
20
10
51
108
65
114
69
1
116
7
30
101


input
50
14
38
99
71
96
128
82
92
166
60
178
117
45
157
48
129
67



37
94
89
53
100
54
91
173
169
63
149
104
70
61
102
110
124
80



29
18
19
24
0
36
22
58
62
33
64
42
28
8
26
112
85
74



13
21
105
44
5
87
76
106
25
81
90
11
3
168
121
153
140
152



135
174
23
139
12
16
9
146
164
142
15
147
2
161
120
133
155
123



158
167
154
148
137
160
145
159
4
17
126
143
151
162
156
172
171
131



41
179
132
136
32
175
163
165
141
138
122
127
125
144
170
134
130
176









In the case of Table 20, Equation 21 may be expressed as Y0=Xπ(0)=X113, Y1=Xπ(1)=X115, Y2=Xπ(2)=X47, . . . , Y178=Xπ(178)=X130, and Y179=Xπ(179)=X176. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 113th bit group to the 0th bit group, the 115th bit group to the 1st bit group, the 47th bit group to the 2nd bit group, . . . , the 130th bit group to the 178th bit group, and the 176th bit group to the 179th bit group.
In another example, when the length of the LDPC codeword is 64800, the code rate is 12/15, and the modulation method is 64-QAM, π(j) may be defined as in table 21 presented below. In particular, table 21 may be applied when LDPC encoding is performed based on the parity check matrix defined by table 8.








TABLE 21






Order of bit groups to be block interleaved π(j) (0 ≦ j < 180)

































j-th block of
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17


group-wise
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35


interleaver
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53


output
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


π(j)th block of
83
93
94
47
55
40
38
77
110
124
87
61
102
76
33
35
92
59


group-wise
74
11
138
72
67
37
10
95
139
131
44
57
97
53
142
0
136
9


interleaver
143
86
100
21
15
75
62
19
65
129
101
79
22
68
73
23
18
81


input
98
112
8
128
103
25
43
126
54
90
28
109
46
91
41
82
113
134



52
105
78
27
135
96
56
140
64
66
89
34
120
108
63
45
69
121



88
39
29
133
106
117
127
32
42
58
71
118
51
84
85
80
104
132



111
30
26
48
50
31
141
116
123
114
70
107
178
145
173
36
144
130



176
171
175
125
99
162
159
20
164
115
169
172
165
161
151
119
122
152



157
4
137
148
153
170
154
166
13
150
16
167
174
163
49
6
168
147



146
1
149
158
179
12
5
160
177
60
24
156
7
155
17
3
2
14









In the case of Table 21, Equation 21 may be expressed as Y0=Xπ(0)=X83, Y1=Xπ(1)=X93, Y2=Xπ(2)=X94, . . . , Y178=Xπ(178)=X2, and Y179=Xπ(179)=X14. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 83rd bit group to the 0th bit group, the 93rd bit group to the 1st bit group, the 94th bit group to the 2nd bit group, . . . , the 2nd bit group to the 178th bit group, and the 14th bit group to the 179th bit group.
In another example, when the length of the LDPC codeword is 64800, the code rate is 6/15, and the modulation method is 64-QAM, π(j) may be defined as in table 22 presented below. In particular, table 22 may be applied when LDPC encoding is performed based on the parity check matrix defined by table 10.








TABLE 22






Order of bit groups to be block interleaved π(j) (0 ≦ j < 180)

































