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CN102055485A - Quasi-cyclic low-density parity-check (QC-LDPC) code and correcting and linear coding method thereof - Google Patents

Quasi-cyclic low-density parity-check (QC-LDPC) code and correcting and linear coding method thereof Download PDF

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CN102055485A
CN102055485A CN2010106058385A CN201010605838A CN102055485A CN 102055485 A CN102055485 A CN 102055485A CN 2010106058385 A CN2010106058385 A CN 2010106058385A CN 201010605838 A CN201010605838 A CN 201010605838A CN 102055485 A CN102055485 A CN 102055485A
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吴晓富
崔龙
赵春明
尤肖虎
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PLA University of Science and Technology
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Abstract

准循环低密度奇偶校验码及其修正和线性编码方法，该低密度校验码维度大于2的变量节点都是信息节点，而维度为2的变量节点在二分图上形成一个首尾相连的大环。其修正方法实施步骤包括：在维度为2的大环上任选一条边，将其截去，也即在低密度校验矩阵的相应位置填0，从而得到该编码一种修正结构。修正后的线性编码方法实施步骤包括：首先利用输入信息矢量s，与校验矩阵的列重大于2的部分做矢量与矩阵的相乘运算得到中间矢量u；变量节点维度为1的编码矢量直接截取中间矢量u的相应位置得到；变量节点维度为2的编码矢量则通过其在二分图上的大环特性由启动位开始逐比特计算可得，将两部分编码矢量拼合起来最终形成编码矢量。

The quasi-cyclic low-density parity-check code and its correction and linear coding method, the variable nodes with a dimension greater than 2 in the low-density check code are all information nodes, and the variable nodes with a dimension of 2 form a large end-to-end connection on the bipartite graph ring. The implementation steps of the correction method include: selecting a side on the large ring with a dimension of 2 and truncating it, that is, filling 0 in the corresponding position of the low-density parity check matrix, so as to obtain a correction structure of the code. The implementation steps of the modified linear coding method include: firstly, using the input information vector s, multiplying the vector and the matrix with the part of the check matrix whose column weight is greater than 2 to obtain the intermediate vector u; the coding vector with variable node dimension 1 It is obtained by directly intercepting the corresponding position of the intermediate vector u; the coded vector whose variable node dimension is 2 Then it can be calculated bit by bit from the start bit through its large cycle characteristics on the bipartite graph, and the two parts of the coded vector are combined to form the coded vector .

Description

准循环低密度奇偶校验码及其修正和线性编码方法Quasi-Cyclic Low Density Parity Check Code and Its Correction and Linear Coding Method

技术领域technical field

本发明为低密度奇偶校验码的编码方法，属于信道纠错编码的编码构造及编码方法领域。The invention relates to an encoding method of a low-density parity check code, and belongs to the field of encoding structures and encoding methods of channel error correction encoding.

背景技术Background technique

在低密度奇偶校验（Low-Density Parity-Check,简称LDPC）码的编码方法当中，Richardson在文献(T.J. Richardson and R.L. Urbanke, “Efficient encoding of low-density parity-check codes,” IEEE Trans. Inform. Theory, vol.47, no.2, pp. 638-656, Feb. 2001.)中提出了基于类下三角形校验矩阵的编码方法。但是如果校验阵无法调整成理想的类下三角形矩阵形式，则编码的复杂度还是很高。从LDPC编译码器硬件实现的角度而言，无结构的LDPC码不利于硬件实现。为此，具有准循环(Quasi-Cyclic, 简称QC)结构的LDPC码得到了学术界和工业界的广泛青睐，QC结构反映到LDPC码的校验矩阵上具有以下特点：校验矩阵由循环移位子阵组成，而循环移位子阵则是单位矩阵经循环移位所得到的方阵，因此循环移位矩阵在矩阵大小给定的前提下完全决定于移位系数。研究发现，QC结构能简化编码器的设计，很多QC-LDPC码的编码器可以利用循环移位寄存器来有效实现。然而，QC结构简化编码器也存在着严重的制约关系：校验矩阵必须存在一个由循环子阵构成的满秩子矩阵。在实际构造中，该条件并不容易满足。  Among the encoding methods of Low-Density Parity-Check (LDPC) codes, Richardson in the literature (T.J. Richardson and R.L. Urbane, "Efficient encoding of low-density parity-check codes," IEEE Trans. Inform . Theory, vol.47, no.2, pp. 638-656, Feb. 2001.) An encoding method based on the class lower triangular check matrix is proposed. However, if the check matrix cannot be adjusted into an ideal lower triangular matrix form, the coding complexity is still very high. From the point of view of LDPC codec hardware implementation, unstructured LDPC codes are not conducive to hardware implementation. For this reason, LDPC codes with a quasi-cyclic (Quasi-Cyclic, QC for short) structure have been widely favored by academia and industry. The QC structure is reflected in the check matrix of LDPC codes and has the following characteristics: The cyclic shift sub-array is a square matrix obtained by cyclically shifting the unit matrix, so the cyclic shift matrix is completely determined by the shift coefficient under the premise of a given matrix size. It is found that the QC structure can simplify the design of encoders, and many encoders of QC-LDPC codes can be effectively implemented by using circular shift registers. However, the QC structure simplifies the encoder and there are serious constraints: the parity check matrix must have a full-rank sub-matrix composed of cyclic sub-matrixes. In actual construction, this condition is not easy to satisfy. the

