PATENT ABSTRACT
The present invention relates to a method for constructing LPDC code check matrix and encoding and decoding devices using the same. The encoding device encodes the inputted binary information and outputs the encoded system code sequence of position transformation. The encoding device comprises: a matrix multiplication module outputting a check sequence p which is obtained through the binary information sequence m multiplied with a matrix; a sorting index module having N memory units storing index values of a sorting table IDX in turn; and a sorting output module for sorting the m and p and outputting a code word c based on the index value stored in the sorting index table. The present invention constructs the LDPC code check matrix using an algebraic structure, obtaining the LDPC code with stable performance. In addition, the encoding and decoding devices of the present invention occupy less memory, which is preferable for optimization of the devices.

PATENT DESCRIPTION
TECHNICAL FIELD 
       [0001]    The present invention relates to a method for constructing forward error correction code in digital information transmission technology, and more particularly, to a method for constructing Low Density Parity Check (LDPC) code, and encoding and decoding devices using the same. 
       BACKGROUND 
       [0002]    In 1948, Claude Shannon initially proposed his famous “noisy channel encoding theory” which firstly gives the maximum transmission rate of the noisy channel information, i.e., channel capacity. Meanwhile, Shannon also derived the maximum transmission capability of the noisy channel, i.e., the minimum Signal-to-Noise Ratio required by errorless information transmission, which is also called as Shannon&#39;s limit. The Shannon&#39;s limit is the most important feature for evaluating the capability of channel error correction. Closer the error correction performance curve to the Shannon&#39;s limit, the more excellent is the error correction performance. Otherwise, farther to the Shannon&#39;s limit, the worse is the performance. Although the encoding theory of Shannon gives the channel capacity which can be obtained by the optimal encoding scheme, detailed encoding scheme is not provided, and the complexity degree is not described either. 
         [0003]    The Low Density Parity Check (LDPC) is a kind of excellent channel error correction encoding scheme which may approach the Shannon&#39;s limit. The LDPC code is a special linear parity block code, whose parity matrix is “sparse”, i.e. there is only very few non-zero elements (for the binary code, non-zero element is 1), and the remaining elements are all zero. In 1960, Robert Gallager firstly proposed the concept of LDPC code in his Ph.D. dissertation and also suggested two iterated decoding algorithms, thus the LDPC code is also called as Gallager code. Gallager indicated theoretically that the LDPC code may approach the channel capacity with lower complexity by using iterated decoding algorithms (or message delivering algorithms). This is a great invention. However, in the following 30 years, researchers did not pay enough attention to the invention. 
         [0004]    From the current viewpoint, one reasons why the LDPC code was ignored might consist in that the software and hardware levels of the computers were very inferior at that time, and thus the researches could not know the excellent performance of the LDPC code from results of computer simulations; as another reason, the LDPC code needs a larger storage space which could not be born at that time. Additionally, at that time, other codes such as Reed-Solomon code and Hamming code were available, which might be considered as temporarily usable channel encoding schemes, and thus the researchers did not intently forward their researches onto the LDPC code. 
         [0005]    Even today, if it is intended to apply the LDPC code to actual communication systems, the LDPC code still needs to be carefully studied and designed. Because the actual communication systems put some special requirements on the LDPC code, such as hardware schemes of codec with lower complexity, excellent error correction performance, and the like, thus, besides the deep studies on the encoding/decoding method, it is also required to specially limit the construction of the parity matrix of the LDPC code. Generally, there are two methods of constructing the parity matrix of the LDPC code: one is to firstly set some limitations on the attribute of parity matrix such as minimum girth or junction degree distribution etc., and then randomly or pseudo-randomly generate the parity matrix by using the computer searching methods, the searching method takes a long period of time and it can not ensure the convergence of search procedure. Since the generated check matrices have high randomicity level and low regularity level, the check matrices have to be stored during the process of encoding and decoding, thus it increases the memory demand. The other method is to construct the parity matrix of the LDPC code by using the mathematical formulae to make it have regular structure. The method solves the problem of storing the check matrices. However, each row and column of a single check matrix lacks of rule, which is hard for parallel processing. 
       SUMMARY OF INVENTION 
       [0006]    To solve the above problem, the present invention provides a method for constructing a LPDC code check matrix. With the method thereof, a LPDC code check matrix with stable performance can be constructed, and any code rate can be obtained. And the check matrix generated by the method is preferable for encoding and decoding. 
         [0007]    According to an aspect of the invention, a method for constructing a LDPC check matrix is provided, which constructs a fundamental matrix firstly, then extends the fundamental matrix by extending columns firstly and then extending rows to obtain the objective check matrix. 
         [0008]    The method for constructing the check matrix H with dimensions of M×N, comprises the following steps: 
         [0009]    a step of obtaining a common factor set F c  of M and N; 
         [0010]    a step of selecting proper extending ratio KεF c  and generating a fundamental matrix M B ×N B  with dimensions M B ×N B  using any manner, in which M B =M/K, N B =N/K; 
         [0011]    a step of extending by columns and constructing a matrix H R  with dimensions of M B ×N based on the fundamental matrix, which comprises the following steps: for non-zero elements with row-column coordinate (m, n) in the fundamental matrix, selecting a set of column extending coefficients {k i , 0≦k i ≦K−1, iεZ + } which are different from each other, with “1” on positions (m, k i ×N B +n) of the matrix H R ; a step of extending by rows, and extending K rows based on each row of H R , and the method comprising: the t row (0≦t≦K−1) extended by a certain row of H R  is obtained by cyclic shifting t×N B  positions rightward. 
         [0012]    To facilitate encoding, the H R  generated according to the above constructing method can be stored in code table form. Each row of the code table records the positions of “1” in each row of H R . 
         [0013]    According to another aspect of the invention, a method for constructing LDPC code check matrix is provided, which constructs a fundamental matrix firstly, then extends the fundamental matrix by extending rows firstly and then extending columns to obtain the objective check matrix. 
         [0014]    The method for constructing the check matrix H with dimensions of M×N, comprises the following steps: 
         [0015]    a step of obtaining a common factor set F c  of M and N; 
         [0016]    a step of selecting proper extending ratio KεF c  and generating a fundamental matrix M B ×N B  with dimensions of using any manner, in which M B =M/K, N B =N/K, as shown in  FIG. 1 , in which black blocks denote “1” and white blocks represent “0”; 
         [0017]    a step of extending by rows and constructing a matrix H C  with dimensions of M×N B  based on the fundamental matrix, which comprises the following steps: for non-zero elements with row-column coordinate (m, n) in the fundamental matrix, selecting a set of row extending coefficients {k i , 0≦k i ≦K−1, iεZ′} which are different from each other, with “1” on positions (k i ×M B +m, n) of the matrix H C ; 
         [0018]    a step of extending by columns, and extending out K columns by each column of H C , and the step thereof comprises: the t th  column (0≦t≦K−1) extended by a certain column of H C  is obtained by cyclic shifting t×N B  positions downward. 
         [0019]    To facilitate encoding, the H C  generated according to the above constructing method can be stored in code table form. Each row of the code table records the positions of “1” in each column of Hc. 
         [0020]    According to still another aspect of the invention, a method of encoding a check matrix with dimensions of M×N constructed by the method for constructing a LDPC check matrix of the invention is provided, comprising the following steps: 
         [0021]    a step of constructing a sort table IDX with a length of N, in which IDX={I k }, 0≦k&lt;N, 0≦I k &lt;N; 
         [0022]    a step of re-sorting the column of the check matrix with the dimensions of M×N according to the sort table IDX to generate a matrix H′ with dimensions of M×N. The k th  column of the matrix H′ is the I k   th  column of the original M×N matrix. The obtained matrix can be further separated into two sub matrices H′=[H P  H I ], in which H I  is a matrix with a dimension of M×(N−M) and H P  is a matrix with a dimension of M×M; 
         [0023]    a step of inputting sequence, constructing a column vector m with a dimension of (N−M)×1, and calculating the column vector with a dimension of M×1 p T =m T (H P   −1 H I ) T ; a step of outputting the sorting result based on the sorting table IDX in which 
         [0000]    
       