j-th block of
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17


group-wise
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35


interleaver
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53


output
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


π(j)th block of
175
177
173
125
89
37
165
85
82
34
17
162
92
161
88
137
149
115


group-wise
113
172
123
43
4
152
76
143
98
139
20
150
13
52
50
25
24
153


interleaver
133
122
55
10
83
18
27
51
15
8
46
164
155
81
102
53
11
21


input
47
61
7
126
1
57
26
148
56
171
22
166
101
67
119
178
121
118



96
80
99
68
167
90
62
147
36
140
103
5
87
157
176
59
66
3



64
91
29
71
107
77
111
42
35
38
23
100
45
69
40
129
33
163



49
112
145
54
105
117
0
108
94
79
12
19
106
60
39
104
28
2



73
97
75
154
84
58
144
95
136
16
170
44
151
70
63
48
128
114



41
174
116
9
86
6
141
109
78
127
142
159
65
130
124
93
30
110



32
160
135
132
134
14
146
74
120
158
138
179
169
156
131
168
31
72









In the case of Table 22, Equation 21 may be expressed as Y0=Xπ(0)=X175, Y1=Xπ(1)=X177, Y2=Xπ(2)=X173, . . . , Y178=Xπ(178)=X31, and Y179=Xπ(179)=X72. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 175th bit group to the 0th bit group, the 177th bit group to the 1st bit group, the 173rd bit group to the 2nd bit group, . . . , the 31st bit group to the 178th bit group, and the 72nd bit group to the 179th bit group.
In the above-described examples, the length of the LDPC codeword is 64800 and the code rate is 6/15, 8/15, 10/15, and 12/15. However, this is merely an example and the interleaving pattern may be defined variously when the length of the LDPC codeword is 16200 or the code rate has different values.
As described above, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by using Equation 21 and Tables 11 to 22.
“j-th block of Group-wise Interleaver output” in tables 11 to 22 indicates the j-th bit group output from the group interleaver 122 after interleaving, and “π(j)-th block of Group-wise Interleaver input” indicates the π(j)-th bit group input to the group interleaver 122.
In addition, since the order of the bit groups constituting the LDPC codeword is rearranged by the group interleaver 122 in bit group wise, and then the bit groups are block-interleaved by the block interleaver 124, which will be described below, “Order of bit groups to be block interleaved” is set forth in Tables 11 to 22 in relation to π(j).
The LDPC codeword which is group-interleaved in the above-described method is illustrated in FIG. 7. Comparing the LDPC codeword of FIG. 7 and the LDPC codeword of FIG. 6 before group interleaving, it can be seen that the order of the plurality of bit groups constituting the LDPC codeword is rearranged.
That is, as shown in FIGS. 6 and 7, the groups of the LDPC codeword are arranged in order of bit group X0, bit group X1, . . . , bit group XNgroup-1 before being group-interleaved, and are arranged in an order of bit group Y0, bit group Y1, . . . , bit group YNgroup-1 after being group-interleaved. In this case, the order of arranging the bit groups by the group interleaving may be determined based on Tables 11 to 22.
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 bit group by changing the order of the bits in the same bit group.
In this case, the group twist interleaver 123 may rearrange the order of the bits in the same bit group by cyclic-shifting a predetermined number of bits from among the bits in the same bit group.
For example, as shown in FIG. 8, the group twist interleaver 123 may cyclic-shift bits included in the bit group Y1 to the right by 1 bit. In this case, the bits located in the 0th position, the 1st position, the 2nd position, . . . , the 358th position, and the 359th position in the bit group Y1 as shown in FIG. 8 are cyclic-shifted to the right by 1 bit. As a result, the bit located in the 359th position before being cyclic-shifted is located in the front of the bit group Y1 and the bits located in the 0th position, the 1st position, the 2nd position, . . . , the 358th 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 bit group by cyclic-shifting a different number of bits in each bit group.
For example, the group twist interleaver 123 may cyclic-shift the bits included in the bit group Y1 to the right by 1 bit, and may cyclic-shift the bits included in the bit group Y2 to the right by 3 bits.
However, the above-described 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 bit group and does not change the order of the bit groups. Therefore, the group twist interleaver 123 may be placed before the group interleaver 122.
The block interleaver 124 interleaves the plurality of bit groups the order of which has been rearranged. Specifically, the block interleaver 124 may interleave the plurality of bit groups the order of which has been rearranged by the group interleaver 122 in bit group wise (or bits group unit). The block interleaver 124 is formed of a plurality of columns each including a plurality of rows and may interleave by dividing the plurality of rearranged bit groups based on a modulation order determined according to a modulation method.
In this case, the block interleaver 124 may interleave the plurality of bit groups the order of which has been rearranged by the group interleaver 122 in bit group wise. Specifically, the block interleaver 124 may interleave by dividing the plurality of rearranged bit groups according to a modulation order by using a first part and a second part.
Specifically, the block interleaver 124 interleaves by dividing each of the plurality of columns into a first part and a second part, writing the plurality of bit groups in the plurality of columns of the first part serially in bit group wise, dividing the bits of the other bit groups into groups (or sub bit groups) each including a predetermined number of bits based on the number of columns, and writing the sub bit groups in the plurality of columns of the second part serially.
Herein, the number of bit groups which are interleaved in bit group wise may be determined by at least one of the number of rows and columns constituting the block interleaver 124, the number of bit groups and the number of bits included in each bit group. In other words, the block interleaver 124 may determine the bit groups which are to be interleaved in bit group wise considering at least one of the number of rows and columns constituting the block interleaver 124, the number of bit groups and the number of bits included in each bit group, interleave the corresponding bit groups in bit group wise, and divide bits of the other bit groups into sub bit groups and interleave the sub bit groups. For example, the block interleaver 124 may interleave at least part of the plurality of bit groups in bit group wise using the first part, and divide bits of the other bit groups into sub bit groups and interleave the sub bit groups using the second part.
Meanwhile, interleaving bit groups in bit group wise means that the bits included in the same bit group are written in the same column. In other words, the block interleaver 124, in case of bit groups which are interleaved in bit group wise, may not divide the bits included in the same bit groups and write the bits in the same column, and in case of bit groups which are not interleaved in bit group wise, may divide the bits in the bit groups and write the bits in different columns.
Accordingly, the number of rows constituting the first part is a multiple of the number of bits included in one bit group (for example, 360), and the number of rows constituting the second part may be less than the number of bits included in one bit group.
In addition, in all bit groups interleaved by the first part, the bits included in the same bit group are written and interleaved in the same column of the first part, and in at least one group interleaved by the second part, the bits are divided and written in at least two columns of the second part.
The specific interleaving method will be described later.
Meanwhile, the group twist interleaver 123 changes only the order of bits in the bit group and does not change the order of bit groups by interleaving. Accordingly, the order of the bit groups to be block-interleaved by the block interleaver 124, that is, the order of the bit groups to be input to the block interleaver 124, may be determined by the group interleaver 122. Specifically, the order of the bit groups to be block-interleaved by the block interleaver 124 may be determined by π(j) defined in Tables 11 to 22.
As described above, the block interleaver 124 may interleave the plurality of bit groups the order of which has been rearranged in bit group wise by using the plurality of columns each including the plurality of rows.
In this case, the block interleaver 124 may interleave the LDPC codeword by dividing the plurality of columns into at least two parts. For example, the block interleaver 124 may divide each of the plurality of columns into the first part and the second part and interleave the plurality of bit groups constituting the LDPC codeword.
In this case, the block interleaver 124 may divide each of the plurality of columns into N number of parts (N is an integer greater than or equal to 2) according to whether the number of bit groups constituting the LDPC codeword is an integer multiple of the number of columns constituting the block interleaver 124, and may perform interleaving.
When the number of bit groups constituting the LDPC codeword is an integer multiple of the number of columns constituting the block interleaver 124, the block interleaver 124 may interleave the plurality of bit groups constituting the LDPC codeword in bit group wise without dividing each of the plurality of columns into parts.
Specifically, the block interleaver 124 may interleave by writing the plurality of bit groups of the LDPC codeword on each of the columns in bit group wise in a column direction, and reading each row of the plurality of columns in which the plurality of bit groups are written in bit group wise in a row direction.
In this case, the block interleaver 124 may interleave by writing bits included in a predetermined number of bit groups, which corresponds to a quotient obtained by dividing the number of bit groups of the LDPC codeword by the number of columns of the block interleaver 124, on each of the plurality of columns serially in a column direction, and reading each row of the plurality of columns in which the bits are written in a row direction.
Hereinafter, the group located in the jth position after being interleaved by the group interleaver 122 will be referred to as group Yj.
For example, it is assumed that the block interleaver 124 is formed of C number of columns each including R1 number of rows. In addition, it is assumed that the LDPC codeword is formed of Ngroup number of bit groups and the number of bit groups Ngroup is a multiple of C.
In this case, when the quotient obtained by dividing Ngroup number of bit groups constituting the LDPC codeword by C number of columns constituting the block interleaver 124 is A (=Ngroup/C) (A is an integer greater than 0), the block interleaver 124 may interleave by writing A (=Ngroup/C) number of bit groups on each column serially in a column direction and reading bits written on each column in a row direction.
For example, as shown in FIG. 9, the block interleaver 124 writes bits included in bit group Y0, bit group Y1, . . . , bit group YA−1 in the 1st column from the 1st row to the R1th row, writes bits included in bit group YA, bit group YA+1, . . . , bit group Y2A−1 in the 2nd column from the 1st row to the R1th row, . . . , and writes bits included in bit group YCA-A, bit group YCA-A+1, . . . , bit group YCA-1 in the column C from the 1st row to the R1th row. The block interleaver 124 may read the bits written in each row of the plurality of columns in a row direction.
Accordingly, the block interleaver 124 interleaves all bit groups constituting the LDPC codeword in bit group wise.
However, when the number of bit groups of the LDPC codeword is not an integer multiple of the number of columns of the block interleaver 124, the block interleaver 124 may divide each column into 2 parts and interleave a part of the plurality of bit groups of the LDPC codeword in bit group wise, and divide bits of the other bit groups into sub bit groups and interleave the sub bit groups. In this case, the bits included in the other bit groups, that is, the bits included in the number of groups which correspond to the remainder when the number of bit groups constituting the LDPC codeword is divided by the number of columns are not interleaved in bit group wise, but interleaved by being divided according to the number of columns.
Specifically, the block interleaver 124 may interleave the LDPC codeword by dividing each of the plurality of columns into two parts.