在低码率LDPC码构造中，为提高性能，一般需要引入隐含变量节点，则相当于在LDPC码的校验矩阵中引入更多的列（1个变量节点对应于校验矩阵中的1列），也即对应的编码比特并不发送到信道上，因而称之为具有隐含节点的LDPC码，例如文献（T. Richardson and R. Urbanke, “Multi-Edge type LDPC Codes,” http://lthcwww.epfl.ch/）提出的多边型LDPC码或者文献（A. Abbasfar, D. Divsalar, and K. Yao, “Accumulate Repeat Accumulate Codes,” in IEEE International Symposium on Information Theory, (Chicago, Illinois), June 2004.）中提出的累加-重复-累加码(Accumulate-Repeat-Accumulate, 简称ARA)码。In the construction of low code rate LDPC codes, in order to improve performance, it is generally necessary to introduce hidden variable nodes, which is equivalent to introducing more columns in the parity check matrix of LDPC codes (1 variable node corresponds to 1 in the parity check matrix column), that is, the corresponding coded bits are not sent to the channel, so it is called an LDPC code with hidden nodes, such as literature (T. Richardson and R. Urbanke, “Multi-Edge type LDPC Codes,” http: //lthcwww.epfl.ch/) proposed polygonal LDPC codes or literature (A. Abbasfar, D. Divsalar, and K. Yao, "Accumulate Repeat Accumulate Codes," in IEEE International Symposium on Information Theory, (Chicago, Illinois ), the Accumulate-Repeat-Accumulate (ARA) code proposed in June 2004.).

为便于实现，具有隐含节点的LDPC码也应采用准循环结构，也即所谓的具有隐含节点准循环低密度奇偶校验码。但是，这种准循环结构经常找不到很好的编码方法，这是由于准循环结构使得校验矩阵中找到由循环移位子矩构成的信息长度大小的子阵是满秩的可能性并不大。为此，本发明对具有隐含节点准循环低密度奇偶校验码的结构进行调整，并以此为基础给出了一种线形编码方法。For the convenience of realization, the LDPC codes with hidden nodes should also adopt the quasi-cyclic structure, that is, the so-called quasi-cyclic low density parity-check codes with hidden nodes. However, this quasi-cyclic structure often cannot find a good encoding method, because the quasi-cyclic structure makes it possible to find a sub-matrix with a size of information length composed of cyclically shifted sub-moments in the parity check matrix that is full-ranked. not big. For this reason, the present invention adjusts the structure of the quasi-cyclic low-density parity-check code with hidden nodes, and provides a linear coding method based on this.

发明内容Contents of the invention

技术问题：本发明的目的是提供一种准循环低密度奇偶校验码的修正及其线性编码方法，解决该类低密度奇偶校验码线形复杂度编码难以设计的问题。         Technical problem: The purpose of the present invention is to provide a correction of quasi-cyclic low-density parity-check code and its linear coding method, so as to solve the problem that the linear complexity coding of this type of low-density parity-check code is difficult to design.        

技术方案：本发明的准循环低密度奇偶校验码变量节点的维度分为3类：维度为1、维度为2以及维度大于2；维度大于2的变量节点都是信息节点，对应于待编码信息比特位，由于一般不发送到信道上，因而称之为隐含节点；维度为2的变量节点正好在相应的低密度校验矩阵对应的二分图上形成一个首尾相连的大环。   Technical solution: The dimensions of the quasi-cyclic low-density parity-check code variable nodes of the present invention are divided into three categories: dimension 1, dimension 2, and dimension greater than 2; variable nodes with dimension greater than 2 are information nodes, corresponding to the Information bits are generally not sent to the channel, so they are called hidden nodes; variable nodes with a dimension of 2 just form a large ring connected end to end on the bipartite graph corresponding to the corresponding low-density check matrix.

本发明的的准循环低密度奇偶校验码的修正方法为：在所述的维度为2的大环上任选一条边，将其截去，也即在低密度校验矩阵的相应位置填0，从而得到该编码一种修正结构；校验矩阵中填0操作所在的行作为编码开始启动的位置，称为编码启动行。The correction method of the quasi-cyclic low-density parity-check code of the present invention is: select an edge on the large ring whose dimension is 2, cut it off, that is, fill in the corresponding position of the low-density check matrix 0, so as to obtain a modified structure of the code; the row where the 0-fill operation in the check matrix is used as the position where the code starts is called the code start line.

所述修正结构体现在对低密度奇偶校验码的校验矩阵的修改，修改操作对象是校验矩阵中构成大环的列重为2的列，任取其中一列的“1”将其置成“0”，置换发生的行称为启动行，该修正结构结合校验矩阵的定义具体表述为：The correction structure is embodied in the modification of the check matrix of the low-density parity-check code. The object of the modification operation is a column whose column weight is 2 to form a large ring in the check matrix. becomes "0", the line where the replacement occurs is called the start line, and this correction structure is specifically expressed in combination with the definition of the parity check matrix:

定义：一类具有隐含节点准循环低密度奇偶校验码的校验矩阵： Definition: A check matrix for a class of quasi-cyclic low-density parity-check codes with hidden nodes:

Figure 888274DEST_PATH_IMAGE001
Figure 888274DEST_PATH_IMAGE001

其中，是大小为

Figure 550779DEST_PATH_IMAGE003
的循环移位置换子矩阵，该矩阵完全取决于循环移位偏移量，
Figure 903263DEST_PATH_IMAGE004
为校验矩阵中循环移位置换子矩阵占的行数，
Figure 580232DEST_PATH_IMAGE005
为校验矩阵中循环移位置换子矩阵占的列数，该
Figure 80483DEST_PATH_IMAGE006
矩阵的大小为
Figure 766680DEST_PATH_IMAGE007
；为方便编码，此类校验矩阵分为3个部分：in, is the size of
Figure 550779DEST_PATH_IMAGE003
The cyclic shift permutation submatrix of , which depends entirely on the cyclic shift offset,
Figure 903263DEST_PATH_IMAGE004
is the number of rows occupied by the cyclic shift replacement sub-matrix in the parity check matrix,
Figure 580232DEST_PATH_IMAGE005
is the number of columns occupied by the cyclic shift replacement sub-matrix in the parity check matrix, the
Figure 80483DEST_PATH_IMAGE006
The size of the matrix is
Figure 766680DEST_PATH_IMAGE007
; For the convenience of coding, this kind of check matrix is divided into 3 parts:

Figure 35987DEST_PATH_IMAGE008
,其中，
Figure 149436DEST_PATH_IMAGE009
对应于完整码字的信息比特部分,大小为
Figure 136984DEST_PATH_IMAGE010
；单维度校验矩阵
Figure 361292DEST_PATH_IMAGE011
对应于码字单维度列重为1的校验比特部分,大小为
Figure 688368DEST_PATH_IMAGE012
；双维度校验矩阵
Figure 536501DEST_PATH_IMAGE013
对应于码字双维度列重为2的校验比特部分，大小为
Figure 683448DEST_PATH_IMAGE014
；编码的总长度为
Figure 773764DEST_PATH_IMAGE015
；由于
Figure 955347DEST_PATH_IMAGE016
对应的编码码字信息位部分并不发送到信道上，因而是具有隐含节点的低密度校验码；所述双维度校验矩阵
Figure 472916DEST_PATH_IMAGE017
所有的“1”构成一个大环，设双维度校验矩阵
Figure 372738DEST_PATH_IMAGE017
中的“1”依大环的逆时针顺序在该矩阵中的坐标依次为
Figure 938849DEST_PATH_IMAGE018
。
Figure 35987DEST_PATH_IMAGE008
,in,
Figure 149436DEST_PATH_IMAGE009
Corresponding to the information bit part of the complete codeword, the size is
Figure 136984DEST_PATH_IMAGE010
;Single-dimensional check matrix
Figure 361292DEST_PATH_IMAGE011
Corresponding to the parity bit part of the single-dimensional column weight of the codeword is 1, the size is
Figure 688368DEST_PATH_IMAGE012
;Two-dimensional parity check matrix
Figure 536501DEST_PATH_IMAGE013
Corresponding to the parity bit part of the double-dimensional column weight of the codeword is 2, the size is
Figure 683448DEST_PATH_IMAGE014
; The total length of the code is
Figure 773764DEST_PATH_IMAGE015
;because
Figure 955347DEST_PATH_IMAGE016
The corresponding encoded codeword information bit part is not sent to the channel, so it is a low-density check code with hidden nodes; the two-dimensional check matrix
Figure 472916DEST_PATH_IMAGE017
All "1" form a large ring, and a two-dimensional parity check matrix is set
Figure 372738DEST_PATH_IMAGE017
The coordinates of "1" in the matrix in the counterclockwise order of the macrocycle are
Figure 938849DEST_PATH_IMAGE018
.

所述双维度校验矩阵

Figure 37255DEST_PATH_IMAGE017
中任意制定其中的一个“1”，将其置为“0”，修改后的双维度校验矩阵记为
Figure 227190DEST_PATH_IMAGE019
，最终修正结构的低密度校验码具有校验矩阵：The two-dimensional parity check matrix
Figure 37255DEST_PATH_IMAGE017
Arbitrarily formulate one of the "1" in it, and set it to "0", and the modified two-dimensional check matrix is recorded as
Figure 227190DEST_PATH_IMAGE019
, the low-density check code of the final modified structure has a check matrix:

。 .

本发明的准循环低密度奇偶校验码的线性编码方法在于：利用修正结构的低密度校验矩阵及输入信息比特矢量计算编码位：首先利用输入信息矢量s，与校验矩阵的列重大于2的部分做矢量与矩阵的相乘运算得到中间矢量u；变量节点维度为1的编码矢量

Figure 780848DEST_PATH_IMAGE021
直接截取中间矢量u的相应位置得到；变量节点维度为2的编码矢量
Figure 937023DEST_PATH_IMAGE022
则通过其在二分图上的大环特性由启动位开始逐比特计算可得，将两部分编码矢量拼合起来最终形成编码输出矢量。The linear coding method of the quasi-cyclic low-density parity-check code of the present invention is: utilize the low-density check matrix of revised structure and input information bit vector to calculate coding bit: at first utilize input information vector s , and the column weight of check matrix is greater than The part of 2 is multiplied by the vector and the matrix to get the intermediate vector u ; the coded vector whose dimension of the variable node is 1
Figure 780848DEST_PATH_IMAGE021
It is obtained by directly intercepting the corresponding position of the intermediate vector u ; the coded vector whose variable node dimension is 2
Figure 937023DEST_PATH_IMAGE022
Then it can be calculated bit by bit from the start bit through its large ring characteristics on the bipartite graph, and the two parts of the encoded vector are combined to form the encoded output vector .

