CN101807929B

CN101807929B - Minimum sum decoding method of selective annealing of low density parity check code

Info

Publication number: CN101807929B
Application number: CN 201010129242
Authority: CN
Inventors: 吴晓富; 赵春明; 姜明; 尤肖虎
Original assignee: PLA University of Science and Technology
Current assignee: PLA University of Science and Technology
Priority date: 2010-03-19
Filing date: 2010-03-19
Publication date: 2013-04-24
Anticipated expiration: 2030-03-19
Also published as: CN101807929A

Abstract

The selective annealing minimum-sum decoding method for low-density parity-check codes is suitable for soft-decision decoding of low-density parity-check codes, replacing the existing multiplicative modified minimum-sum decoding method. Based on the minimum sum decoding method, the present invention uses a multiplicative factor less than 1 to correct the output of the verification node whose verification is unsuccessful. The implementation steps of the present invention include: the variable node merges the amount of external information flowing into the verification node and the information from the channel as the judgment soft information of this iteration, tests whether the judgment sequence satisfies the verification equation, and records or updates the unsuccessful verification. Node sequence number set U, if U is empty, the decoding ends; if U is not empty, the check node updates the output information to the variable node according to the minimum sum rule, and multiplies the output information of the check nodes belonging to U by a value less than 1 The factors are annealed and transferred to the next iteration of decoding. The performance is obviously better than other improved minimum-sum decoding methods, and the computational complexity is much lower than the sum-product algorithm.

Description

Selective annealing minimum-sum decoding method for low-density parity-check codes

技术领域 technical field

本发明为低密度奇偶校验码的软判决迭代译码简化译码方法，属于信道纠错编码的译码技术领域。The invention relates to a simplified decoding method for soft-judgment iterative decoding of low-density parity check codes, and belongs to the technical field of channel error correction coding decoding.

背景技术 Background technique

在低密度奇偶校验(Low-Density Parity-Check，LDPC)码的译码方法当中，基于二分图的迭代软判决译码方法具有很好的误码率性能，对于较长的非规则LDPC码，可以达到接近香农限的性能。标准的软判决算法称之为和积算法，该算法在计算校验节点信息输出的时候，无论是概率域或是对数似然比域的译码，总是涉及到大量的加法，乘法，对数以及指数运算，加上节点数目较多，运算复杂度较大。最小和译码方法是对该算法的一个简化，直接用校验节点输入的可靠度最低或次低的信息作为输出，省却了和积算法中大量的运算，但性能与和积算法相比有一定差距。Among the decoding methods of Low-Density Parity-Check (LDPC) codes, the iterative soft-decision decoding method based on bipartite graph has good bit error rate performance. For longer irregular LDPC codes , performance close to the Shannon limit can be achieved. The standard soft-decision algorithm is called the sum product algorithm. When the algorithm calculates the information output of the check node, whether it is decoding in the probability domain or the log likelihood ratio domain, it always involves a large number of additions, multiplications, Logarithmic and exponential operations, plus a large number of nodes, make the operation more complex. The minimum-sum decoding method is a simplification of the algorithm, directly using the information with the lowest or second-lowest reliability input by the check node as the output, which saves a large number of operations in the sum-product algorithm, but its performance is better than that of the sum-product algorithm. There must be a gap.

最小和算法的改进方法有偏移修正或乘性归一化方法，是在输出的最小值或次小值信息上，减去一个修正因子或乘上一个归一化因子，从而达到接近和积算法输出的结果。这类方法性能相比最小和译码方法改进幅度较大，而复杂度并未增加很多。由于通信系统对传输速率，误码率性能要求进一步的提高，很多系统开始逐渐采用长度在8000以上的非规则LDPC码。随着码长的增加和非规则分布的影响，偏移修正或乘性归一化修正的最小和译码方法的性能也有所劣化，相距标准的和积算法性能差距逐渐增加。The improvement method of the minimum sum algorithm has offset correction or multiplicative normalization method, which is to subtract a correction factor or multiply a normalization factor on the output minimum or second minimum value information, so as to achieve a close sum product The output of the algorithm. Compared with the minimum sum decoding method, the performance of this kind of method is greatly improved, but the complexity does not increase much. As communication systems require further improvement in transmission rate and bit error rate performance, many systems gradually adopt irregular LDPC codes with a length of more than 8000. With the increase of the code length and the influence of irregular distribution, the performance of the minimum-sum decoding method with offset correction or multiplicative normalization correction also deteriorates, and the performance gap between the standard sum-product algorithm gradually increases.