In this case, the block interleaver 124 may divide the plurality of columns into the first part and the second part based on at least one of the number of columns of the block interleaver 124, the number of bit groups of the LDPC codeword, and the number of bits of bit groups.
Here, each of the plurality of bit groups may be formed of 360 bits. In addition, the number of bit groups of the LDPC codeword is determined based on the length of the LDPC codeword and the number of bits included in the bit group. For example, when an LDPC codeword in the length of 16200 is divided such that each bit group has 360 bits, the LDPC codeword is divided into 45 bit groups. Alternatively, when an LDPC codeword in the length of 64800 is divided such that each bit group has 360 bits, the LDPC codeword may be divided into 180 bit groups. Further, the number of columns constituting the block interleaver 124 may be determined according to a modulation method. This will be explained in detail below.
Accordingly, the number of rows constituting each of the first part and the second part may be determined based on the number of columns constituting the block interleaver 124, the number of bit groups constituting the LDPC codeword, and the number of bits constituting each of the plurality of bit groups.
Specifically, in each of the plurality of columns, the first part may be formed of as many rows as the number of bits included in at least one bit group which can be written in each column in bit group wise from among the plurality of bit groups of the LDPC codeword, according to the number of columns constituting the block interleaver 124, the number of bit groups constituting the LDPC codeword, and the number of bits constituting each bit group.
In each of the plurality of columns, the second part may be formed of rows excluding as many rows as the number of bits included in at least some bit groups which can be written in each of the plurality of columns in bit group wise. Specifically, the number rows of the second part may be the same value as a quotient when the number of bits included in all bit groups excluding bit groups corresponding to the first part is divided by the number of columns constituting the block interleaver 124. In other words, the number of rows of the second part may be the same value as a quotient when the number of bits included in the remaining bit groups which are not written in the first part from among bit groups constituting the LDPC codeword is divided by the number of columns.
That is, the block interleaver 124 may divide each of the plurality of columns into the first part including as many rows as the number of bits included in bit groups which can be written in each column in bit group wise, and the second part including the other rows.
Accordingly, the first part may be formed of as many rows as the number of bits included in bit groups, that is, as many rows as an integer multiple of M. However, since the number of codeword bits constituting each bit group may be an aliquot part of M as described above, the first part may be formed of as many rows as an integer multiple of the number of bits constituting each bit group.
In this case, the block interleaver 124 may interleave by writing and reading the LDPC codeword in the first part and the second part in the same method.
Specifically, the block interleaver 124 may interleave by writing the LDPC codeword in the plurality of columns constituting each of the first part and the second part in a column direction, and reading the plurality of columns constituting the first part and the second part in which the LDPC codeword is written in a row direction.
That is, the block interleaver 124 may interleave by writing the bits included in at least some bit groups which can be written in each of the plurality of columns in bit group wise in each of the plurality of columns of the first part serially, dividing the bits included in the other bit groups except the at least some bit groups and writing in each of the plurality of columns of the second part in a column direction, and reading the bits written in each of the plurality of columns constituting each of the first part and the second part in a row direction.
In this case, the block interleaver 124 may interleave by dividing the other bit groups except the at least some bit groups from among the plurality of bit groups based on the number of columns constituting the block interleaver 124.
Specifically, the block interleaver 124 may interleave by dividing the bits included in the other bit groups by the number of a plurality of columns, writing each of the divided bits in each of a plurality of columns constituting the second part in a column direction, and reading the plurality of columns constituting the second part, where the divided bits are written, in a row direction.
That is, the block interleaver 124 may divide the bits included in the other bit groups except the bit groups written in the first part from among the plurality of bit groups of the LDPC codeword, that is, the bits in the number of bit groups which correspond to the remainder when the number of bit groups constituting the LDPC codeword is divided by the number of columns, by the number of columns, and may write the divided bits in each column of the second part serially in a column direction.
For example, it is assumed that the block interleaver 124 is formed of C number of columns each including R1 number of rows. In addition, it is assumed that the LDPC codeword is formed of Ngroup number of bit groups, the number of bit groups Ngroup is not a multiple of C, and A×C+1=Ngroup (A is an integer greater than 0). In other words, it is assumed that when the number of bit groups constituting the LDPC codeword is divided by the number of columns, the quotient is A and the remainder is 1.
In this case, as shown in FIGS. 10 and 11, the block interleaver 124 may divide each column into a first part including R1 number of rows and a second part including R2 number of rows. In this case, R1 may correspond to the number of bits included in bit groups which can be written in each column in bit group wise, and R2 may be R1 subtracted from the number of rows of each column.
That is, in the above-described example, the number of bit groups which can be written in each column in bit group wise is A, and the first part of each column may be formed of as many rows as the number of bits included in A number of bit groups, that is, may be formed of as many rows as A×M number.
In this case, the block interleaver 124 writes the bits included in the bit groups which can be written in each column in bit group wise, that is, A number of bit groups, in the first part of each column in the column direction.
That is, as shown in FIGS. 10 and 11, the block interleaver 124 writes the bits included in each of bit group Y0, bit group Y1, . . . , group YA−1 in the 1st to R1th rows of the first part of the 1st column, writes bits included in each of bit group YA, bit group YA+1, . . . , bit group Y2A−1 in the 1st to R1th rows of the first part of the 2nd column, . . . , writes bits included in each of bit group YCA-A, bit group YCA-A+1, . . . , bit group YCA−1 in the 1st to R1th rows of the first part of the column C.
As described above, the block interleaver 124 writes the bits included in the bit groups which can be written in each column in bit group wise in the first part of each column.
In other words, in the above exemplary embodiment, the bits included in each of bit group (Y0), bit group (Y1), . . . , bit group (YA−1) may not be divided and all of the bits may be written in the first column, the bits included in each of bit group (YA), bit group (YA+1), . . . , bit group (Y2A−1) may not be divided and all of the bits may be written in the second column, . . . , and the bits included in each of bit group (YCA-A), bit group (YCA-A+1), . . . , group (YCA−1) may not be divided and all of the bits may be written in the C column. As such, all bit groups interleaved by the first part are written in the same column of the first part.
Thereafter, the block interleaver 124 divides bits included in the other bit groups except the bit groups written in the first part of each column from among the plurality of bit 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 bit groups except the bit 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.
In the above-described example, since A×C+1=Ngroup, when the bit groups constituting the LDPC codeword are written in the first part serially, the last bit group YNgroup-1 of the LDPC codeword is not written in the first part and remains. Accordingly, the block interleaver 124 divides the bits included in the bit group YNgroup-1 into C number of sub bit groups as shown in FIG. 10, and writes the divided bits (that is, the bits corresponding to the quotient when the bits included in the last group (YNgroup-1) are divided by C) in the second part of each column serially.
The bits divided based on the number of columns may be referred to as sub bit groups. In this case, each of the sub bit groups may be written in each column of the second part. That is, the bits included in the bit groups may be divided and may form the sub bit groups.
That is, the block interleaver 124 writes the bits in the 1st to R2th rows of the second part of the 1st column, writes the bits in the 1st to R2th rows of the second part of the 2nd column, . . . , and writes the bits in the 1st to R2th 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. 10.
That is, in the second part, the bits constituting the bit group may not be written in the same column and may be written in the plurality of columns. In other words, in the above example, the last bit group (YNgroup-1) is formed of M number of bits and thus, the bits included in the last bit group (YNgroup-1) may be divided by M/C and written in each column. That is, the bits included in the last bit group (YNgroup-1) are divided by M/C, forming M/C number of sub bit groups, and each of the sub bit groups may be written in each column of the second part.
Accordingly, in at least one bit group which is interleaved by the second part, the bits included in the at least one bit group are divided and written in at least two columns constituting the second part.
In the above-described example, the block interleaver 124 writes the bits in the second part in the column direction. However, this is merely an example. That is, the block interleaver 124 may write the bits in the plurality of columns of the second part in the 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. 11, the block interleaver 124 writes the bits from the 1st row of the second part in the 1st column to the 1st row of the second part in the column C, writes the bits from the 2nd row of the second part in the 1st column to the 2nd row of the second part in the column C, . . . , etc., and writes the bits from the R2th row of the second part in the 1st column to the R2th 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 serially in the row direction. That is, as shown in FIGS. 10 and 11, 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.
Accordingly, the block interleaver 124 may interleave a part of the plurality of bit groups constituting the LDPC codeword in bit group wise, and divide and interleave some of the remaining bit groups. That is, the block interleaver 124 may interleave by writing the LDPC codeword constituting a predetermined number of bit groups from among the plurality of bit groups in the plurality of columns of the first part in bit group wise, dividing the bits of the other bit groups and writing the bits in each of the columns of the second part, and reading the plurality of columns of the first and second parts in the row direction.
As described above, the block interleaver 124 may interleave the plurality of bit groups in the methods described above with reference to FIGS. 9 to 11.
In particular, in the case of FIG. 10, the bits included in the bit 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 bit group which does not belong to the first part is rearranged. Since the bits included in the bit group which does not belong to the first part are interleaved as described above, bit rrror rate (BER)/frame error rate (FER) performance can be improved in comparison with a case in which such bits are not interleaved.
However, the bit group which does not belong to the first part may not be interleaved as shown in FIG. 11. That is, since the block interleaver 124 writes and reads the bits included in the group which does not belong to the first part in 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. 10 and 11, the last single bit group of the plurality of bit groups is written in the second part. However, this is merely an example. The number of bit groups written in the second part may vary according to the total number of bit groups of the LDPC codeword, the number of columns and rows, the number of transmission antennas, etc.
The block interleaver 124 may have a configuration as shown in tables 23 and 24 presented below:









TABLE 23








Nldpc = 64800
















16
64
256
1024
4096



QPSK
QAM
QAM
QAM
QAM
QAM
















C
2
4
6
8
10
12


R1
32400
16200
10800
7920
6480
5400


R2
0
0
0
180
0
0


















TABLE 24








Nldpc = 16200
















16
64
256
1024
4096



QPSK
QAM
QAM
QAM
QAM
QAM


















C
2
4
6
8
10
12



R1
7920
3960
2520
1800
1440
1080



R2
180
90
180
225
180
270









Herein, C (or NC) is the number of columns of the block interleaver 124, R1 is the number of rows constituting the first part in each column, and R2 is the number of rows constituting the second part in each column.
Referring to Tables 23 and 24, the number of columns has the same value as a modulation order according to a modulation method, and each of a plurality of columns is formed of rows corresponding to the number of bits constituting the LDPC codeword divided by the number of a plurality of columns.
For example, when the length Nldpc of the LDPC codeword is 64800 and the modulation method is 16-QAM, the block interleaver 124 is formed of 4 columns as the modulation order is 4 in the case of 16-QAM, and each column is formed of rows as many as R1+R2=16200(=64800/4). In another example, when the length Nldpc of the LDPC codeword is 64800 and the modulation method is 64-QAM, the block interleaver 124 is formed of 6 columns as the modulation order is 6 in the case of 64-QAM, and each column is formed of rows as many as R1+R2=10800(=64800/6).
Meanwhile, referring to Tables 23 and 24, when the number of bit groups constituting an LDPC codeword is an integer multiple of the number of columns, the block interleaver 124 interleaves without dividing each column. Therefore, R1 corresponds to the number of rows constituting each column, and R2 is 0. In addition, when the number of bit 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 R1 number of rows, and the second part formed of R2 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 bit group are mapped onto a single bit of each modulation symbol as shown in Tables 23 and 24.
For example, when Nldpc=64800 and the modulation method is 16-QAM, the block interleaver 124 may be formed of four (4) columns each including 16200 rows. In this case, the bits included in each of the plurality of bit groups are written in the four (4) columns and the 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 bit group, that is, bits output from a single column, may be mapped onto a single bit of each modulation symbol. For example, bits included in a bit group written in the 1st column may be mapped onto the first bit of each modulation symbol.
In another example, when Nldpc=64800 and the modulation method is 64-QAM, the block interleaver 124 may be formed of six (6) columns each including 10800 rows. In this case, the bits included in each of the plurality of bit groups are written in the six (6) columns and the bits written in the same row in each column are output serially. In this case, since six (6) bits constitute a single modulation symbol in the modulation method of 64-QAM, bits included in the same bit group, that is, bits output from a single column, may be mapped onto a single bit of each modulation symbol. For example, bits included in a bit group written in the 1st column may be mapped onto the first bit of each modulation symbol.
Referring to Tables 23 and 24, the total number of rows of the block interleaver 124, that is, R1+R2, is Nldpc/C.
In addition, the number of rows of the first part, R1, is an integer multiple of the number of bits included in each group, M (e.g., M=360), and maybe expressed as └Ngroup/C┘×M, and the number of rows of the second part, R2, may be Nldpc/C-R1. Herein, └Ngroup/C┘ is the largest integer below Ngroup/C. Since R1 is an integer multiple of the number of bits included in each group, M, bits may be written in R1 in bit groups wise.
In addition, when the number of bit groups of the LDPC codeword is not a multiple of the number of columns, it can be seen from Tables 23 and 24 that the block interleaver 124 interleaves by dividing each column into two parts.
Specifically, the length of the 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 bit groups of the LDPC codeword is a multiple of the number of columns, each column is not divided into two parts. However, when the number of bit groups of the LDPC codeword is not a 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 28. In this case, each bit group of the LDPC codeword is formed of 360 bits, and the LDPC codeword is formed of 64800/360(=180) bit groups.
When the modulation method is 16-QAM, the block interleaver 124 may be formed of four (4) columns and each column may have 64800/4(=16200) rows.
In this case, since the number of bit groups of the LDPC codeword divided by the number of columns is 180/4(=45), bits can be written in each column in bit group wise without dividing each column into two parts. That is, bits included in 45 bit groups which is the quotient when the number of bit groups constituting the LDPC codeword is divided by the number of columns, that is, 45×360(=16200) bits can be written in each column.
However, when the modulation method is 256-QAM, the block interleaver 124 may be formed of eight (8) columns and each column may have 64800/8(=8100) rows.
In this case, since the number of bit groups of the LDPC codeword divided by the number of columns is 180/8=22.5, the number of bit groups constituting the LDPC codeword is not an integer multiple of the number of columns. Accordingly, the block interleaver 124 divides each of the eight (8) columns into two parts to perform interleaving in bit group wise.
In this case, since the bits should be written in the first part of each column in bit group wise, the number of bit groups which can be written in the first part of each column in bit group wise is 22, which is the quotient when the number of bit groups constituting the LDPC codeword is divided by the number of columns, and accordingly, the first part of each column has 22×360(=7920) rows. Accordingly, 7920 bits included in 22 bit groups may be written in the first part of each column.
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.
In this case, the bits included in the other bit groups which have not been written in the first part are divided and written in the second part of each column.
Specifically, since 22×8(=176) bit groups are written in the first part, the number of bit groups to be written in the second part is 180−176 (=4) (for example, bit group Y176, bit group Y177, bit group Y178, and bit group Y179 from among bit group Y0, bit group Y1, bit group Y2, . . . , bit group Y178, and bit group Y179 constituting the LDPC codeword).
Accordingly, the block interleaver 124 may write the four (4) bit groups which have not been written in the first part and remains from among the groups constituting the LDPC codeword in the second part of each column serially.
That is, the block interleaver 124 may write 180 bits of the 360 bits included in the bit group Y176 in the 1st row to the 180th row of the second part of the 1st column in the column direction, and may write the other 180 bits in the 1st row to the 180th row of the second part of the 2nd column in the column direction. In addition, the block interleaver 124 may write 180 bits of the 360 bits included in the bit group Y177 in the 1st row to the 180th row of the second part of the 3rd column in the column direction, and may write the other 180 bits in the 1st row to the 180th row of the second part of the 4th column in the column direction. In addition, the block interleaver 124 may write 180 bits of the 360 bits included in the bit group Y178 in the 1st row to the 180th row of the second part of the 5th column in the column direction, and may write the other 180 bits in the 1st row to the 180th row of the second part of the 6th column in the column direction. In addition, the block interleaver 124 may write 180 bits of the 360 bits included in the bit group Y179 in the 1st row to the 180th row of the second part of the 7th column in the column direction, and may write the other 180 bits in the 1st row to the 180th row of the second part of the 8th column in the column direction.
Accordingly, the bits included in the bit group which has not been written in the first part and remains are not written in the same column in the second part and may be divided and written in the plurality of columns.
Hereinafter, the block interleaver 124 of FIG. 5 according to an exemplary embodiment will be explained in detail with reference to FIG. 12.
In a group-interleaved LDPC codeword (v0, v1, . . . , vNldpc−1), Yj is continuously arranged like V={Y0, Y1, . . . , YNgroup−1}.
The LDPC codeword after group interleaving may be interleaved by the block interleaver 124 as shown in FIG. 12. In this case, the block interleaver 124 divide a plurality of columns into the first part (Part 1) and the second part (Part 2) based on the number of columns of the block interleaver 124 and the number of bits of bit groups. In this case, in the first part, the bits constituting the bit groups may be written in the same column, and in the second part, the bits constituting the bit groups may be written in a plurality of columns (i.e. the bits constituting the bit groups may be written in at least two columns).
Specifically, input bits vi are written serially from the first part to the second part column wise, and then read out serially from the first part to the second part row wise. That is, the data bits vi are written serially into the block interleaver column-wise starting in the first aprt and continuing column-wise finishing in the second part, and then read out serially row-wise from the first part and then row-wise from the second part. Accordingly, the bit included in the same bit group in the first part may be mapped onto a single bit of each modulation symbol.
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 format and a length of the LDPC codeword as in Table 25 presented below. That is, the first part and the second part block interleaving configurations for each modulation format and code length are specified in Table 25 presented below. Herein, the number of columns of the block interleaver 124 may be equal to the number of bits constituting a modulation symbol. In addition, a sum of the number of rows of the first part, Nr1 and the number of rows of the second part, Nr2, is equal to Nldpc/NC (herein, NC is the number of columns). In addition, since Nr1(=└Ngroup/Nc┘×360) is a multiple of 360, a multiple of bit groups may be written in the first part.











TABLE 25









Rows in Part 1 Nr1
Rows in Part 2 Nr2














Nldpc =

Nldpc =
Nldpc =
Columns


Modulation
64800
Nldpc = 16200
64800
16200
Nc















QPSK
32400
7920
0
180
2


 16-QAM
16200
3960
0
90
4


 64-QAM
10800
2520
0
180
6


 256-QAM
7920
1800
180
225
8


1024-QAM
6480
1440
0
180
10


4096-QAM
5400
1080
0
270
12









Hereinafter, an operation of the block interleaver 124 will be explained in detail.
Specifically, as shown in FIG. 12, the input bit vi (0≦i<NC×Nr1) is written in ri row of ci column of the first part of the block interleaver 124. Herein, ci and ri are




  
    c
    i
  
  =
  
    ⌊
    
      i
      
        N
        
          r
          ⁢
          
            
          
          ⁢
          1
        
      
    
    ⌋
  




and ri=(i mod Nr1), respectively.

In addition, the input bit vi(NC×Nr1≦i<Nldpc) is written in row ri row of ci column of the second part of the block interleaver 124. Herein, ci and ri satisfy




  
    c
    i
  
  =
  
    ⌊
    
      
        (
        
          i
          -
          
            
              N
              C
            
            ×
            
              N
              
                r
                ⁢
                
                  
                
                ⁢
                1
              
            
          
        
        )
      
      
        N
        
          r
          ⁢
          
            
          
          ⁢
          2
        
      
    
    ⌋
  




and ri=Nr1+{(i−NC×Nr1)mod Nr2}, respectively.

An output bit qj(0≦j<Nldpc) is read from cj column of rj row. Herein, rj and cj satisfy




  
    r
    j
  
  =
  
    ⌊
    
      j
      
        N
        c
      
    
    ⌋
  




and cj=(j mod NC), respectively.