7.根据权利要求6所述的准循环低密度奇偶校验码的线性编码方法，其特征在于所述编码矢量分成两部分进行，一部分对应于校验矩阵列重为1的列，通过信息矢量直接编码而得；另一部分对应于校验矩阵列重为2的列，相应的编码矢量可通过大环特性逐比特计算而得，该编码算法具体表述为按如下顺序执行的几个步骤：定义： 设编码器的输入矢量为

Figure 467547DEST_PATH_IMAGE024
，其中
Figure 375461DEST_PATH_IMAGE025
；编码器的输出为编码码字，记为；如果信息位对应隐含节点，则信息位并不发送，编码器输出为
Figure 980197DEST_PATH_IMAGE027
，其中，对应于单维度校验矩阵的编码矢量，其大小设为；对应于双维度校验矩阵的编码矢量，其大小设为
Figure 745973DEST_PATH_IMAGE031
；将矩阵
Figure 63821DEST_PATH_IMAGE009
写成分块矩阵，其中
Figure 626707DEST_PATH_IMAGE033
的大小为
Figure 936465DEST_PATH_IMAGE034
,的大小为，且
Figure 759431DEST_PATH_IMAGE037
；步骤1：利用输入信息比特矢量
Figure 240091DEST_PATH_IMAGE038
以及校验矩阵
Figure 798111DEST_PATH_IMAGE033
，相乘直接计算
Figure 941692DEST_PATH_IMAGE039
；步骤2∶利用输入信息比特矢量以及校验矩阵
Figure 615436DEST_PATH_IMAGE035
，相乘直接计算
Figure 395173DEST_PATH_IMAGE040
；步骤3：利用中间结果矢量
Figure 790383DEST_PATH_IMAGE041
及校验矩阵中输入信息比特矢量
Figure 667072DEST_PATH_IMAGE038
以及校验矩阵中
Figure 818884DEST_PATH_IMAGE013
的大环特性，计算码字矢量如下所示：7. the linear coding method of quasi-cyclic low-density parity-check code according to claim 6, it is characterized in that described coding vector is divided into two parts and carries out, and a part is corresponding to the column that check matrix column weight is 1, passes information vector It is directly encoded; the other part corresponds to the column with a check matrix column weight of 2, and the corresponding encoding vector can be calculated bit by bit through the macrocycle characteristic. The encoding algorithm is specifically expressed as several steps executed in the following order: Definition : Let the input vector of the encoder be
Figure 467547DEST_PATH_IMAGE024
,in
Figure 375461DEST_PATH_IMAGE025
; The output of the encoder is the encoded codeword, denoted as ; If the information bit corresponds to the hidden node, the information bit is not sent, and the output of the encoder is
Figure 980197DEST_PATH_IMAGE027
,in, An encoding vector corresponding to a single-dimensional parity check matrix whose size is set to ; The encoding vector corresponding to the two-dimensional parity check matrix, whose size is set to
Figure 745973DEST_PATH_IMAGE031
; the matrix
Figure 63821DEST_PATH_IMAGE009
write block matrix ,in
Figure 626707DEST_PATH_IMAGE033
is of size
Figure 936465DEST_PATH_IMAGE034
, is of size ,and
Figure 759431DEST_PATH_IMAGE037
; Step 1: Use the input information bit vector
Figure 240091DEST_PATH_IMAGE038
and check matrix
Figure 798111DEST_PATH_IMAGE033
, directly calculate by multiplying
Figure 941692DEST_PATH_IMAGE039
; Step 2: Using the input information bit vector and check matrix
Figure 615436DEST_PATH_IMAGE035
, directly calculate by multiplying
Figure 395173DEST_PATH_IMAGE040
; Step 3: Utilize the intermediate result vector
Figure 790383DEST_PATH_IMAGE041
and the input information bit vector in the parity check matrix
Figure 667072DEST_PATH_IMAGE038
and check matrix middle
Figure 818884DEST_PATH_IMAGE013
The macrocyclic properties of the calculation codeword vector As follows:

Figure 250445DEST_PATH_IMAGE044
Figure 250445DEST_PATH_IMAGE044

步骤4：：将步骤１与步骤３的结果合并，最终得到编码码字。 Step 4: : Merge the results of step 1 and step 3, and finally get the encoded codeword .

有益效果：本发明的主要创新点在于根据维度为2的变量节点构成大环的特点，在大环上任意选取一变量节点并截取其一条边，这样使得编码可以完全根据校验矩阵的联接关系来直接计算完成。 Beneficial effects: the main innovation of the present invention is that according to the characteristics of the large ring formed by variable nodes with a dimension of 2, a variable node is arbitrarily selected on the large ring and one of its edges is intercepted, so that the encoding can be completely based on the connection relationship of the parity check matrix to complete the calculation directly.