发明内容 Contents of the invention

技术问题：本发明的目的是提供一种低密度奇偶校验码的选择退火最小和译码方法，该方法是一种改进的最小和译码方法，解决现有简化的LDPC码软判决译码方法在处理较长的非规则码时性能较差，以及现有的和积算法复杂度仍然较高的问题；同时该方法对信道估计参数更加鲁棒。Technical problem: the purpose of this invention is to provide a kind of selective annealing minimum sum decoding method of low density parity check code, this method is a kind of improved minimum sum decoding method, solves existing simplified LDPC code soft decision decoding The performance of the method is poor when dealing with longer irregular codes, and the complexity of the existing sum-product algorithm is still high; at the same time, the method is more robust to channel estimation parameters.

技术方案：低密度奇偶校验码的一种选择退火最小和译码方法，其特征在于：其特征在于：在低密度奇偶校验码的最小和迭代译码过程中，变量节点和校验节点依次进行软信息量更新；在一次迭代过程中，变量节点对总信息量进行硬判，判断各个校验式校验是否成功；如果校验式校验全部成功，则迭代译码自动停止，否则在随即进行的校验节点软值更新时，对校验成功的校验节点根据原有的最小和原则进行软值更新，而对校验不成功的校验节点在最小和原则软值更新的基础上乘以一个小于1的系数β完成退火处理。Technical solution: A selective annealing minimum-sum decoding method for low-density parity-check codes, characterized in that: during the minimum-sum iterative decoding process of low-density parity-check codes, the variable nodes and check nodes The amount of soft information is updated sequentially; in an iterative process, the variable node makes a hard judgment on the total amount of information to determine whether each check-type check is successful; if the check-type checks are all successful, the iterative decoding automatically stops, otherwise When the soft value of the verification node is updated immediately, the soft value of the verification node that is successfully verified is updated according to the original minimum sum principle, and the verification node that is unsuccessful in the verification is updated according to the soft value of the minimum sum principle. On the basis of multiplication by a coefficient β less than 1 to complete the annealing treatment.

退火系数β可以通过仿真来优化确定，并在迭代译码开始前预先设定存储。The annealing coefficient β can be optimally determined through simulation, and is preset and stored before iterative decoding starts.

基于选择退火的低密度奇偶校验码最小和译码方法可以表述为按照如下顺序执行的步骤：The minimum-sum decoding method of LDPC based on selective annealing can be expressed as the steps performed in the following order:

1)初始化：BPSK调制x_n＝1-2u_n，n∈[1，N]经过零均值方差σ²的高斯白噪声信道，得到接收信号序列Y＝{y_n|y_n＝x_n+w_n，n∈[1，N]}，初始的变量节点v_n，n∈[1，N]向校验节点c_m，m∈A(n)输出边信息

初始的校验节点c_m，m∈[1，M]向变量节点v_n，n∈B(m)输出边信息

迭代次数k＝0；1) Initialization: BPSK modulation x _n =1-2u _n , n∈[1, N] passes through a Gaussian white noise channel with zero mean variance σ ² to obtain the received signal sequence Y={y _n |y _n =x _n +w _n , n∈[1, N]}, the initial variable node v _n , n∈[1, N] outputs side information to the check node c _m , m∈A(n)

The initial check node c _m , m∈[1, M] outputs side information to the variable node v _n , n∈B(m)

The number of iterations k=0;

2)变量节点计算：各变量节点v_n将参与的校验式输出信息L_m，n ^k相加，作为变量节点v_n到校验节点c_m的输出边信息：2) Calculation of variable nodes: Each variable node v _n adds the output information L _{m and n} ^k of the verification formula involved, and serves as the output edge information from variable node v _n to check node c _m :

${L L}_{nm nm}^{k k} = = \underset{{m m}^{' '} &Element; &Element; A A ((n no)) \ \ m m}{Σ Σ} {L L}_{{m m}^{' '} n no}^{k k};;$

变量节点v_n将所有参与的校验节点c_m，m∈A(n)的输出边信息L_mn ^k相加，作为当前迭代的变量节点总输出The variable node v _n adds up the output edge information L _mn ^k of all participating check nodes c _m , m∈A(n) as the total output of the variable node of the current iteration

${L L}_{n no}^{k k} = = {y the y}_{n no} + + \underset{m m &Element; &Element; A A ((n no))}{Σ Σ} {L L}_{mn mn}^{k k}$

根据当前迭代各个变量节点的输出信息L_n ^k，按照下式作符号硬判得到输出序列According to the output information L _n ^k of each variable node in the current iteration, the output sequence is obtained by making a hard judgment of the sign according to the following formula