         
           
             
               c 
               
                 I 
                 k 
               
             
             = 
             
               { 
               
                 
                   
                     
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                       k 
                     
                   
                   
                     
                       0 
                       ≤ 
                       k 
                       &lt; 
                       
                         N 
                         - 
                         M 
                       
                     
                   
                 
                 
                   
                     
                       m 
                       
                         k 
                         - 
                         N 
                         + 
                         M 
                       
                     
                   
                   
                     
                       
                         N 
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                         M 
                       
                       ≤ 
                       k 
                       &lt; 
                       
                         N 
                         . 
                       
                     
                   
                 
               
             
           
         
       
     
         [0024]    According to a still further aspect of the invention, an encoding device is provided which encodes inputted binary information using the above encoding method and outputs system code sequence which is encoded and position transformed. The encoding device comprises: a matrix multiply module outputting a check sequence p which is obtained by multiplying the binary information sequence with a matrix (H P   −1 H I ) T , i.e., p T =m T (H P   −1 H I ) T ; a sorting index module having N memory units which store index values of a sorting table IDX in turn; and a sorting output module which sorts m and p based on the index values stored in the sorting index table and outputs a code word c. 
         [0025]    According to a still another aspect of the invention, a method of decoding the system code sequence formed by the above encoding method is provided comprising the following steps: a step of decoding the system code sequence outputted by the encoding device based on the M×N check matrix using any decoding algorithm; and a step of extracting information sequence after decoding using the same sorting table IDX as that for encoding. 
         [0026]    According to a still further aspect of the invention, a decoding device is provided, which decodes the input encoded system code sequence using the above decoding method and outputs the decoded information sequence, the decoding device comprises: a LDPC decoding module which decodes an inputted system code sequence LLR using any LDPC decoding algorithm and outputs a hard-decision sequence ĉ; a sorting index module having N memory units which stores index values of a sorting table IDX; and a sorting output module which extracts an information sequence {circumflex over (m)} from the hard-decision sequence ĉ, i.e., {circumflex over (m)} k =ĉ I     k+M   , 0≦k≦N−M based on the stored index values in the sorting index table. 
         [0027]    The present invention constructs the LDPC code check matrix using an algebraic structure, obtaining the LDPC code with stable performance. In addition, the LDPC code can be obtained using any code rate. Further, the encoding and decoding devices of the invention occupy less memory, which is preferable for optimization of the devices. 
     
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         [0028]    The present invention is described but not limited in conjunction with the embodiments shown in the drawings throughout which the similar reference signs represent the similar elements, in which: 
           [0029]      FIG. 1  is a schematic view of a fundamental matrix according to the first embodiment of the invention; 
           [0030]      FIG. 2  is a schematic view of extending per column of the fundamental matrix according to the first embodiment of the invention; 
           [0031]      FIG. 3  is a schematic view of extending per column of the fundamental matrix and then extending per row according to the first embodiment of the invention; 
           [0032]      FIG. 4  is a schematic view of a structure of the encoder according to the embodiment of the invention; 
           [0033]      FIG. 5  is a schematic view of a structure of the decoder according to the embodiment of the invention; and 
           [0034]      FIG. 6  is a performance curve chart of the LDPC code constructed according to the method of the invention. 
       
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
       [0035]    The preferred embodiment of the invention will be described in detail with reference to accompanying figures. 
         [0036]    The preferred embodiment of the invention adopts the same configuration as the conventional communication system, i.e., the mobile multimedia broadcasting system constructed according to the LDPC code check matrix of the invention comprises an encoder, a modulator, a de-modulator, and a decoder. The data are transmitted through channels. 
         [0037]    The encoder performs forward error correction encoding to the information sequence including encoding by computer software, encoding by embedded hardware and encoding by special hardware. 
         [0038]    The modulator transforms the output of the encoder into signals which are suitable for physical channel transmission. 
         [0039]    The de-modulator transforms the signals received from the channels into the information sequence to be inputted into the decoder. 
         [0040]    The decoder restores the information sequence outputted from the de-modulator into information sequence which may have errors. 
         [0041]    The channel can be any possible data transmission physical channel, including wired communication and wireless communication channels. And the channel includes any possible storage media, including magnetic storage medium, optical storage medium and electronic storage medium. 
         [0042]    Mobile multimedia digital broadcasting system STiMi achieves broadcasting coverage in large area and transmits multicasting services through satellites. And users can realize mobile receiving with a terminal. 
         [0043]    Now an illustrational LDPC code with a code length of 9216 will be described. 
       First Embodiment 
       [0044]    A 4608×9126 check matrix is constructed according to the first method of the invention. 
         [0045]    Firstly, a common factor set of 4608 and 9216 is obtained, which is denoted as F c . 
         [0046]    Secondly, a proper extending ratio K is selected, wherein KεF c . In the present embodiment, the extending ratio is selected to be a common factor 256. Thus, the dimensions of the fundamental matrix are 18×36. The fundamental matrix can be generated in any manner known in the art, as shown in  FIG. 1  in which the black block represents “1” and the white block represents “0”. 
         [0047]    For each non-zero element in the fundamental matrix with dimensions of 18×36, a set of column extending coefficients {k i , 0≦k i ≦255, iεZ + } which are different from each other are selected for extension, to be specific: 
         [0048]    If the non-zero element has a row-column coordinate (m, n), there will be “1” in the positions (m, k i ×36+n), thus after extension, a 18×9216 matrix will be generated as shown in  FIG. 2 . 
         [0049]    After column extension, the generated 18×9216 matrix is extended per row, and each row of the matrix is extended to 256 rows. Specifically, for the first row of the 18×9216 matrix, it is cyclic shift rightward by t×36 to obtain the t th  row of the extended first row, where 0≦t≦255. For the second row, the above extending method is repeated, and according to this rule, all rows thereof are traversed as shown in  FIG. 3 . 
         [0050]    The code table of the 18×9216 matrix generated according to the above method is as follows: 
         [0000]    
       