For example, when the length Nldpc of an LDPC codeword is 64800 and the modulation method is 256-QAM, the order of bits output from the block interleaver 124 may be (q0,q1,q2, . . . , q63357,q63358,q63359,q63360,q63361, . . . , q64799)=(v0,v7920,v15840, . . . , v47519,v55439,v63359,v63360,v63540, . . . , v64799). 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.
Hereinafter, the interleaving operation of the block interleaver 124 will be explained in detail.
The block interleaver 124 may interleave by writing a plurality of bit groups in each column in bit group wise in a column direction, and reading each row of the plurality of columns in which the plurality of bit groups are written in bit group wise in a row direction.
In this case, the number of columns constituting the block interleaver 124 may vary according to a modulation method, and the number of rows may be the length of the LDPC codeword/the number of columns.
For example, when the modulation method is 16-QAM, the block interleaver 124 may be formed of 4 columns. In this case, when the length Nldpc of the LDPC codeword is 16200, the number of rows is 16200 (=64800/4). In another example, when the modulation method is 64-QAM, the block interleaver 124 may be formed of 6 columns. In this case, when the length Nldpc of the LDPC codeword is 64800, the number of rows is 10800 (=64800/6).
Hereinafter, the method for interleaving the plurality of bit groups in bit group wise by the block interleaver 124 will be explained in detail.
When the number of bit groups constituting the LDPC codeword is an integer multiple of the number of columns, the block interleaver 124 may interleave by writing the bit groups as many as the number of bit groups divided by the number of columns in each column serially in bit group wise.
For example, when the modulation method is 16-QAM and the length Nldpc of the LDPC codeword is 64800, the block interleaver 124 may be formed of four (4) columns each including 16200 rows. In this case, since the LDPC codeword is divided into (64800/360=180) number of bit groups when the length Nldpc of the LDPC codeword is 64800, the number of bit groups (=180) of the LDPC codeword may be an integer multiple of the number of columns (=4) when the modulation method is 16-QAM. That is, no remainder is generated when the number of bit groups of the LDPC codeword is divided by the number of columns.
In this case, as shown in FIG. 13, the block interleaver 124 writes the bits included in each of the bit group Y0, bit group Y1, . . . , bit group Y44 in the 1st row to 16200th row of the first column, writes the bits included in each of the bit group Y45, the bit group Y46, . . . , the bit group Y89 in the 1st row to 16200th row of the second column, writes the bits included in each of the bit group Y90, the bit group Y91, . . . , the bit group Y134 in the 1st row to 16200th row of the third column, and writes the bits included in each of the bit group Y135, the bit group Y136, . . . , the bit group Y179 in the 1st row to 16200th row of the fourth column. In addition, the block interleaver 124 may read the bits written in each row of the two columns serially in the row direction.
In another, when the modulation method is 64-QAM and the length Nldpc of the LDPC codeword is 64800, the block interleaver 124 may be formed of six (6) columns each including 10800 rows. In this case, since the LDPC codeword is divided into (64800/360=180) number of bit groups when the length Nldpc of the LDPC codeword is 64800, the number of bit groups (=180) of the LDPC codeword may be an integer multiple of the number of columns (=4) when the modulation method is 64-QAM. That is, no remainder is generated when the number of bit groups of the LDPC codeword is divided by the number of columns.
In this case, as shown in FIG. 14, the block interleaver 124 writes the bits included in each of the bit group Y0, bit group Y1, . . . , bit group Y29 in the 1st row to 10800th row of the first column, writes the bits included in each of the bit group Y30, the bit group Y31, . . . , the bit group Y59 in the 1st row to 10800th row of the second column, writes the bits included in each of the bit group Y60, the bit group Y61, . . . , the bit group Y89 in the 1st row to 10800th row of the third column, writes the bits included in each of the bit group Y90, the bit group Y91, . . . , the bit group Y119 in the 1st row to 10800th row of the fourth column, writes the bits included in each of the bit group Y120, the bit group Y121, . . . , the bit group Y149 in the 1st row to 10800th row of the fifth column, and writes the bits included in each of the bit group Y150, the bit group Y151, . . . , the bit group Y179 in the 1st row to 10800th row of the sixth column. In addition, the block interleaver 124 may read the bits written in each row of the two columns serially in the row direction.
As described above, when the number of bit groups constituting the LDPC codeword is an integer multiple of the number of columns of the block interleaver 124, the block interleaver 124 may interleave the plurality of bit groups in bit group wise, and accordingly, the bits belonging to the same bit group may be written in the same column.
As described above, the block interleaver 124 may interleave the plurality of bit groups of the LDPC codeword in the method described above with reference to FIGS. 13 and 14.
The modulator 130 maps the interleaved LDPC codeword onto a modulation symbol. Specifically, the modulator 130 may demultiplex the interleaved LDPC codeword, modulate the demultiplexed LDPC codeword, and map the LDPC codeword onto a constellation.
In this case, the modulator 130 may generate a modulation symbol using the bits included in each of a plurality of bit groups.
In other words, as described above, the bits included in different bit groups are written in each column of the block interleaver 124, and the block interleaver 124 reads the bits written in each column in the row direction. In this case, the modulator 130 generates a modulation symbol by mapping the bits read in each column onto each bit of the modulation symbol. Accordingly, each bit of the modulation symbol belongs to a different bit group.
For example, it is assumed that the modulation symbol consists of C number of bits. In this case, the bits which are read from each row of C number of columns of the block interleaver 124 may be mapped onto each bit of the modulation symbol and thus, each bit of the modulation symbol consisting of C number of bits belong to C number of different bit groups.
Hereinbelow, the above feature will be described in greater detail.
First, the modulator 130 demultiplexes the interleaved LDPC codeword. To achieve this, the modulator 130 may include a demultiplexer (not shown) to demultiplex the interleaved LDPC codeword.
The demultiplexer (not shown) demultiplexes the interleaved LDPC codeword. Specifically, the demultiplexer (not shown) 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. 15, the demultiplexer (not shown) receives the LDPC codeword Q=(q0, q1, q2, . . . ) output from the interleaver 120, outputs the received LDPC codeword bits to a plurality of substreams serially, converts the input LDPC codeword bits into cells, and outputs the cells.
In this case, the bits having the same index in each of the plurality of substreams may constitute the same cell. Accordingly, the cells may be configured like (y0,0, y1,0, . . . , yηMOD−1.0)=(q0, q1, qηMOD−1), (y0,1, y1,1, . . . , yηMOD−1,1)=(qη MOD, qηMOD+1, . . . , q2xηMOD−1), . . . .
Herein, the number of substreams, Nsubstreams, may be equal to the number of bits constituting a modulation symbol, ηMOD. Accordingly, the number of bits constituting each cell may be equal to the number of bits constituting a modulation symbol (that is, a modulation order).
For example, when the modulation method is 16-QAM, the number of bits constituting the modulation symbol, ηMOD, is 4 and thus the number of substreams, Nsubstreams, is 4, and the cells may be configured like (y0,0, y1,0, y2,0, y3,0)=(q0, q1, q2, q3), (y0,1, y1,1, y2,1, y3,1)=(q4, q5, q6, q7), (y0,2, y1,2, y2,2, y3,2)=(q8, q9, q10, q11), . . . .
In another example, when the modulation method is 64-QAM, the number of bits constituting the modulation symbol, ηMOD, is 6 and thus the number of substreams, Nsubstreams, is 6, and the cells may be configured like (y0,0, y1,0, y2,0, y3,0, y4,0, y5,0)=(q0, q1, q2, q3, q4, q5), (y0,1, y1,1, y2,1, y3,1, y4,1, y5,1)=(q6, q7, q8, q9, q10, q11), (y0,2, y1,2, y2,2, y3,2, y4,2, y5,2)=(q12, q13, q14, q15, q16, q17), . . . .
The modulator 130 may map the demultiplexed LDPC codeword onto modulation symbols.
Specifically, the modulator 130 may modulate bits (that is, cells) output from the demultiplexer (not shown) in various modulation methods such as Quadrature Phase Shift Keying (QPSK), 16-QAM, 64-QAM, 256-QAM, 1024-QAM, 4096-QAM, etc. For example, when the modulation method is QPSK, 16-QAM, 64-QAM, 256-QAM, 1024-QAM, and 4096-QAM, the number of bits constituting the modulation symbol, ηMOD (that is, the modulation order), may be 2, 4, 6, 8, 10 and 12, respectively.
In this case, since each cell output from the demultiplexer (not shown) is formed of as many bits as the number of bits constituting the modulation symbol, the modulator 130 may generate the modulation symbol by mapping each cell output from the demultiplexer (not shown) onto a constellation point serially. Herein, the modulation symbol corresponds to a constellation point on the constellation.
However, the above-described demultiplexer (not shown) may be omitted according to circumstances. In this case, the modulator 130 may generate modulation symbols by grouping a predetermined number of bits from interleaved bits serially and mapping the predetermined number of bits onto constellation points. In this case, the modulator 130 may generate the modulation symbols by mapping ηMOD number of bits onto the constellation points serially according to a modulation method.
The modulator 130 may modulate by mapping cells output from the demultiplexer (not shown) onto constellation points in a non-uniform constellation (NUC) method.
In the non-uniform constellation method, once a constellation point of the first quadrant is defined, 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={z0, z1, . . . , zM−1}. In this case, when the constellation points existing in the first quadrant are defined as {x0, x1, x2, . . . , XM/4−1}, z may be defined as follows:
from z0 to zM/4−1=from x0 to xM/4 
from zM/4 to z2xM/4−1=−conj(from x0 to xM/4)
from z2xM/4 to z3xM/4−1=conj(from x0 to xM/4)
from z3xM/4 to z4xM/4−1=−(from x0 to xM/4)
Accordingly, the modulator 130 may map the bits [y0, . . . , ym-1] output from the demultiplexer (not shown) onto constellation points in the non-uniform constellation method by mapping the output bits onto zL having an index of




  L
  =
  
    
      ∑
      
        i
        =
        0
      
      
        m
        -
        1
      
    
    ⁢
    
      
    
    ⁢
    
      
        (
        
          
            y
            1
          
          ×
          
            2
            
              m
              -
              1
            
          
        
        )
      
      .
    