${z z}^{k k} = = (({z z}_{11}^{k k},, {z z}_{22}^{k k},, \cdot \cdot \cdot \cdot \cdot \cdot,, {z z}_{n no}^{k k},, \cdot \cdot \cdot \cdot \cdot &Center Dot;,, {z z}_{N N}^{k k}))$

${z z}_{n no}^{k k} = = \{\begin{matrix} 00,, & if if & {L L}_{n no}^{k k} > > 00 \\ 11,, & if if & {L L}_{n no}^{k k} \leq \leq 00 \end{matrix};;$

3)校验节点计算预处理：通过硬判序列，计算各个校验式是否成功：3) Check node calculation preprocessing: through the hard judgment sequence, calculate whether each check formula is successful:

${s the s}_{m m}^{k k} = = \underset{n no &Element; &Element; B B ((m m))}{Σ Σ} &CirclePlus; &CirclePlus; {z z}_{n no}^{k k},, m m &Element; &Element; [[11,, M m]]$

表示异或累加操作。记下所有不满足校验的校验节点序号

同时令

表示所有满足校验的校验节点序号集。如果不满足校验的节点个数为0，也即|U|＝0，则步骤(2)输出结果将作为最终的译码输出

同时终止该帧的译码，如果不能满足且迭代次数k等于最大迭代次数，则译码失败，终止译码，否则继续迭代译码，k++；

Represents an XOR-accumulate operation. Write down the serial numbers of all check nodes that do not meet the check

Simultaneous order

Indicates the sequence number set of all check nodes that satisfy the check. If the number of nodes that do not satisfy the check is 0, that is, |U|=0, the output result of step (2) will be used as the final decoding output

At the same time, the decoding of the frame is terminated. If it cannot be satisfied and the number of iterations k is equal to the maximum number of iterations, the decoding fails, and the decoding is terminated, otherwise, continue iterative decoding, k++;

4)校验节点计算：各校验节点c_m根据第k-1次迭代的变量节点输出边信息L_n′m ^k-1，根据最小和原则计算第k次迭代节点c_m向变量节点v_n输出的边信息，如果校验节点m属于集合U，则进行退火处理，否则不退火；也即执行以下操作：4) Calculation of check nodes: each check node c _m outputs edge information L _n′m ^k-1 according to the variable node of the k-1th iteration, and calculates the k-th iteration node c _m to the variable node v according to the minimum sum principle For the edge information output by _n , if the check node m belongs to the set U, it will be annealed, otherwise it will not be annealed; that is, the following operations are performed:

$\{\begin{matrix} {L L}_{mn mn}^{k k} = = β β \cdot &Center Dot; ((\underset{{n no}^{' '} &Element; &Element; B B ((m m)) \ \ n no}{Π Π} sign sign (({L L}_{{n no}^{' '} m m}^{k k - - 11})))) \cdot &Center Dot; ((\underset{{n no}^{' '} &Element; &Element; B B ((m m)) \ \ n no}{min min} | | {L L}_{{n no}^{' '} m m}^{k k - - 11} | |)),, & ifm ifm &Element; &Element; U u \\ ((\underset{{n no}^{' '} &Element; &Element; B B ((m m)) \ \ n no}{Π Π} sign sign (({l l}_{{n no}^{' '} m m}^{k k - - 11})))) \cdot &Center Dot; ((\underset{{n no}^{' '} &Element; &Element; B B ((m m)) \ \ n no}{min min} | | {L L}_{{n no}^{' '} m m}^{k k - - 11} | |)),, & ifm ifm &Element; &Element; S S \end{matrix};;$

然后跳转至步骤2)。Then skip to step 2).

有益效果：本发明的主要创新点在于根据校验是否成功的测定，在最小和规则的基础上对校验不成功的校验节点更新信息进行退火。Beneficial effects: the main innovation of the present invention is that according to the determination of whether the verification is successful, annealing is performed on the update information of the verification nodes whose verification is unsuccessful on the basis of the minimum sum rule.

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

1)根据校验是否成功的情况有选择性地退火，该新机制使得最小和解码算法性能更好。1) Selective annealing according to whether the verification is successful or not, this new mechanism makes the minimum sum decoding algorithm perform better.

2)和现有的乘性修正最小和方法相比，修正效果更好，译码收敛速度更快。2) Compared with the existing multiplicative correction minimum sum method, the correction effect is better, and the decoding convergence speed is faster.