         
               
               
               
               
               
               
               
             
           
               
                   
                   
               
             
             
               
                   
                 0 
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                 30 
               
               
                   
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                 7 
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                 26 
                 31 
                 5664 
               
               
                   
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                 8 
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                 20 
                 32 
                 8270 
               
               
                   
                 1 
                 6 
                 14 
                 21 
                 3085 
                 8959 
               
               
                   
                 1 
                 15 
                 27 
                 33 
                 9128 
                 9188 
               
               
                   
                 1 
                 9 
                 16 
                 34 
                 8485 
                 9093 
               
               
                   
                 2 
                 6 
                 28 
                 35 
                 4156 
                 7760 
               
               
                   
                 2 
                 10 
                 17 
                 7335 
                 7545 
                 9138 
               
               
                   
                 2 
                 11 
                 22 
                 5278 
                 8728 
                 8962 
               
               
                   
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                 7 
                 2510 
                 4765 
                 8637 
                 8875 
               
               
                   
                 3 
                 4653 
                 4744 
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                 9175 
                 9198 
               
               
                   
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                 23 
                 2349 
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                 9107 
                 9168 
               
               
                   
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                 7 
                 29 
                 5921 
                 7774 
                 8946 
               
               
                   
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                 7224 
                 8074 
                 8339 
                 8725 
                 9212 
               
               
                   
                 4 
                 4169 
                 8650 
                 8780 
                 9023 
                 9159 
               
               
                   
                 5 
                 8 
                 6638 
                 8986 
                 9064 
                 9210 
               
               
                   
                 5 
                 2107 
                 7787 
                 8655 
                 9141 
                 9171 
               
               
                   
                 5 
                 24 
                 5939 
                 8507 
                 8906 
                 9173 
               
               
                   
                   
               
             
          
         
       
     
         [0051]    The encoder encodes based on the above constructed LDPC code check matrix. The encoder comprises: a matrix multiply module  402  outputting a check sequence p which is obtained by multiplying the binary information sequence m with a matrix (H P   −1 H I ) T , i.e., p T =m T (H P   −1 H I ) T ; a sorting index module  403  having 9216 memory units which store index values of a sorting table IDX in turn; and a sorting output module  404  which sorts m and p based on the index values stored in the sorting index table and outputs a code word c, as shown in  FIG. 4 . The flows of the processes conducted by the encoder are as follows: 
         [0052]    constructing a sorting table IDX with a length of 9216, in which IDX={I k }, 0≦k&lt;N, 0≦I k &lt;N, in which N=9216; 
         [0053]    re-sorting the column of the 4608×9216 check matrix according to the sorting table IDX to generate a matrix H′=[H P  H I ] in which H I  is a 4608×(9216−4608) matrix, and H P  is a 4608×4608 matrix. The object of constructing the sorting table IDX is to ensure that the H P   −1  is also a sparse matrix; 
         [0054]    inputting a (9216−4608)×1 column vector as sequence construction column to calculate a 4608×1 column vector p T =m T (H P   −1 H I ) T    
         [0055]    outputting sorting results based on the sort table IDX, in which 
         [0000]    
       
         
           
             
               c 
               
                 I 
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               { 
               
                 
                   
                     
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                       k 
                     
                   
                   
                     
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                       ≤ 
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                       &lt; 
                       
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                         - 
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                         M 
                       
                     
                   
                   
                     
                       
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                       &lt; 
                       
                         N 
                         . 
                       
                     
                   
                 
               
             
           
         
       
     
         [0056]    The system code sequence which is position-transformed after encoding is transferred to a decoder through channels and decodes therein. 
         [0057]    As shown in  FIG. 5 , the decoder comprises: a LDPC decoding module  502  which decodes an inputted system code sequence LLR using any kind of LDPC decoding algorithm and outputs a hard-decision sequence ĉ; a sorting index module  503  having 9216 memory units which stores index values of the sorting table IDX; and a sorting output module  503  which extracts an information sequence {circumflex over (m)} from the hard-decision sequence ĉ based on the stored index values in the sorting index table. 
         [0058]    The flows of the process conducted by the decoder are as follows: 
         [0059]    In light of the 4608×9216 check matrix, the inputted system code sequence is decoded using any kind of decoding algorithm, and the decoded hard-decision sequence {ĉ i , 0≦i≦9216} is outputted; 
         [0060]    The decoded binary information sequence {{circumflex over (m)} k , 0≦k≦4607} is extracted using the same sort table IDX as that stored in the encoder, in which {circumflex over (m)} k =ĉ k+4608 , 0≦k&lt;4608. 
         [0061]    For the 4608×9216 check matrix, the sorting table IDX in the encoding device is as follows: 
         [0000]    
       
         
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                   
               
             
             
               
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                 48 
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                 1958 
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                 109 
               
               
                 681 
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                 213 
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                 683 
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                 1098 
                 1968 
                 6695 
                 3903 
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                 893 
                 6699 
               
               
                 6700 
                 4278 
                 1051 
                 6703 
                 1971 
                 6705 
                 1387 
                 3224 
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                 4523 
                 1268 
                 6712 
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                 3640 
                 2522 
                 1973 
                 6717 
                 1269 
                 6719 
               
               
                 6720 
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                 2729 
                 2523 
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                 188 
                 685 
                 352 
                 3280 
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                 290 
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                 1978 
                 3141 
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                 1052 
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                 6740 
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                 183 
                 6744 
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                 3486 
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                 4241 
                 689 
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                 6755 
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                 4125 
                 2731 
               