主要体现在以下几个方面：It is mainly reflected in the following aspects:

1)        结构修正后的LDPC码相比于原有的LDPC码改动小，截除一条边1) Compared with the original LDPC code, the modified LDPC code has little change, and one side is cut off

的操作使得性能基本没有变化，而译码设计仍可沿用准循环结构来有效—4—The operation makes the performance basically unchanged, and the decoding design can still use the quasi-circular structure to be effective—4—

进行；conduct;

2)    无需对校验矩阵进行高斯消除变化即能编码，由于LDPC码校验矩阵的低密度特性，使得编码复杂度低。2) It can be encoded without Gaussian elimination of the parity check matrix. Due to the low-density characteristics of the parity check matrix of the LDPC code, the encoding complexity is low.

附图说明Description of drawings

图1是一类准循环LDPC码校验矩阵中由变量维度为2的子矩阵形成的大环结构。Fig. 1 is a large ring structure formed by sub-matrices with a variable dimension of 2 in the parity check matrix of a class of quasi-cyclic LDPC codes.

所有的符号注解：All symbol annotations:

LDPC：Low-Density Parity-Check的缩写，低密度奇偶校验码；LDPC: the abbreviation of Low-Density Parity-Check, low-density parity check code;

：原始LDPC码的校验矩阵；                          : check matrix of the original LDPC code;

Figure 63046DEST_PATH_IMAGE042
：结构修正后LDPC码的校验矩阵；       
Figure 63046DEST_PATH_IMAGE042
: check matrix of LDPC code after structure modification;

Figure 586431DEST_PATH_IMAGE009
：LDPC码校验矩阵对应于信息比特的子矩阵；
Figure 586431DEST_PATH_IMAGE009
: The LDPC code check matrix corresponds to the sub-matrix of the information bits;

Figure 813013DEST_PATH_IMAGE011
：对应于码字单维度（列重为1）校验比特部分；                 
Figure 813013DEST_PATH_IMAGE011
: Corresponding to the single-dimensional codeword (column weight is 1) parity bit part;

Figure 54639DEST_PATH_IMAGE013
：对应于码字双维度（列重为2）校验比特部分；
Figure 54639DEST_PATH_IMAGE013
: Corresponding to the codeword double-dimensional (column weight is 2) parity bit part;

Figure 657659DEST_PATH_IMAGE019
：修改后的双维度校验矩阵；
Figure 657659DEST_PATH_IMAGE019
: Modified two-dimensional check matrix;

Figure 35550DEST_PATH_IMAGE046
：编码器的输入矢量；
Figure 35550DEST_PATH_IMAGE046
: the input vector of the encoder;

Figure 636296DEST_PATH_IMAGE047
：编码器的输出，编码码字矢量；
Figure 636296DEST_PATH_IMAGE047
: the output of the encoder, the encoded codeword vector;

：对应于单维度校验矩阵的编码矢量； : Corresponding to the encoding vector of the single-dimensional parity check matrix;

Figure 7814DEST_PATH_IMAGE030
：对应于双维度校验矩阵的编码矢量；
Figure 7814DEST_PATH_IMAGE030
: Corresponding to the encoding vector of the double-dimensional parity check matrix;

Figure 302529DEST_PATH_IMAGE018
：
Figure 74176DEST_PATH_IMAGE017
中的“1”所处的位置，依大环的逆时针顺序在该矩阵中的坐标。
Figure 302529DEST_PATH_IMAGE018
:
Figure 74176DEST_PATH_IMAGE017
The position of "1" in is the coordinates in the matrix in the counterclockwise order of the macrocycle.

具体实施方式Detailed ways

本发明的准循环低密度奇偶校验码在维度为2的大环上任选一条边，将其截去，也即在低密度校验矩阵的相应位置填0，从而得到该编码一种修正结构。设原始编码的校验矩阵可以分为3个部分：In the quasi-cyclic low-density parity-check code of the present invention, one side is randomly selected on the large ring with a dimension of 2, and it is truncated, that is, 0 is filled in the corresponding position of the low-density check matrix, thereby obtaining a correction of the code structure. Suppose the check matrix of the original code can be divided into three parts:

Figure 24814DEST_PATH_IMAGE008
,且双维度校验矩阵
Figure 969636DEST_PATH_IMAGE017
所有的“1”构成一个大环。设
Figure 322120DEST_PATH_IMAGE017
中的“1”依大环的逆时针顺序在该矩阵中的坐标依次为
Figure 326985DEST_PATH_IMAGE018
。结构修正方法具体步骤为：任意制定双维度校验矩阵
Figure 764920DEST_PATH_IMAGE017
中的一个“1”，将其置为“0”，修改后的双维度校验矩阵记为
Figure 14898DEST_PATH_IMAGE019
，最终结构修改的低密度校验码具有校验矩阵：
Figure 24814DEST_PATH_IMAGE008
, and the two-dimensional check matrix
Figure 969636DEST_PATH_IMAGE017
All "1"s form a big ring. set up
Figure 322120DEST_PATH_IMAGE017
The coordinates of "1" in the matrix in the counterclockwise order of the macrocycle are
Figure 326985DEST_PATH_IMAGE018
. The specific steps of the structure correction method are as follows: arbitrarily formulate a two-dimensional check matrix
Figure 764920DEST_PATH_IMAGE017
A "1" in it, set it to "0", and the modified two-dimensional check matrix is recorded as
Figure 14898DEST_PATH_IMAGE019
, the final modified low-density check code has a check matrix:

Figure 221888DEST_PATH_IMAGE020
。
Figure 221888DEST_PATH_IMAGE020
.