附图说明 Description of drawings

图1是一个LDPC码二分图连接示意图。其中，图1a是校验节点和变量节点的连接示意图，图1b是某个变量节点与其参与的校验节点连接示意图，图1c是某个校验节点与其包含的变量节点连接示意图。FIG. 1 is a schematic diagram of a bipartite graph connection of an LDPC code. Among them, Figure 1a is a schematic diagram of the connection between a check node and a variable node, Figure 1b is a schematic diagram of the connection between a variable node and its participating check nodes, and Figure 1c is a schematic diagram of the connection between a certain check node and its variable nodes.

图2是一个变量节点计算单元的方法流程图。Fig. 2 is a flow chart of a method of a variable node computing unit.

图3是一个校验节点计算输出单元的总的译码方法流程图。Fig. 3 is a flow chart of a general decoding method of a check node calculation output unit.

图4是校验节点单元计算最小值，次小值和最小索引的方法流程图。FIG. 4 is a flowchart of a method for calculating the minimum value, the next minimum value and the minimum index by a check node unit.

图5是校验节点单元最小和退火更新输出的方法流程图。FIG. 5 is a flow chart of a method for checking node cell minimum sum annealing update outputs.

图6是(8064，4032)的1/2码率非规则LDPC码在各译码方法下的误比特率曲线。Fig. 6 is (8064, 4032) 1/2 code rate irregular LDPC code under each decoding method bit error rate curve.

图7是(8064，6048)的3/4码率非规则LDPC码在各译码方法下的误帧率曲线。Fig. 7 is the frame error rate curves of (8064, 6048) 3/4 code rate irregular LDPC codes under various decoding methods.

所有的符号注解：All symbol annotations:

v_n：第n个变量节点；v _n : the nth variable node;

c_m：第m个校验节点；c _m : the mth check node;

A(n)：变量节点v_n参与的校验节点集合；A(n): the set of check nodes that variable node v _n participates in;

B(m)：变量节点c_m包含的变量节点集合；B(m): variable node set contained in variable node c _m ;

L(v_n→c_m)＝(L(v_n→c_m)，z_n)：变量节点v_n向校验节点c_m传递的似然比信息L(c_m→v_n)以及符号信息z_n；L(v _n →c _m )=(L(v _n →c _m ), z _n ): the likelihood ratio information L(c _m →v _n ) and sign information transmitted by the variable node v _n to the check node c _m z _n ;

L(c_n→v_n)：变量节点c_m向校验节点v_n传递的似然比信息；L(c _n →v _n ): likelihood ratio information transmitted from variable node c _m to check node v _n ;

|L(v_n→c_m)|：变量节点v_n向校验节点c_m传递的似然比信息的可靠度；|L(v _n →c _m )|: the reliability of the likelihood ratio information transmitted from variable node v _n to check node c _m ;

sign(L(v_n→c_m))：变量节点v_n向校验节点c_m传递似然比信息的正负符号；sign(L(v _n →c _m )): variable node v _n transmits the sign of likelihood ratio information to check node c _m ;

sign(c_m)：校验节点c_m输出信号的正负符号；sign(c _m ): the positive and negative sign of the output signal of the check node c _m ;

min(c_m)：校验节点c_m输出信号的最小可靠度；min(c _m ): the minimum reliability of the output signal of the check node c _m ;

sub-min(c_m)：校验节点c_m输出信号的次最小可靠度；sub-min(c _m ): the sub-minimum reliability of the output signal of the check node c _m ;

min-ind(c_m)：校验节点c_m输出最小可靠度信号对应的变量节点序号min-ind(c _m ): the serial number of the variable node corresponding to the minimum reliability signal output by the check node c _m

MSA：最小和译码方法；MSA: minimum sum decoding method;

NMSA：乘性修正最小和译码方法；NMSA: multiplicative modified minimum sum decoding method;

AN-MSA：洗择退火最小和译码方法。AN-MSA: Washed Selective Annealing Minimal Sum Decoding Method.

具体实施方式 Detailed ways

本发明的选择退火最小和译码方法通过变量节点合并校验节点流入的外信息量以及来自信道的信息作为该次迭代的判决软信息，试探判决序列是否满足校验方程，记下或者更新校验不成功的节点序号集合，如果校验不成功的校验节点序号集为空，则解码结束；如果校验不成功的校验节点序号集非空，则校验节点根据最小和规则向变量节点更新输出信息，对校验不成功的校验节点输出信息乘以一小于1的因子进行退火处理，转入下次迭代译码。The selective annealing minimum-sum decoding method of the present invention uses the variable node to merge the external information flowing into the check node and the information from the channel as the judgment soft information of this iteration, to test whether the judgment sequence satisfies the check equation, write down or update the check If the serial number set of the unsuccessful check node is empty, the decoding ends; if the serial number set of the unsuccessful check node is not empty, the check node sends the variable The node updates the output information, and multiplies the output information of the verification node whose verification is unsuccessful by a factor less than 1 for annealing processing, and transfers to the next iterative decoding.