               
                 6760 
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                 1257 
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                 291 
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                 4335 
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                 112 
               
               
                 6780 
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                 1991 
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                 148 
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                 1053 
                 2733 
                 6796 
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                 293 
               
               
                 4387 
                 891 
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                 1998 
                 3064 
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                 3230 
                 43 
                 4098 
                 896 
                 4182 
                 954 
                 1329 
                 6817 
                 2001 
                 4486 
               
               
                 3215 
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                 6822 
                 3282 
                 2002 
                 295 
                 2004 
                 4427 
                 6828 
                 3818 
                 3494 
                 375 
                 6832 
                 1365 
                 3063 
                 2005 
                 699 
                 3373 
                 3374 
                 1326 
               
               
                 3953 
                 6841 
                 2528 
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                 6844 
                 2529 
                 4545 
                 2008 
                 2443 
                 6849 
                 1399 
                 855 
                 4285 
                 4059 
                 4218 
                 6855 
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                 6857 
                 3561 
                 296 
               
               
                 6860 
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                 2831 
                 1296 
                 702 
                 3516 
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                 6868 
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                 3774 
                 2014 
                 6872 
                 3235 
                 149 
                 3484 
                 150 
                 6877 
                 299 
                 4410 
               
               
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                 2463 
                 3145 
                 3867 
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                 6888 
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                 3641 
                 2424 
                 2019 
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                 2021 
                 2897 
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                 185 
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                 856 
               
               
                 300 
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                 75 
                 6946 
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                 709 
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                 8545 
                 8546 
                 8547 
                 8548 
                 8549 
                 8550 
                 3907 
                 972 
                 2778 
                 8554 
                 8555 
                 8556 
                 3069 
                 829 
                 356 
               
               
                 8560 
                 3990 
                 8562 
                 4458 
                 8564 
                 2595 
                 8566 
                 3301 
                 801 
                 222 
                 8570 
                 8571 
                 8572 
                 4027 
                 8574 
                 8575 
                 8576 
                 8577 
                 1435 
                 8579 
               
               
                 8580 
                 8581 
                 3183 
                 8583 
                 8584 
                 8585 
                 8586 
                 1006 
                 8588 
                 332 
                 8590 
                 8591 
                 8592 
                 8593 
                 8594 
                 2914 
                 8596 
                 3864 
                 8598 
                 2351 
               
               
                 8600 
                 3843 
                 8602 
                 1324 
                 2352 
                 8605 
                 8606 
                 1068 
                 8608 
                 2908 
                 8610 
                 8611 
                 8612 
                 8613 
                 8614 
                 8615 
                 8616 
                 472 
                 8618 
                 363 
               
               
                 8620 
                 8621 
                 8622 
                 4013 
                 8624 
                 162 
                 8626 
                 3037 
                 2597 
                 8629 
                 2598 
                 8631 
                 8632 
                 8633 
                 8634 
                 1244 
                 2356 
                 8637 
                 8638 
                 2599 
               
               
                 804 
                 8641 
                 8642 
                 8643 
                 8644 
                 2358 
                 8646 
                 8647 
                 8648 
                 8649 
                 8650 
                 399 
                 8652 
                 8653 
                 1252 
                 8655 
                 8656 
                 8657 
                 8658 
                 3018 
               
               
                 8660 
                 2780 
                 8662 
                 8663 
                 2600 
                 8665 
                 2848 
                 93 
                 4515 
                 8669 
                 8670 
                 806 
                 2361 
                 8673 
                 8674 
                 8675 
                 2362 
                 8677 
                 8678 
                 3550 
               
               
                 8680 
                 8681 
                 8682 
                 8683 
                 2363 
                 8685 
                 8686 
                 8687 
                 8688 
                 3555 
                 2676 
                 2364 
                 8692 
                 8693 
                 8694 
                 3713 
                 8696 
                 935 
                 3302 
                 4385 
               
               
                 8700 
                 8701 
                 2601 
                 8703 
                 8704 
                 8705 
                 8706 
                 8707 
                 2365 
                 8709 
                 8710 
                 8711 
                 807 
                 8713 
                 8714 
                 3608 
                 8716 
                 2367 
                 8718 
                 357 
               
               
                 8720 
                 8721 
                 2636 
                 8723 
                 8724 
                 876 
                 3669 
                 8727 
                 8728 
                 8729 
                 8730 
                 2604 
                 8732 
                 382 
                 8734 
                 8735 
                 824 
                 8737 
                 508 
                 2607 
               
               
                 8740 
                 1401 
                 8742 
                 808 
                 8744 
                 8745 
                 8746 
                 8747 
                 2369 
                 2370 
                 8750 
                 8751 
                 8752 
                 2608 
                 8754 
                 2436 
                 2371 
                 8757 
                 8758 
                 8759 
               
               
                 3497 
                 8761 
                 8762 
                 2881 
                 3186 
                 8765 
                 459 
                 975 
                 937 
                 8769 
                 8770 
                 8771 
                 8772 
                 457 
                 4446 
                 878 
                 8776 
                 3663 
                 8778 
                 2373 
               
               
                 2610 
                 8781 
                 8782 
                 4170 
                 2374 
                 8785 
                 8786 
                 2850 
                 8788 
                 8789 
                 8790 
                 8791 
                 2784 
                 8793 
                 8794 
                 8795 
                 8796 
                 3231 
                 335 
                 8799 
               
               
                 3502 
                 810 
                 3303 
                 4271 
                 2434 
                 2377 
                 8806 
                 8807 
                 8808 
                 8809 
                 3420 
                 8811 
                 8812 
                 8813 
                 4481 
                 2379 
                 1183 
                 8817 
                 8818 
                 3498 
               
               
                 336 
                 8821 
                 8822 
                 880 
                 4100 
                 2381 
                 8826 
                 393 
                 8828 
                 8829 
                 8830 
                 8831 
                 8832 
                 8833 
                 3741 
                 8835 
                 8836 
                 8837 
                 8838 
                 2613 
               
               
                 383 
                 2787 
                 8842 
                 8843 
                 3304 
                 8845 
                 2382 
                 8847 
                 8848 
                 3509 
                 8850 
                 4357 
                 8852 
                 8853 
                 8854 
                 171 
                 2384 
                 8857 
                 8858 
                 1136 
               