准循环低密度奇偶校验码的线性编码方法，利用低密度校验矩阵及输入信息比特矢量直接计算编码位。首先利用输入信息矢量

Figure 335338DEST_PATH_IMAGE048
，与校验矩阵的列重(也即变量节点维度)大于2的部分做矢量与矩阵的相乘运算得到中间矢量；变量节点维度为1的编码矢量
Figure 547194DEST_PATH_IMAGE021
直接截取中间矢量的相应位置得到；变量节点维度为2的编码矢量
Figure 955358DEST_PATH_IMAGE022
则通过其在二分图上的大环特性由启动位开始逐比特计算可得，将两部分编码矢量拼合起来最终形成编码矢量
Figure 367885DEST_PATH_IMAGE023
。准循环低密度奇偶校验码的线性编码方法可以表述为按照如下顺序执行的步骤：The linear coding method of the quasi-cyclic low-density parity-check code uses the low-density check matrix and the input information bit vector to directly calculate coded bits. First use the input information vector
Figure 335338DEST_PATH_IMAGE048
, with the column weight of the check matrix (that is, the dimension of the variable node) greater than 2, do the multiplication operation of the vector and the matrix to obtain the intermediate vector ;Coding vector of variable node dimension 1
Figure 547194DEST_PATH_IMAGE021
Intercept the intermediate vector directly The corresponding position is obtained; the code vector of variable node dimension is 2
Figure 955358DEST_PATH_IMAGE022
Then it can be calculated bit by bit from the start bit through its large cycle characteristics on the bipartite graph, and the two parts of the coded vector are combined to form the coded vector
Figure 367885DEST_PATH_IMAGE023
. The linear coding method of the quasi-cyclic LDPC code can be expressed as steps performed in the following order:

步骤1：利用输入信息比特矢量

Figure 458201DEST_PATH_IMAGE038
以及校验矩阵
Figure 639783DEST_PATH_IMAGE033
，相乘直接计算
Figure 658817DEST_PATH_IMAGE049
； Step 1: Utilize the input information bit vector
Figure 458201DEST_PATH_IMAGE038
and check matrix
Figure 639783DEST_PATH_IMAGE033
, directly calculate by multiplying
Figure 658817DEST_PATH_IMAGE049
;

步骤2∶利用输入信息比特矢量

Figure 293061DEST_PATH_IMAGE038
以及校验矩阵
Figure 859171DEST_PATH_IMAGE035
，相乘直接计算
Figure 223157DEST_PATH_IMAGE050
； Step 2: Use the input information bit vector
Figure 293061DEST_PATH_IMAGE038
and check matrix
Figure 859171DEST_PATH_IMAGE035
, directly calculate by multiplying
Figure 223157DEST_PATH_IMAGE050
;

步骤3：利用中间结果矢量及校验矩阵中输入信息比特矢量

Figure 33167DEST_PATH_IMAGE038
以及校验矩阵
Figure 402968DEST_PATH_IMAGE042
中
Figure 621460DEST_PATH_IMAGE013
的大环特性，计算码字矢量
Figure 418515DEST_PATH_IMAGE043
如下所示： Step 3: Utilize the intermediate result vector and the input information bit vector in the parity check matrix
Figure 33167DEST_PATH_IMAGE038
and check matrix
Figure 402968DEST_PATH_IMAGE042
middle
Figure 621460DEST_PATH_IMAGE013
The macrocyclic properties of the calculation codeword vector
Figure 418515DEST_PATH_IMAGE043
As follows:

Figure 27350DEST_PATH_IMAGE044
Figure 27350DEST_PATH_IMAGE044

步骤4：：将步骤１与步骤３的结果合并，最终得到编码码字

Figure 499045DEST_PATH_IMAGE023
。 Step 4: : Merge the results of step 1 and step 3, and finally get the encoded codeword
Figure 499045DEST_PATH_IMAGE023
.

例：本发明的一种准循环低密度奇偶校验码的修正及其线性编码方法可以通过Example: the correction of a kind of quasi-cyclic low-density parity-check code of the present invention and its linear coding method can pass

以下实例来说明。设一个码长为6，信息长度为2，码率为1/3的具有隐含节点的准循环LDPC码的原始校验矩阵如下：The following examples to illustrate. The original check matrix of a quasi-cyclic LDPC code with hidden nodes with a code length of 6, an information length of 2, and a code rate of 1/3 is as follows:

Figure 509727DEST_PATH_IMAGE051
。
Figure 509727DEST_PATH_IMAGE051
.

该校验矩阵可以分解成3个部分

Figure 540000DEST_PATH_IMAGE008
，其中，The check matrix can be decomposed into 3 parts
Figure 540000DEST_PATH_IMAGE008
,in,

Figure 636132DEST_PATH_IMAGE052
,
Figure 410053DEST_PATH_IMAGE053
,
Figure 275240DEST_PATH_IMAGE054
。
Figure 636132DEST_PATH_IMAGE052
,
Figure 410053DEST_PATH_IMAGE053
,
Figure 275240DEST_PATH_IMAGE054
.