  




An example of the constellation defined according to the non-uniform constellation method may be expressed as in tables 26 to 30 presented below when the code rate is 5/15, 7/15, 9/15, 11/15, 13/15:











TABLE 26







Input data cell y
Constellation point Zs









(00)
  (1 + 1i)/{square root over (2)}



(01)
  (1 − 1i)/{square root over (2)}



(10)
(−1 + 1i)/{square root over (2)}



(11)
(−1 − 1i)/{square root over (2)}






















TABLE 27







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 28







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 29







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 + 0.8133i


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 + 0.3035i
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 + 0.2141i
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 30







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 + 0.1166i
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 + 0.1167i
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 26 indicates non-uniform QPSK, table 27 indicates non-uniform 16-QAM, Tables 28 and 29 indicate non-uniform 64-QAM, and table 30 indicates non-uniform 256-QAM.
Referring to these tables, the constellation point of the first quadrant may be defined with reference to tables 26 to 30, and the constellation points in the other three quadrants may be defined in the above-described method.
However, this is merely an example and the modulator 130 may map the output bits outputted from the demultiplexer (not shown) onto the constellation points in various methods.
The interleaving is performed in the above-described method for the following reasons.
Specifically, when the LDPC codeword bits are mapped onto the modulation symbol, the bits may have different reliability (that is, receiving performance or receiving probability) according to where the bits are mapped onto in the modulation symbol. The LDPC codeword bits may have different codeword characteristics according to the 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 column of the parity check matrix, that is, the column degree.
Accordingly, the interleaver 120 may interleave to map the LDPC codeword bits having a specific codeword characteristic onto specific bits in the modulation symbol by considering both the codeword characteristics of the LDPC codeword bits and the reliability of the bits constituting the modulation symbol.
For example, when the LDPC codeword formed of bit groups x0 to X179 is group-interleaved based on Equation 21 and Table 11, the group interleaver 122 may output the bit groups in the order of X55, X146, X83, . . . , X132, X135.
In this case, when the modulation method is 16-QAM, the number of columns of the block interleaver 124 is four (4) and each column may be formed of 16200 rows.
Accordingly, from among the 180 groups constituting the LDPC codeword, 45 bit groups (X55, X146, X83, X52, X62, X176, X160, X68, X53, X56, X81, X97, X79, X113, X163, X61, X58, X69, X133, X108, X66, X71, X86, X144, X57, X67, X116, X59, X70, X156, X172, X65, X149, X155, X82, X138, X136, X141, X111, X96, X170, X90, X140, X64, X159) may be inputted to the first column of the block interleaver 124, 45 bit groups (X15, X14, X37, X54, X44, X63, X43, X18, X47, X7, X25, X34, X29, X30, X26, X39, X16, X41, X45, X36, X0, X23, X32, X28, X27, X38, X48, X33, X22, X49, X51, X60, X46, X21, X4, X3, X20, X13, X50, X35, X24, X40, X17, X42, X6) may be inputted to the second column of the block interleaver 124, 45 bit groups (X112, X93, X127, X101, X94, X115, X105, X31, X19, X177, X74, X10, X145, X162, X102, X120, X126, X95, X73, X152, X129, X174, X125, X72, X128, X78, X171, X8, X142, X178, X154, X85, X107, X75, X12, X9, X151, X77, X117, X109, X80, X106, X134, X98, X1) may be inputted to the third column of the block interleaver 124, and 45 bit groups (X122, X173, X161, X150, X110, X175, X166, X131, X119, X103, X139, X148, X157, X114, X147, X87, X158, X121, X164, X104, X89, X179, X123, X118, X99, X88, X11, X92, X165, X84, X168, X124, X169, X2, X130, X167, X153, X137, X143, X91, X100, X5, X76, X132, X135) may be inputted to the fourth column of the block interleaver 124.
In addition, the block interleaver 124 may output the bits inputted to the 1st row to the last row of each column serially, and the bits outputted from the block interleaver 124 may be inputted to the modulator 130 serially. In this case, the demultiplexer (not shown) may be omitted or the bits may be outputted serially without changing the order of bits inputted to the demultiplexer (not shown). Accordingly, the bits included in each of the bit groups X55, X15, X112, and X122 may constitute the modulation symbol.
When the modulation method is 64-QAM, the number of columns of the block interleaver 124 is six (6) and each column may be formed of 10800 rows.
Accordingly, from among the 180 groups constituting the LDPC codeword, 30 bit groups (X55, X146, X83, X52, X62, X176, X160, X68, X53, X56, X81, X97, X79, X113, X163, X61, X58, X69, X133, X108, X66, X71, X86, X144, X57, X67, X116, X59, X70, X156) may be inputted to the first column of the block interleaver 124, 30 bit groups (X172, X65, X149, X155, X82, X138, X136, X141, X111, X96, X170, X90, X140, X64, X159, X15, X14, X37, X54, X44, X63, X43, X18, X47, X7, X25, X34, X29, X30, X26) may be inputted to the second column of the block interleaver 124, 30 bit groups (X39, X16, X41, X45, X36, X0, X23, X32, X28, X27, X38, X48, X33, X22, X49, X51, X60, X46, X21, X4, X3, X20, X13, X50, X35, X24, X40, X17, X42, X6) may be inputted to the third column of the block interleaver 124, 30 bit groups (X112, X93, X127, X101, X94, X115, X105, X31, X19, X177, X74, X10, X145, X162, X102, X120, X126, X95, X73, X152, X129, X174, X125, X72, X128, X78, X171, X8, X142, X178) may be inputted to the fourth column of the block interleaver 124, 30 bit groups (X154, X85, X107, X75, X12, X9, X151, X77, X117, X109, X80, X106, X134, X98, X1, X122, X173, X161, X150, X110, X175, X166, X131, X119, X103, X139, X148, X157, X114, X147) may be inputted to the fifth column of the block interleaver 124, and 30 bit groups (X87, X158, X121, X164, X104, X89, X179, X123, X118, X99, X88, X11, X92, X165, X84, X168, X124, X169, X2, X130, X167, X153, X137, X143, X91, X100, X5, X76, X132, X135) may be inputted to the sixth column of the block interleaver 124.
In addition, the block interleaver 124 may output the bits inputted to the 1st row to the last row of each column serially, and the bits outputted from the block interleaver 124 may be inputted to the modulator 130 serially. In this case, the demultiplexer (not shown) may be omitted or the bits may be outputted serially without changing the order of bits inputted to the demultiplexer (not shown). Accordingly, the bits included in each of the bit groups X55, X172, X39, X112, X154, and X87 may constitute the modulation symbol.
As described above, since a specific bit is mapped onto a specific bit in a modulation symbol through interleaving, a receiver side can achieve high receiving performance and high decoding performance.
That is, when LDPC codeword bits of high decoding performance are mapped onto high reliability bits from among bits of each modulation symbol, the receiver side may show high decoding performance, but there is a problem that the LDPC codeword bits of the high decoding performance may not be 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 receiving 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 the receiver side. Accordingly, the receiver side can achieve high receiving performance and decoding performance.
Hereinafter, a method for determining π(j), which is a parameter used for group interleaving, according to various exemplary embodiments, will be explained.
According to an exemplary embodiment, when the length of the LDPC codeword is 64800, the size of the bit group is determined to be 360 and thus 180 bit groups exist. In addition, there may be 180! possible interleaving patterns (Herein, factorial means A!=A×(A−1)× . . . ×2×1) regarding an integer A.
In this case, since a reliability level between the bits constituting a modulation symbol may be the same according to a modulation order, many number of interleaving patterns may be regarded as the same interleaving operation when theoretical performance is considered. For example, when an MSB bit of the X-axis (or rear part-axis) and an MSB bit the Y-axis (or imaginary part-axis) of a certain modulation symbol have the same theoretical reliability, the same theoretical performance can be achieved regardless of the way how specific bits are interleaved to be mapped onto the two MSB bits.
However, such a theoretical prediction may become incorrect as a real channel environment is established. For example, in the case of the QPSK modulation method, two bits of a symbol in a part of a symmetric channel like an additive white Gaussian noise (AWGN) channel theoretically have the same reliability. Therefore, there should be no difference in the performance theoretically when any interleaving method is used. However, in a real channel environment, the performance may be different depending on the interleaving method. In the case of a well-known Rayleigh channel which is not a real channel, the performance of QPSK greatly depends on the interleaving method and thus the performance can be predicted somewhat only by the reliability between bits of a symbol according to a modulation method. However, there should be a limit to predicting the performance.
In addition, since code performance by interleaving may be greatly changed according to a channel which evaluates performance, channels should be always considered to drive an interleaving pattern. For example, a good interleaving pattern in the AWGN channel may be not good in the Rayleigh channel. If a channel environment where a given system is used is closer to the Rayleigh channel, an interleaving pattern which is better in the Rayleigh channel than in the AWGN channel may be selected.
As such, not only a specific channel environment but also various channel environments considered in a system should be considered in order to derive a good interleaving pattern. In addition, since there is a limit to predicting real performance only by theoretical performance prediction, the performance should be evaluated by directly conducting computation experiments and then the interleaving pattern should be finally determined.
However, since there are so many number of possible interleaving patterns to be applied (for example, 180!), reducing the number of interleaving patterns used to predict and test performance is an important factor in designing a high performance interleaver.
Therefore, the interleaver is designed through the following steps according to an exemplary embodiment.
1) Channels C1, C2, . . . , Ck to be considered by a system are determined.
2) A certain interleaver pattern is generated.
3) A theoretical performance value is predicted by applying the interleaver generated in step 2) to each of the channels determined in step 1). There are various methods for predicting a theoretical performance value, but a well-known noise threshold determining method like density evolution analysis is used according to an exemplary embodiment. The noise threshold recited herein refers to a value that can be expressed by a minimum necessary signal-to-noise ratio (SNR) capable of error-free transmission on the assumption that a cycle-free characteristic is satisfied when the length of a code is infinite and the code is expressed by the Tanner graph. The density evolution analysis may be implemented in various ways, but is not the subject matter of the inventive concept and thus a detailed description thereof is omitted.
4) When noise thresholds for the channels are expressed as TH1[i], TH2[i], . . . , THk[i] for the i-th generated interleaver, a final determination threshold value may be defined as follows:

TH[i]=W1×TH1[i]+W2×TH2[i]+ . . . +Wk×THk[i], 

where W1+W2+ . . . +Wk=1, W1, W2, . . . , Wk>0
Here, W1, W2, . . . , Wk are adjusted according to importance of the channels. That is, W1, W2, . . . , Wk are adjusted to a larger value in a more important channel and W1, W2, . . . , Wk are adjusted to a smaller value in a less important channel (for example, if the weight values of AWGN and Rayleigh channels are W1 and W2, respectively, W1 may be set to 0.25 and W2 may be set to 0.75 when one of the channels is determined to be more important.).
5) B number of interleaver patterns are selected in an ascending order of TH[i] values from among the tested interleaver patterns and are directly tested by conducting performance computation experiments. An FER level for the test is determined as 10^−3 (for example, B=100).
6) D number of best interleaver patterns are selected from among the B number of interleaver patterns tested in step 5) (for example, D=5).
In general, an interleaver pattern which has a great SNR gain in the area of FER=10^−3 may be selected as a good performance interleaver in step of 5). However, according to an exemplary embodiment, as shown in FIG. 16, performance of FER required in the system based on the result of real computation experiments for the area of FER=10^−3 may be predicted through extrapolation, and then an interleaver pattern having good performance in comparison with the expected performance in the FER required in the system may be determined as a good interleaver pattern. According to an exemplary embodiment, the extrapolation based on a linear function may be applied. However, various extrapolation methods may be applied. FIG. 16 illustrates an example of performance extrapolation predicted by the result of computation experiments.
7) The D number of interleaver patterns selected in step 6) are tested by conducting performance computation experiments in each channel. Herein, the FER level for testing is selected as FER required in the system (for example, FER=10^−6)
8) When an error floor is not observed after the computation experiments, an interleaving pattern having the greatest SNR gain is determined as a final interleaving pattern.
FIG. 17 is a view schematically showing a process of determining B number of interleaver patterns in the steps 2), 3), 4), and 5) of the above-described method for determining the interleaving pattern in the case of AWGN and Rayleigh channels for example.
Referring to FIG. 17, necessary variables i, j, and etc. are initialized in operation S1701, and a noise threshold for the AWGN channel THIN and a noise threshold for the Rayleigh channel TH2[i] are calculated in operation S1702. Then, a final determination noise threshold TH[i] defined in step 4) is calculated in operation S1703, and is compared with a previously calculated final determination noise threshold TH[i−1] in operation S1704. When the final determination noise threshold TH[i] is smaller than the previously calculated final determination noise threshold TH[i−1], TH S[i] is replaced with the TH[i] and is sotred in operation S1706. Next, i, j values increase by 1 in operation S1707 and this process is repeated until the i value exceeds A which is pre-defined in operation S1708. In this case, A is the total number of interleaver patterns to be tested in steps 2), 3), 4), and 5) and A is typically determined to be greater than or equal to 10000. When all operations described above are completed, interleaver patterns corresponding to TH S[0], TH S[1], . . . , TH S[B−1] which are stored in a descending order of final noise thresholds values in operation S1709.
The transmitting apparatus 100 may transmit the signal mapped onto the constellation to a receiving apparatus (for example, 1200 of FIG. 18). For example, the transmitting apparatus 100 may map the signal mapped onto the constellation onto an Orthogonal Frequency Division Multiplexing (OFDM) frame using OFDM, and may transmit the signal to the receiving apparatus 1200 through an allocated channel.
FIG. 18 is a block diagram to illustrate a configuration of a receiving apparatus according to an exemplary embodiment. Referring to FIG. 18, the receiving apparatus 1200 includes a demodulator 1210, a multiplexer 1220, a deinterleaver 1230 and a decoder 1240.
The demodulator 1210 receives and demodulates a signal transmitted from the transmitting apparatus 100. Specifically, the demodulator 1210 generates a value corresponding to an LDPC codeword by demodulating the received signal, and outputs the value to the multiplexer 1220. In this case, the demodulator 1210 may use a demodulation method corresponding to a modulation method used in the transmitting apparatus 100. To do so, the transmitting apparatus 100 may transmit information regarding the modulation method to the receiving apparatus 1200, or the transmitting apparatus 100 may perform modulation using a pre-defined modulation method between the transmitting apparatus 100 and the receiving apparatus 1200.
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 transmitting 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 transmitting apparatus 100 is 0 or 1 belongs.
The multiplexer 1220 multiplexes the output value of the demodulator 1210 and outputs the value to the deinterleaver 1230.
Specifically, the multiplexer 1220 is an element corresponding to a demultiplexer (not shown) provided in the transmitting apparatus 100, and performs an operation corresponding to the demultiplexer (not shown). That is, the multiplexer 1220 performs an inverse operation of the operation of the demultiplexer (not shown), and performs cell-to-bit conversion with respect to the output value of the demodulator 1210 and outputs the LLR value in the unit of bit. However, when the demultiplexer (not shown) is omitted from the transmitting apparatus 100, the multiplexer 1220 may be omitted from the receiving apparatus 1200.
The information regarding whether the demultiplexing operation is performed or not may be provided by the transmitting apparatus 100, or may be pre-defined between the transmitting apparatus 100 and the receiving apparatus 1200.
The deinterleaver 1230 deinterleaves the output value of the multiplexer 1220 and outputs the values to the decoder 1240.
Specifically, the deinterleaver 1230 is an element corresponding to the interleaver 120 of the transmitting apparatus 100 and performs an operation corresponding to the interleaver 120. That is, the deinterleaver 1230 deinterleaves the LLR value by performing the interleaving operation of the interleaver 120 inversely.
To do so, the deinterleaver 1230 may include a block deinterleaver 1231, a group twist deinterleaver 1232, a group deinterleaver 1233, and a parity deinterleaver 1234 as shown in FIG. 18.
The block deinterleaver 1231 deinterleaves the output of the multiplexer 1220 and outputs the value to the group twist deinterleaver 1232.
Specifically, the block deinterleaver 1231 is an element corresponding to the block interleaver 124 provided in the transmitting apparatus 100 and performs the interleaving operation of the block interleaver 124 inversely.
That is, the block deinterleaver 1231 deinterleaves by writing the LLR value output from the multiplexer 1220 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 by using at least one row formed of the plurality of columns.
In this case, when the block interleaver 124 interleaves by dividing the column into two parts, the block deinterleaver 1231 may deinterleave by dividing the row into two parts.
In addition, when the block interleaver 124 writes and reads in and from the bit group that does not belong to the first part in the row direction, the block deinterleaver 1231 may deinterleave by writing and reading values corresponding to the group that does not belong to the first part in the row direction.
Hereinafter, the block deinterleaver 1231 will be explained with reference to FIG. 20. However, this is merely an example and the block deinterleaver 1231 may be implemented in other methods.
An input LLR vi (0≦i<Nldpc) is written in a ri row and a ci column of the block deinterleaver 1231. Herein, ci=(i mod Nc) and




  
    
      r
      i
    
    =
    
      ⌊
      
        i
        
          N
          c
        
      
      ⌋
    
  
  ,




On the other hand, an output LLR qi(0≦i<Nc×Nr1) is read from a ci column and a ri row of the first part of the block deinterleaver 1231. Herein,




  
    
      c
      i
    
    =
    
      ⌊
      
        i
        
          N
          
            r
            ⁢
            
              
            
            ⁢
            1
          
        
      
      ⌋
    
  
  ,




ri=(i mod Nr1).

In addition, an output LLR qi(Nc×Nr1≦i<Nldpc) is read from a ci column and a ri row of the second part. Herein,




  
    
      c
      i
    
    =
    
      ⌊
      
        
          (
          
            i
            -
            
              
                N
                C
              
              ×
              
                N
                
                  r
                  ⁢
                  
                    
                  
                  ⁢
                  1
                
              
            
          
          )
        
        
          N
          
            r
            ⁢
            
              
            
            ⁢
            2
          
        
      
      ⌋
    
  
  ,




ri=Nr1+{(i−Nc×Nr1) mode Nr2}.