               
                 8860 
                 40 
                 8862 
                 8863 
                 8864 
                 8865 
                 8866 
                 2916 
                 8868 
                 8869 
                 8870 
                 8871 
                 3499 
                 8873 
                 8874 
                 8875 
                 8876 
                 2788 
                 3236 
                 3010 
               
               
                 2615 
                 8881 
                 2616 
                 4535 
                 8884 
                 8885 
                 8886 
                 165 
                 8888 
                 8889 
                 4566 
                 2617 
                 2387 
                 8893 
                 8894 
                 3348 
                 4107 
                 2388 
                 8898 
                 3066 
               
               
                 8900 
                 939 
                 8902 
                 8903 
                 8904 
                 3188 
                 8906 
                 8907 
                 8908 
                 1454 
                 8910 
                 8911 
                 2790 
                 4259 
                 8914 
                 8915 
                 2618 
                 8917 
                 1008 
                 3919 
               
               
                 3210 
                 3830 
                 8922 
                 2853 
                 8924 
                 8925 
                 8926 
                 2619 
                 339 
                 8929 
                 8930 
                 1289 
                 8932 
                 2620 
                 8934 
                 2391 
                 3344 
                 8937 
                 8938 
                 8939 
               
               
                 8940 
                 8941 
                 8942 
                 8943 
                 8944 
                 4569 
                 8946 
                 4590 
                 100 
                 3803 
                 8950 
                 1070 
                 882 
                 8953 
                 3191 
                 8955 
                 8956 
                 8957 
                 8958 
                 8959 
               
               
                 3011 
                 8961 
                 8962 
                 2622 
                 815 
                 8965 
                 8966 
                 4002 
                 8968 
                 2394 
                 8970 
                 8971 
                 8972 
                 8973 
                 816 
                 8975 
                 8976 
                 8977 
                 8978 
                 8979 
               
               
                 8980 
                 8981 
                 8982 
                 364 
                 1076 
                 817 
                 8986 
                 941 
                 4381 
                 8989 
                 8990 
                 2449 
                 8992 
                 2623 
                 8994 
                 8995 
                 8996 
                 8997 
                 8998 
                 2397 
               
               
                 2398 
                 9001 
                 9002 
                 64 
                 9004 
                 2399 
                 9006 
                 2400 
                 9008 
                 9009 
                 9010 
                 9011 
                 9012 
                 3013 
                 9014 
                 9015 
                 9016 
                 9017 
                 4529 
                 1214 
               
               
                 9020 
                 9021 
                 9022 
                 3347 
                 3658 
                 1432 
                 3777 
                 9027 
                 9028 
                 9029 
                 9030 
                 9031 
                 9032 
                 9033 
                 3659 
                 2401 
                 340 
                 9037 
                 9038 
                 1284 
               
               
                 9040 
                 2403 
                 4228 
                 4092 
                 980 
                 9045 
                 9046 
                 4417 
                 3430 
                 3193 
                 9050 
                 9051 
                 9052 
                 9053 
                 1345 
                 3425 
                 9056 
                 9057 
                 9058 
                 1408 
               
               
                 960 
                 9061 
                 2624 
                 9063 
                 9064 
                 1292 
                 9066 
                 9067 
                 4479 
                 9069 
                 9070 
                 2625 
                 2406 
                 9073 
                 9074 
                 3426 
                 1231 
                 9077 
                 9078 
                 365 
               
               
                 2407 
                 9081 
                 9082 
                 9083 
                 9084 
                 1114 
                 9086 
                 9087 
                 2658 
                 9089 
                 9090 
                 9091 
                 9092 
                 3900 
                 9094 
                 4383 
                 9096 
                 9097 
                 9098 
                 9099 
               
               
                 9100 
                 2627 
                 9102 
                 9103 
                 9104 
                 9105 
                 4076 
                 172 
                 3549 
                 9109 
                 9110 
                 3306 
                 9112 
                 1227 
                 9114 
                 820 
                 821 
                 4332 
                 2413 
                 9119 
               
               
                 9120 
                 9121 
                 9122 
                 9123 
                 2629 
                 9125 
                 9126 
                 9127 
                 1368 
                 3603 
                 9130 
                 9131 
                 4519 
                 9133 
                 2856 
                 9135 
                 9136 
                 9137 
                 9138 
                 9139 
               
               
                 9140 
                 9141 
                 3759 
                 2631 
                 2414 
                 9145 
                 2793 
                 9147 
                 9148 
                 2415 
                 9150 
                 9151 
                 822 
                 486 
                 9154 
                 9155 
                 3014 
                 9157 
                 9158 
                 9159 
               
               
                 2417 
                 9161 
                 9162 
                 9163 
                 1072 
                 9165 
                 9166 
                 9167 
                 2632 
                 9169 
                 9170 
                 9171 
                 9172 
                 9173 
                 9174 
                 9175 
                 2457 
                 9177 
                 9178 
                 9179 
               
               
                 2418 
                 9181 
                 9182 
                 9183 
                 4233 
                 9185 
                 1333 
                 4302 
                 3307 
                 9189 
                 2420 
                 9191 
                 9192 
                 9193 
                 4207 
                 9195 
                 2421 
                 9197 
                 9198 
                 1009 
               
               
                 435 
                 1224 
                 9202 
                 9203 
                 1073 
                 9205 
                 9206 
                 9207 
                 4351 
                 9209 
                 4276 
                 9211 
                 2427 
                 9213 
                 3696 
                 9215 
               
               
                   
               
             
          
         
       
     
       Second Embodiment 
       [0062]    A 2304×9216 check matrix is constructed according to a first method of the invention. 
         [0063]    Firstly, a common factor set of 2304 and 9216 is obtained, which is denoted as F c . 
         [0064]    Secondly, a proper extending ratio K is selected, KεF c . In the present embodiment, the extending ratio is selected to be a common factor 256. The dimensions of the fundamental matrix are 9×36. The fundamental matrix can be generated in any way known in the art. 
         [0065]    For each non-zero element in the fundamental matrix with dimensions of 18×36, a set of column extending coefficients {k i , 0≦k i ≦255, iεZ + } which are different from each other, are selected for extension, specifically: 
         [0066]    If the non-zero element has a row-column coordinate (m, n), there will be “1” in the positions (m, k i ×36+n), thus after the extension, to be a 9×9216 matrix will be generated. 
         [0067]    After column extension, the generated 9×9216 matrix is extended by rows, and each row of the matrix is extended to 256 rows. Specifically, for the first row of the 9×9216 matrix, it is cyclic shift rightward by t×36 to obtain the t th  row of the extended first row, where 0≦t≦255. For the second row, the above extending method is repeated, and according to this rule, all rows thereof are traversed. 
         [0068]    The code table of the 9×9216 matrix generated according to the above method is as follows: 
         [0000]    
       