Figure 414098DEST_PATH_IMAGE009
对应于完整码字的信息比特部分,大小为
Figure 59843DEST_PATH_IMAGE010
，在本例子中并不发送到信道上，因而是所谓的隐含节点部分；
Figure 575138DEST_PATH_IMAGE011
对应于码字维度为1的校验比特部分,大小为
Figure 858614DEST_PATH_IMAGE012
；
Figure 168372DEST_PATH_IMAGE013
对应于码字维度为2的校验比特部分，大小为
Figure 301413DEST_PATH_IMAGE014
；参数
Figure 354820DEST_PATH_IMAGE055
,。该校验矩阵的对应的节点构成一个大环，如图1所示。
Figure 414098DEST_PATH_IMAGE009
Corresponding to the information bit part of the complete codeword, the size is
Figure 59843DEST_PATH_IMAGE010
, which is not sent to the channel in this example, so it is the so-called hidden node part;
Figure 575138DEST_PATH_IMAGE011
Corresponding to the parity bit part of codeword dimension 1, the size is
Figure 858614DEST_PATH_IMAGE012
;
Figure 168372DEST_PATH_IMAGE013
Corresponding to the parity bit part of codeword dimension 2, the size is
Figure 301413DEST_PATH_IMAGE014
;parameter
Figure 354820DEST_PATH_IMAGE055
, . The parity check matrix The corresponding nodes form a large ring, as shown in Figure 1.

本发明的结构修正是在该大环上选取一点截去一条边，也即校验矩阵相应位置的“1” 填 “0”，如图1画圈的位置置成“0”，因而修正后的可以写成：The structural modification of the present invention is to select a point on the large ring to cut off a side, that is, to fill the "1" in the corresponding position of the parity check matrix with "0", as shown in Figure 1. of can be written as:

Figure 949432DEST_PATH_IMAGE058
，
Figure 949432DEST_PATH_IMAGE058
,

因而结构修改后的LDPC码校验矩阵可以写成：Therefore, the structure-modified LDPC code check matrix can be written as:

Figure 643719DEST_PATH_IMAGE059
。
Figure 643719DEST_PATH_IMAGE059
.

结构修改后LDPC码的线性编码算法其具体步骤如下： The specific steps of the linear coding algorithm of the LDPC code after structure modification are as follows:

步骤1：利用输入信息比特矢量以及校验矩阵

Figure 904378DEST_PATH_IMAGE061
，相乘直接计算
Figure 299587DEST_PATH_IMAGE062
； Step 1: Utilize the input information bit vector and check matrix
Figure 904378DEST_PATH_IMAGE061
, directly calculate by multiplying
Figure 299587DEST_PATH_IMAGE062
;

步骤2∶利用输入信息比特矢量

Figure 176277DEST_PATH_IMAGE060
以及校验矩阵，相乘直接计算； Step 2: Use the input information bit vector
Figure 176277DEST_PATH_IMAGE060
and check matrix , directly calculate by multiplying ;

步骤3：利用中间结果矢量

Figure 526989DEST_PATH_IMAGE041
以及校验矩阵
Figure 258185DEST_PATH_IMAGE042
中
Figure 251549DEST_PATH_IMAGE013
的大环特性，计算码字矢量
Figure 5878DEST_PATH_IMAGE064
如下逐步计算所示(
Figure 318391DEST_PATH_IMAGE065
,
Figure 841776DEST_PATH_IMAGE066
)： Step 3: Utilize the intermediate result vector
Figure 526989DEST_PATH_IMAGE041
and check matrix
Figure 258185DEST_PATH_IMAGE042
middle
Figure 251549DEST_PATH_IMAGE013
The macrocyclic properties of the calculation codeword vector
Figure 5878DEST_PATH_IMAGE064
Step-by-step calculations are shown below (
Figure 318391DEST_PATH_IMAGE065
,
Figure 841776DEST_PATH_IMAGE066
):

Figure 333937DEST_PATH_IMAGE067
,
Figure 575563DEST_PATH_IMAGE068
,
Figure 913003DEST_PATH_IMAGE069
,
Figure 556474DEST_PATH_IMAGE070
；
Figure 333937DEST_PATH_IMAGE067
,
Figure 575563DEST_PATH_IMAGE068
,
Figure 913003DEST_PATH_IMAGE069
,
Figure 556474DEST_PATH_IMAGE070
;

步骤4：：将步骤１与步骤３的结果合并，最终得到编码码字

Figure 891640DEST_PATH_IMAGE023
。 Step 4: : Merge the results of step 1 and step 3, and finally get the encoded codeword
Figure 891640DEST_PATH_IMAGE023
.

 the

图1是一种准循环LDPC码校验矩阵中由变量维度为2的子矩阵的大环结构。环各点在矩阵中的坐标为

Figure 682879DEST_PATH_IMAGE071
, 其中
Figure 761693DEST_PATH_IMAGE065
,
Figure 823452DEST_PATH_IMAGE066
。Fig. 1 is a macrocyclic structure of a sub-matrix whose variable dimension is 2 in the parity check matrix of a quasi-cyclic LDPC code. The coordinates of each point of the ring in the matrix are
Figure 682879DEST_PATH_IMAGE071
, in
Figure 761693DEST_PATH_IMAGE065
,
Figure 823452DEST_PATH_IMAGE066
.