The group twist deinterleaver 1232 deinterleaves the output value of the block deinterleaver 1231 and outputs the value to the group deinterleaver 1233.
Specifically, the group twist deinterleaver 1232 is an element corresponding to the group twist interleaver 123 provided in the transmitting apparatus 100, and may perform the interleaving operation of the group twist interleaver 123 inversely.
That is, the group twist deinterleaver 1232 may rearrange the LLR values of the same bit group by changing the order of the LLR values existing in the same bit group. When the group twist operation is not performed in the transmitting apparatus 100, the group twist deinterleaver 1232 may be omitted.
The group deinterleaver 1233 (or the group-wise deinterleaver) deinterleaves the output value of the group twist deinterleaver 1232 and outputs the value to the parity deinterleaver 1234.
Specifically, the group deinterleaver 1233 is an element corresponding to the group interleaver 122 provided in the transmitting apparatus 100 and may perform the interleaving operation of the group interleaver 122 inversely.
That is, the group deinterleaver 1233 may rearrange the order of the plurality of bit groups in bit group wise. In this case, the group deinterleaver 1233 may rearrange the order of the plurality of bit groups in bit group wise by applying the interleaving method of Tables 11 to 22 inversely according to a length of the LDPC codeword, a modulation method and a code rate.
The parity deinterleaver 1234 performs parity deinterleaving with respect to the output value of the group deinterleaver 1233 and outputs the value to the decoder 1240.
Specifically, the parity deinterleaver 1234 is an element corresponding to the parity interleaver 121 provided in the transmitting apparatus 100 and may perform the interleaving operation of the parity interleaver 121 inversely. That is, the parity deinterleaver 1234 may deinterleave the LLR values corresponding to the parity bits from among the LLR values output from the group deinterleaver 1233. In this case, the parity deinterleaver 1234 may deinterleave the LLR value corresponding to the parity bits inversely to the parity interleaving method of Equation 18.
However, the parity deinterleaver 1234 may be omitted depending on the decoding method and embodiment of the decoder 1240.
Although the deinterleaver 1230 of FIG. 18 includes three (3) or four (4) elements as shown in FIG. 19, 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, Xd constitute a single modulation symbol, the deinterleaver 1230 may deinterleave these bits to locations corresponding to their bit groups based on the received single modulation symbol.
For example, when the code rate is 6/15 and the modulation method is 16-QAM, the group deinterleaver 1233 may perform deinterleaving based on table 11.
In this case, bits each of which belongs to each of bit groups X55, X15, X112, X122 may constitute a single modulation symbol. Since one bit in each of the bit groups X55, X15, X112, X122 constitutes a single modulation symbol, the deinterleaver 1230 may map bits onto decoding initial values corresponding to the bit groups X55, X15, X112, X122 based on the received single modulation symbol.
The decoder 1240 may perform LDPC decoding by using the output value of the deinterleaver 1230. To achieve this, the decoder 1240 may include an LDPC decoder (not shown) to perform the LDPC decoding.
Specifically, the decoder 1240 is an element corresponding to the encoder 110 of the transmitting apparatus 100 and may correct an error by performing the LDPC decoding by using the LLR value output from the deinterleaver 1230.
For example, the decoder 1240 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 1240 may use a parity check matrix when performing the LDPC decoding. In this case, the parity check matrix used in the decoding may have the same configuration as that of the parity check matrix used in the encoding of the encoder 110, and this has been described above with reference to FIGS. 2 to 4.
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 receiving apparatus 1200 or may be provided by the transmitting apparatus 100.
FIG. 21 is a flowchart to illustrate an interleaving method of a transmitting apparatus according to an exemplary embodiment.
First, an LDPC codeword is generated by LDPC encoding based on a parity check matrix (S1410), and the LDPC codeword is interleaved (S1420).
Then, the interleaved LDPC codeword is mapped onto a modulation symbol (S1430). In this case, a bit included in a predetermined bit group from among a plurality of bit groups constituting the LDPC codeword may be mapped onto a predetermined bit in the modulation symbol.
Each of the plurality of bit groups may be formed of M number of bits, and M may be a common divisor of Nldpc and Kldpc and may be determined to satisfy Qldpc=(Nldpc−Kldpc)/M. Herein, Qldpc is a cyclic shift parameter value regarding columns in a column group of an information word submatrix of the parity check matrix, Nldpc is a length of the LDPC codeword, and Kldpc is a length of information word bits of the LDPC codeword.
Operation S1420 may include interleaving parity bits of the LDPC codeword, dividing the parity-interleaved LDPC codeword by the plurality of bit groups and rearranging the order of the plurality of bit groups in bit group wise, and interleaving the plurality of bit groups the order of which is rearranged.
The order of the plurality of bit groups may be rearranged in bit group wise based on the above-described Equation 21 presented above.
As described above, π(j) in Equation 21 may be determined based on at least one of a length of the LDPC codeword, a modulation method, and a code rate.
For example, when the LDPC codeword has a length of 64800, the modulation method is 16-QAM, and the code rate is 6/15, π(j) may be defined as in table 11.
In addition, when the LDPC codeword has a length of 64800, the modulation method is 16-QAM, and the code rate is 10/15, π(j) may be defined as in table 14.
In addition, when the LDPC codeword has a length of 64800, the modulation method is 16-QAM, and the code rate is 12/15, π(j) may be defined as in table 15.
In addition, when the LDPC codeword has a length of 64800, the modulation method is 64-QAM, and the code rate is 6/15, π(j) may be defined as in table 17.
In addition, when the LDPC codeword has a length of 64800, the modulation method is 64-QAM, and the code rate is 8/15, π(j) may be defined as in table 18.
In addition, when the LDPC codeword has a length of 64800, the modulation method is 64-QAM, and the code rate is 12/15, π(j) may be defined as in table 21.
The interleaving the plurality of bit groups may include: writing the plurality of bit groups in each of a plurality of columns in bit group wise in a column direction, and reading each row of the plurality of columns in which the plurality of bit groups are written in bit group wise in a row direction.
In addition, the interleaving the plurality of bit groups may include: serially write, in the plurality of columns, at least some bit group which is writable in the plurality of columns in bit group wise from among the plurality of bit groups, and then dividing and writing the other bit groups in an area which remains after the at least some bit group is written in the plurality of columns in bit group wise.
A non-transitory computer readable medium, which stores a program for performing the interleaving 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.
At least one of the components, elements or units represented by a block as illustrated in FIGS. 1, 5, 15, 18 and 19 may be embodied as various numbers of hardware, software and/or firmware structures that execute respective functions described above, according to an exemplary embodiment. For example, at least one of 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. Also, at least one of 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 these 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. Further, although a bus is not illustrated in the above block diagrams, communication between the components, elements or units may be performed through the bus. Functional aspects of the above exemplary embodiments may be implemented in algorithms that execute on one or more processors. Furthermore, the components, elements or units represented by a block or processing steps may employ any number of related art techniques for electronics configuration, signal processing and/or control, data processing and the like.
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.

## Claims

1. An interleaving method comprising:
encoding input bits to generate parity bits, wherein the parity bits are generated based on a low density parity check (LDPC) code according to a code rate of 6/15 and a code length of 64800;
interleaving the parity bits;
splitting a codeword comprising the input bits and the interleaved parity bits into a plurality of bit groups;
interleaving the plurality of bit groups to provide an interleaved codeword;
mapping bits of the interleaved codeword onto constellation points for 16-quadrature amplitude modulation (QAM); and
transmitting, using a transmitter, a signal based on the constellation points,
wherein the plurality of bit groups are interleaved the based on a following equation:


Yj=Xπ(j) for (0≦j<Ngroup),


where Xj is a jth bit group among the plurality of bit groups, Yj is a jth bit group among the interleaved plurality of bit groups, Ngroup is a total number of the plurality of bit groups, and π(j) denotes a permutation order for the interleaving of the plurality of bit groups, and
wherein the π(j) is defined as follows:















Order of interleaving



π(j) (0 ≦ j < 180)























Code
j
0
1
2
3
4
5
6
7
8
9
10
11


Rate

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
π(j)
55
146
83
52
62
176
160
68
53
56
81
97




144
57
67
116
59
70
156
172
65
149
155
82




14
37
54
44
63
43
18
47
7
25
34
29




27
38
48
33
22
49
51
60
46
21
4
3




127
101
94
115
105
31
19
177
74
10
145
162




78
171
8
142
178
154
85
107
75
12
9
151




150
110
175
166
131
119
103
139
148
157
114
147




11
92
165
84
168
124
169
2
130
167
153
137












Order of interleaving



π(j) (0 ≦ j < 180)
























Code
j
12
13
14
15
16
17
18
19
20
21
22



Rate

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
π(j)
79
113
163
61
58
69
133
108
66
71
86





138
136
141
111
96
170
90
140
64
159
15





30
26
39
16
41
45
36
0
23
32
28





20
13
50
35
24
40
17
42
6
112
93





102
120
126
95
73
152
129
174
125
72
128





77
117
109
80
106
134
98
1
122
173
161





87
158
121
164
104
89
179
123
118
99
88





143
91
100
5
76
132
135.

2. The interleaving method of claim 1, wherein each of the plurality of bit groups comprises 360 bits.

3. The interleaving method of claim 1, wherein the interleaving of the plurality of bit groups comprises:
interleaving the interleaved plurality of bit groups using a plurality of columns, each plurality of columns comprising a first part and a second part.

4. The interleaving method of claim 1, wherein n(j) is determined based on at least one of the code length, a modulation method for the mapping, and the code rate.