         
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                   
               
             
             
               
                 0 
                 3 
                 6 
                 12 
                 16 
                 18 
                 21 
                 24 
                 27 
                 31 
                 34 
                 7494 
               
               
                 0 
                 4 
                 10 
                 13 
                 25 
                 28 
                 5233 
                 6498 
                 7018 
                 8358 
                 8805 
                 9211 
               
               
                 0 
                 7 
                 11 
                 19 
                 22 
                 6729 
                 6831 
                 7913 
                 8944 
                 9013 
                 9133 
                 9184 
               
               
                 1 
                 3 
                 8 
                 14 
                 17 
                 20 
                 29 
                 32 
                 5000 
                 5985 
                 7189 
                 7906 
               
               
                 1 
                 9 
                 4612 
                 5523 
                 6456 
                 7879 
                 8487 
                 8952 
                 9081 
                 9129 
                 9164 
                 9214 
               
               
                 1 
                 5 
                 23 
                 26 
                 33 
                 35 
                 7135 
                 8525 
                 8983 
                 9015 
                 9048 
                 9154 
               
               
                 2 
                 3 
                 30 
                 3652 
                 4067 
                 5123 
                 7808 
                 7838 
                 8231 
                 8474 
                 8791 
                 9162 
               
               
                 2 
                 35 
                 3774 
                 4310 
                 6827 
                 6917 
                 8264 
                 8416 
                 8542 
                 8834 
                 9044 
                 9089 
               
               
                 2 
                 15 
                 631 
                 1077 
                 6256 
                 7859 
                 8069 
                 8160 
                 8657 
                 8958 
                 9094 
                 9116 
               
               
                   
               
             
          
         
       
     
         [0069]    The encoder encodes based on the above constructed LDPC code check matrix. The encoder comprises: a matrix multiply module outputting a check sequence p which is obtained by multiplying the binary information sequence m with a matrix (H P   −1 H I ) T , i.e., p T =m T (H P   −1 H I ) T ; a sorting index module having 9216 memory units which store index values of a sorting table IDX in turn; and a sorting output module which sorts m and p based on the index values stored in the sorting index table and outputs a code word c. The detailed encoding steps are as follows: 
         [0070]    constructing a sorting table IDX with a length of 9216, in which IDX={I k }, 0≦k&lt;N, 0≦I k &lt;N, i.e., N=9216; 
         [0071]    re-sorting the column of the 2304×9216 check matrix according to the sorting table IDX to generate a matrix H′=[H P  H I ] in which H I  is a 2304×(9216−2304) matrix, and H P  is a 2304×2304 matrix. The object of constructing the sorting table IDX is to ensure that the H P   −1  is also a sparse matrix; 
         [0072]    inputting sequence to construct (9216−2304)×1 column vector m, calculating 2304×1 column vector p T =m T (H P   −1 H I ) T ;
       outputting sorting results based on the sorting table IDX, in which       
 
         [0000]    
       
         
           
             
               c 
               
                 I 
                 k 
               
             
             = 
             
               { 
               
                 
                   
                     
                       p 
                       k 
                     
                   
                   
                     
                       0 
                       ≤ 
                       k 
                       &lt; 
                       2304 
                     
                   
                 
                 
                   
                     
                       m 
                       
                         k 
                         - 
                         2304 
                       
                     
                   
                   
                     
                       2304 
                       ≤ 
                       k 
                       &lt; 
                       9216. 
                     
                   
                 
               
             
           
         
       
     
         [0074]    The system code sequence which is position-transformed after encoding is transferred to a decoder through channels and decodes therein, specifically: 
         [0075]    In light of the 2304×9216 check matrix, the inputted system code sequence is decoded using any kind of decoding algorithm, and the decoded hard-decision sequence {ĉ i , 0≦i≦9216} is outputted; 
         [0076]    The decoded binary information sequence {{circumflex over (m)} k , 0≦k≦6911} is extracted using the same sorting table IDX as that stored in the encoder, in which {circumflex over (m)} k =ĉ I     k+2304   , 0≦k&lt;6912. 
         [0077]    Since the decoder has the same configuration as the decoder in the above embodiment, the detailed description is omitted. 
         [0078]    For the 2304×9216 check matrix, the sorting table IDX in the encoder is as follows: 
         [0000]    
       
         
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                   
               
             
             
               
                 0 
                 1 
                 2 
                 4 
                 5 
                 7 
                 9 
                 10 
                 11 
                 13 
                 15 
                 19 
                 22 
                 23 
                 25 
                 26 
                 28 
                 33 
                 35 
                 37 
               
               
                 38 
                 40 
                 41 
                 42 
                 45 
                 59 
                 62 
                 69 
                 71 
                 72 
                 74 
                 79 
                 80 
                 81 
                 82 
                 83 
                 85 
                 87 
                 91 
                 94 
               
               
                 97 
                 100 
                 109 
                 110 
                 112 
                 113 
                 114 
                 117 
                 131 
                 134 
                 141 
                 143 
                 144 
                 151 
                 152 
                 155 
                 157 
                 163 
                 166 
                 169 
               
               
                 172 
                 174 
                 182 
                 185 
                 186 
                 193 
                 194 
                 219 
                 224 
                 225 
                 229 
                 230 
                 233 
                 236 
                 245 
                 246 
                 248 
                 254 
                 258 
                 260 
               
               
                 265 
                 267 
                 291 
                 292 
                 296 
                 305 
                 317 
                 318 
                 320 
                 324 
                 331 
                 332 
                 333 
                 335 
                 337 
                 343 
                 346 
                 349 
                 352 
                 354 
               
               
                 363 
                 364 
                 377 
                 380 
                 383 
                 389 
                 390 
                 392 
                 396 
                 400 
                 403 
                 405 
                 407 
                 409 
                 410 
                 415 
                 418 
                 421 
                 424 
                 426 
               
               
                 432 
                 436 
                 437 
                 439 
                 442 
                 443 
                 445 
                 449 
                 451 
                 460 
                 468 
                 475 
                 477 
                 479 
                 481 
                 482 
                 487 
                 490 
                 493 
                 496 
               
               
                 498 
                 510 
                 512 
                 513 
                 517 
                 541 
                 546 
                 549 
                 553 
                 563 
                 566 
                 570 
                 573 
                 575 
                 582 
                 584 
                 585 
                 589 
                 615 
                 620 
               