Claims (7)

1. A quasi-cyclic low-density parity-check code is characterized in that the dimension of variable nodes of the parity-check code is divided into 3 types: dimension 1, dimension 2, and dimension greater than 2; variable nodes with dimension larger than 2 are all information nodes, correspond to information bits to be coded, and are called hidden nodes because the variable nodes are not generally sent to a channel; the variable nodes with the dimension of 2 just form a large ring connected end to end on the bipartite graph corresponding to the corresponding low-density check matrix.
2. A method for correcting quasi-cyclic low density parity check codes according to claim 1, characterized in that the method comprises: optionally selecting one edge on the large ring with the dimension of 2, and cutting off the edge, namely filling 0 in the corresponding position of the low-density check matrix, thereby obtaining a modified structure of the code; and filling a row in which the 0 operation is positioned in the check matrix as a position for starting coding, and calling the row as a coding starting row.
3. The method of correcting a quasi-cyclic low density parity check code according to claim 2, wherein the correcting structure now modifies the check matrix of the low density parity check code, the modifying operation is to take the columns of which the column constituting the large ring is 2 in the check matrix, and to set "1" of any one column to "0", the row where the replacement occurs is called a start row, and the correcting structure is specifically expressed by combining the definition of the check matrix as follows:
defining: a class of check matrices with implicit node quasi-cyclic low density parity check codes:
Figure FDA0000040551030000011
wherein Hi，jIs a cyclic shift permutation sub-matrix of size zxz, which is completely dependent on the cyclic shift offset, mbPermuting the number of rows occupied by a sub-matrix for cyclic shifts in a check matrix, nbPermuting the number of columns occupied by the submatrix for cyclic shifts in the check matrix, HoThe matrix size is m × n ═ mbz×mbz; for ease of encoding, such check matrices are divided into 3 parts:
Ho＝[Hs|Hp1|Hp2]，
wherein HsThe information bit portion corresponding to the complete codeword, size m × k; single-dimensional check matrix Hp1To pair
-1-
Check bit part with size of m × n corresponding to code word single dimension column weight of 11(ii) a Two-dimensional check matrix Hp2A check bit part with a length of m × n corresponding to a two-dimensional column of 2 of a codeword2(ii) a The total length of the code is n ═ k + n1+n2(ii) a Due to HsThe information bit portion of the corresponding encoded codeword is not sent onto the channel and is thus a low density check code with implicit nodes.
4. The method of claim 3, wherein the bi-dimensional check matrix H is a parity check matrixp2All '1's form a large ring, and a two-dimensional check matrix H is arrangedp2The coordinates of the '1' in the matrix in the counterclockwise sequence of the macrocycle are sequentially
Figure FDA0000040551030000021
5. The method of claim 3, wherein the bi-dimensional check matrix H is a parity check matrixp2One of the '1' is arbitrarily established, the '0' is set, and the modified two-dimensional check matrix is recorded as
Figure FDA0000040551030000022
The final modified structure low density check code has a check matrix:
Figure FDA0000040551030000023
6. a method for linear coding of a quasi-cyclic low density parity check code according to claim 3, characterized in that: and calculating the coding bit by using the low-density check matrix of the modified structure and the input information bit vector: firstly, multiplying an input information vector s and a part of a check matrix with the column weight more than 2 by a vector and the matrix to obtain an intermediate vector u; coding vector with variable node dimension of 1
Figure FDA0000040551030000024
Directly intercepting the corresponding position of the intermediate vector u; coding vector with variable node dimension of 2Then the binary code vector is calculated bit by starting from the starting bit through the large ring characteristic of the binary code vector on the bipartite graph, and the two parts of code vectors are spliced to finally form the code output vector
Figure FDA0000040551030000026
7. The linear coding method of quasi-cyclic low density parity check code according to claim 6, wherein the coding vector is divided into two parts, one part corresponding to the column with the column weight of 1 of the check matrix is obtained by directly coding the information vector; the other part corresponds to the column with the check matrix column weight of 2, the corresponding coding vector can be obtained by bit-by-bit calculation through the large ring characteristic, and the coding algorithm is specifically expressed as a plurality of steps which are executed in the following sequence:
defining: let the input vector of the encoder be s ═ s1，s2，L，L，sk) Where k is kbz; the output of the encoder is a coded codeword, noted
Figure FDA0000040551030000027
If the information bit corresponds to the hidden node, the information bit is not transmitted and the output of the encoder is
Figure FDA0000040551030000028
Wherein,
Figure FDA0000040551030000029
a code vector corresponding to the one-dimensional check matrix, the size of which is set to n1：
Figure FDA0000040551030000031
A code vector corresponding to the two-dimensional check matrix and having a size of n2(ii) a Will matrix HsWrite to a partitioned matrix
Figure FDA0000040551030000032
Wherein Hs1Is n1×k，Hs2Has a size of (m-n)1) X k, and m-n1＝n2；
Step 1: using the input information bit vector s ═ s1，s2，L，sk]And a check matrix Hs1Multiplication direct calculation
Figure FDA0000040551030000033
Step 2: using the input information bit vector s ═ s1，s2，L，sk]And a check matrix Hs2Multiplication direct calculation
Figure FDA0000040551030000034
And step 3: using intermediate result vector u and input information bit vector s ═ s in check matrix1，s2，L，sk]And H in the check matrix Hp2Computing a codeword vector
Figure FDA0000040551030000035
As follows:
and 4, step 4: : combining the results of the step 1 and the step 3 to finally obtain the code word
Figure FDA0000040551030000037
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Application publication date: 20110511