               
                 625 
                 626 
                 627 
                 635 
                 641 
                 642 
                 644 
                 651 
                 657 
                 661 
                 665 
                 668 
                 677 
                 680 
                 686 
                 688 
                 690 
                 692 
                 699 
                 720 
               
               
                 724 
                 727 
                 729 
                 730 
                 731 
                 733 
                 734 
                 739 
                 745 
                 748 
                 750 
                 756 
                 757 
                 760 
                 761 
                 763 
                 765 
                 767 
                 769 
                 779 
               
               
                 781 
                 782 
                 784 
                 789 
                 791 
                 792 
                 794 
                 796 
                 799 
                 802 
                 803 
                 805 
                 811 
                 817 
                 821 
                 828 
                 832 
                 835 
                 837 
                 839 
               
               
                 841 
                 850 
                 856 
                 857 
                 864 
                 871 
                 875 
                 877 
                 883 
                 884 
                 892 
                 906 
                 908 
                 913 
                 928 
                 939 
                 944 
                 945 
                 949 
                 950 
               
               
                 956 
                 965 
                 968 
                 975 
                 981 
                 985 
                 989 
                 992 
                 1000 
                 1001 
                 1004 
                 1014 
                 1016 
                 1021 
                 1023 
                 1050 
                 1057 
                 1061 
                 1069 
                 1072 
               
               
                 1082 
                 1086 
                 1090 
                 1094 
                 1095 
                 1120 
                 1122 
                 1129 
                 1130 
                 1141 
                 1144 
                 1152 
                 1153 
                 1157 
                 1159 
                 1161 
                 1163 
                 1165 
                 1174 
                 1178 
               
               
                 1180 
                 1185 
                 1189 
                 1192 
                 1193 
                 1194 
                 1197 
                 1211 
                 1214 
                 1223 
                 1224 
                 1232 
                 1233 
                 1235 
                 1237 
                 1243 
                 1252 
                 1261 
                 1264 
                 1265 
               
               
                 1266 
                 1269 
                 1283 
                 1286 
                 1296 
                 1304 
                 1307 
                 1309 
                 1321 
                 1324 
                 1334 
                 1338 
                 1342 
                 1361 
                 1364 
                 1371 
                 1377 
                 1381 
                 1382 
                 1385 
               
               
                 1388 
                 1393 
                 1396 
                 1397 
                 1398 
                 1400 
                 1409 
                 1410 
                 1417 
                 1419 
                 1424 
                 1432 
                 1433 
                 1436 
                 1437 
                 1439 
                 1446 
                 1453 
                 1463 
                 1465 
               
               
                 1468 
                 1469 
                 1478 
                 1479 
                 1486 
                 1496 
                 1505 
                 1508 
                 1516 
                 1518 
                 1532 
                 1535 
                 1547 
                 1548 
                 1553 
                 1555 
                 1559 
                 1561 
                 1562 
                 1574 
               
               
                 1576 
                 1585 
                 1588 
                 1589 
                 1590 
                 1593 
                 1599 
                 1610 
                 1620 
                 1629 
                 1633 
                 1639 
                 1640 
                 1645 
                 1648 
                 1660 
                 1662 
                 1665 
                 1685 
                 1688 
               
               
                 1692 
                 1701 
                 1702 
                 1703 
                 1705 
                 1706 
                 1711 
                 1717 
                 1720 
                 1733 
                 1734 
                 1741 
                 1748 
                 1760 
                 1770 
                 1772 
                 1773 
                 1774 
                 1777 
                 1780 
               
               
                 1785 
                 1788 
                 1789 
                 1791 
                 1792 
                 1795 
                 1806 
                 1809 
                 1839 
                 1842 
                 1846 
                 1848 
                 1852 
                 1854 
                 1863 
                 1867 
                 1875 
                 1885 
                 1887 
                 1889 
               
               
                 1897 
                 1901 
                 1904 
                 1912 
                 1913 
                 1914 
                 1916 
                 1918 
                 1920 
                 1921 
                 1924 
                 1929 
                 1932 
                 1933 
                 1935 
                 1936 
                 1939 
                 1943 
                 1944 
                 1948 
               
               
                 1955 
                 1957 
                 1958 
                 1972 
                 1986 
                 1989 
                 1991 
                 1992 
                 1994 
                 1996 
                 2001 
                 2004 
                 2007 
                 2008 
                 2011 
                 2018 
                 2022 
                 2045 
                 2058 
                 2065 
               
               
                 2067 
                 2077 
                 2080 
                 2081 
                 2084 
                 2092 
                 2093 
                 2094 
                 2108 
                 2123 
                 2124 
                 2128 
                 2135 
                 2137 
                 2138 
                 2146 
                 2149 
                 2152 
                 2153 
                 2156 
               
               
                 2160 
                 2165 
                 2169 
                 2170 
                 2171 
                 2173 
                 2180 
                 2188 
                 2192 
                 2193 
                 2202 
                 2209 
                 2213 
                 2221 
                 2224 
                 2225 
                 2228 
                 2235 
                 2236 
                 2237 
               
               
                 2238 
                 2253 
                 2255 
                 2259 
                 2263 
                 2272 
                 2273 
                 2274 
                 2275 
                 2276 
                 2278 
                 2281 
                 2286 
                 2291 
                 2294 
                 2296 
                 2299 
                 2307 
                 2309 
                 2310 
               
               
                 2311 
                 2315 
                 2316 
                 2320 
                 2325 
                 2331 
                 2332 
                 2335 
                 2346 
                 2365 
                 2368 
                 2372 
                 2382 
                 2386 
                 2404 
                 2417 
                 2418 
                 2429 
                 2430 
                 2435 
               
               
                 2438 
                 2439 
                 2440 
                 2446 
                 2447 
                 2451 
                 2461 
                 2465 
                 2476 
                 2477 
                 2480 
                 2485 
                 2489 
                 2490 
                 2494 
                 2499 
                 2501 
                 2504 
                 2513 
                 2516 
               
               
                 2519 
                 2526 
                 2533 
                 2537 
                 2543 
                 2548 
                 2549 
                 2552 
                 2555 
                 2561 
                 2562 
                 2569 
                 2576 
                 2591 
                 2598 
                 2605 
                 2609 
                 2620 
                 2629 
                 2633 
               
               
                 2634 
                 2637 
                 2643 
                 2644 
                 2652 
                 2654 
                 2655 
                 2659 
                 2661 
                 2664 
                 2669 
                 2675 
                 2677 
                 2686 
                 2689 
                 2692 
                 2693 
                 2701 
                 2705 
                 2706 
               
               
                 2709 
                 2723 
                 2726 
                 2730 
                 2739 
                 2740 
                 2742 
                 2748 
                 2749 
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                 8615 
                 8616 
                 8617 
                 8618 
                 8619 
               
               
                 8620 
                 314 
                 8622 
                 8623 
                 8624 
                 8625 
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                 8628 
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                 8640 
                 1365 
                 8642 
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                 1366 
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                 1367 
                 8656 
                 8657 
                 1368 
                 1489 
               
               
                 1369 
                 8661 
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                 8664 
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                 8666 
                 8667 
                 8668 
                 116 
                 8670 
                 8671 
                 8672 
                 1740 
                 8674 
                 8675 
                 8676 
                 8677 
                 8678 
                 8679 
               
               
                 8680 
                 24 
                 8682 
                 391 
                 8684 
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                 8691 
                 8692 
                 8693 
                 8694 
                 1370 
                 8696 
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                 8700 
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                 8705 
                 8706 
                 8707 
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                 2199 
                 8710 
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                 315 
                 92 
                 8716 
                 8717 
                 8718 
                 1372 
               
               
                 8720 
                 8721 
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                 8724 
                 8725 
                 8726 
                 8727 
                 8728 
                 1373 
                 8730 
                 8731 
                 334 
                 8733 
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                 8739 
               
               
                 8740 
                 8741 
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                 8743 
                 1925 
                 8745 
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                 8749 
                 358 
                 1374 
                 8752 
                 8753 
                 8754 
                 8755 
                 8756 
                 8757 
                 8758 
                 8759 
               
               
                 8760 
                 8761 
                 1375 
                 8763 
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                 1742 
                 8767 
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                 8771 
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                 8780 
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                 1376 
                 8788 
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                 316 
                 8798 
                 8799 
               
               
                 8800 
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                 1438 
                 8815 
                 1890 
                 8817 
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                 8819 
               
               
                 8820 
                 8821 
                 8822 
                 1378 
                 8824 
                 1379 
                 8826 
                 8827 
                 93 
                 8829 
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                 8833 
                 1843 
                 8835 
                 8836 
                 1380 
                 8838 
                 8839 
               
               
                 8840 
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                 86 
                 1801 
                 8879 
               
               
                 8880 
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                 1947 
                 8885 
                 1440 
                 8887 
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                 8 
                 8896 
                 8897 
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                 8900 
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                 1441 
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                 1844 
                 8911 
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                 8919 
               
               
                 8920 
                 8921 
                 1611 
                 8923 
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                 1383 
                 8937 
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                 8940 
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                 1384 
                 319 
                 8948 
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                 1386 
                 2218 
                 8986 
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                 1442 
                 8989 
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                 1802 
                 8992 
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                 1387 
                 8999 
               
               
                 9000 
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                 9020 
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                 9027 
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                 9030 
                 88 
                 9032 
                 465 
                 9034 
                 9035 
                 1389 
                 9037 
                 1443 
                 9039 
               
               
                 9040 
                 9041 
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                 9046 
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                 9050 
                 9051 
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                 9054 
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                 9056 
                 9057 
                 1650 
                 9059 
               
               
                 9060 
                 2265 
                 9062 
                 9063 
                 9064 
                 1983 
                 9066 
                 9067 
                 9068 
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                 9070 
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                 9080 
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                 1390 
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                 9090 
                 1563 
                 9092 
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                 1743 
                 9101 
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                 9110 
                 9111 
                 9112 
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                 9119 
               
               
                 9120 
                 9121 
                 1391 
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                 9128 
                 1445 
                 9130 
                 9131 
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                 9133 
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                 9135 
                 9136 
                 9137 
                 9138 
                 9139 
               
               
                 9140 
                 9141 
                 9142 
                 9143 
                 9144 
                 9145 
                 9146 
                 336 
                 9148 
                 9149 
                 9150 
                 9151 
                 1564 
                 9153 
                 9154 
                 9155 
                 1888 
                 9157 
                 9158 
                 9159 
               
               
                 9160 
                 9161 
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                 2134 
                 9175 
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                 9180 
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                 9200 
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                 9208 
                 9209 
                 9210 
                 9211 
                 9212 
                 9213 
                 1392 
                 9215 
               
               
                   
               
             
          
         
       
     
         [0079]    Performances of the LDPC code constructed based on above two embodiments are shown in  FIG. 6 . According to theoretical analysis, when the error code rate of a (3, 6) regular LDPC code with a code rate of ½ approaches the theoretical limit of 10e-5, Eb/No is 1.12 dB. From the simulation result in the figure, when the error code rate of the LDPC code constructed according to the constructing method of the present invention is 10e-5, the Eb/No is about 1.6 dB which is approximating theoretical limit and has very excellent performance. And the LDPC code with a code rate of ¾ has the similar conclusion. 
       Third Embodiment 
       [0080]    A 2304×9216 check matrix is constructed according to another method of the invention. 
         [0081]    Firstly, a common factor set of 2304 and 9216 is obtained, which is denoted as F c . 
         [0082]    Secondly, a proper extending ratio K is selected, wherein KεF c . In the present embodiment, the extending ratio is selected to be a common factor 256. Thus, the fundamental matrix with dimensions of 9×36 is obtained. The fundamental matrix can be generated in any manner known in the art. 
         [0083]    For each non-zero element in the fundamental matrix with dimensions of 18×36, a set of row extending coefficients {k i , 0≦k i ≦255, iεZ + } which are different from each other are selected for extension, in which 0≦k i ≦255. Specifically: 
         [0084]    If the non-zero element has a row-column coordinate (m, n), there will be “1” in the positions (k i ×9+m, n), thus after the extension, a 2304×36 matrix will be generated. 
         [0085]    After row extension, the generated 2304×36 matrix is extended by columns, and each column of the matrix is extended to 256 columns. Specifically, for the first column of the 2304×36 matrix, it is cyclic shift rightward by t×9 to obtain the t th  column of the extended first column, where 0≦t≦255. For the second column, the above extending method is repeated, and according to this rule, all columns thereof are traversed, thus generating a 2304×9216 check matrix. 
         [0086]    Although the present invention is described in conjunction with the examples and embodiments, the present invention is not intended to be limited thereto. On the contrary, the present invention obviously covers the various modifications and may equivalences, which are all enclosed in the scope of the following claims.