其具体步骤如下：The specific steps are as follows:

步骤一：初始化该校验节点的符号变量s_m＝1，sign^k(c_m)＝1，最小值min^k(c_m)＝100和次小值sub-min^k(c_m)＝100。Step 1: Initialize the sign variable s _m =1 of the check node, sign ^k (c _m )=1, the minimum value min ^k (c _m )=100 and the second minimum value sub-min ^k (c _m )=100.

步骤二：对于输入的符号位做校验运算Step 2: Perform a check operation on the input sign bit

s_m＝s_m·z_n；s _m = s _m z _n ;

对输入的信号L^k(v_i→c_m)，i∈B(m)取符号和绝对值，接着依次做如下的符号运算，和最小值，次小值的比较运算。For the input signal L ^k (v _i →c _m ), take the sign and absolute value of i∈B(m), and then perform the following sign operation in turn, and the comparison operation of the minimum value and the second minimum value.

sign^k(c_m)＝sign^k(c_m)·sign(L^k(v_i-c_m))；sign ^k (c _m )＝sign ^k (c _m )·sign(L ^k (v _i -c _m ));

sub-min^k(c_m)＝min{sub-min^k(c_m)，|L^k(v_i→c_m)|}；sub-min ^k (c _m )=min{sub-min ^k (c _m ), |L ^k (v _i →c _m )|};

min^k(c_m)＝min{min^k(c_m)，sub-min^k(c_m)}，同时记录对应的min-ind(c_m)。min ^k (c _m )=min{min ^k (c _m ), sub-min ^k (c _m )}, and record the corresponding min-ind(c _m ) at the same time.

步骤三：依次对参与校验节点c_m的变量节点更新输出：Step 3: Update the output of the variable nodes participating in the verification node c _m in turn:

如果i＝min-ind^k(c_m)，If i=min-ind ^k (c _m ),

则L^k(c_m→v_i)＝sign^k(c_m)·sign(L^k(v_i→c_m))·sub-min^k(c_m)否则L^k(c_m→v_i)＝sign^k(c_m)·sign(L^k(v_i →c_m))·min^k(c_m)Then L ^k (c _m →v _i )＝sign ^k (c _m )·sign(L ^k (v _i →c _m ))·sub-min ^k (c _m ) otherwise L ^k (c _m →v _i )＝ sign ^k (c _m )·sign(L ^k (v _i →c _m ))·min ^k (c _m )

如果s_m＝-1，If s _m = -1,

则L^k(c_m→v_i)＝β·L^k(c_m→v_i)。Then L ^k (c _m →v _i )=β·L ^k (c _m →v _i ).

图1(a)是一个LDPC码二分图结构图，即校验节点和变量节点的连接示意图，变量节点和校验节点分别记为v和c。(b)是变量节点v_n和参与的校验节点连接示意，以及节点间传递的似然比信息。(c)为校验节点c_m与其包含的变量节点连接示意，以及节点间传递的似然比信息。Figure 1(a) is a bipartite graph structure diagram of an LDPC code, that is, a schematic diagram of the connection between check nodes and variable nodes. The variable nodes and check nodes are denoted as v and c, respectively. (b) is a schematic diagram of the connection between the variable node v _n and the participating check nodes, and the likelihood ratio information transmitted between the nodes. (c) is a schematic diagram of the connection between the check node c _m and the variable nodes it contains, and the likelihood ratio information transmitted between the nodes.

图2是校验节点计算单元某次迭代的方法流程。第一步初始化sign(c_m)和s_m。第二步逐个将参与该校验节点的变量节点集合输入信息做取符号和比较运算，得到输入信息绝对值的最小值，次小值，最小索引以及各个输入信息的符号乘积。第三步按最小和算法规则，对每个输入的变量节点，更新反馈的输出信息，根据符号s_m的取值，对输出信息进行选择性退火。Fig. 2 is a method flow of a certain iteration of a computing unit of a check node. The first step is to initialize sign(c _m ) and s _m . In the second step, the input information of the variable node set participating in the verification node is used to perform sign and comparison operations one by one, and obtain the minimum value of the absolute value of the input information, the second minimum value, the minimum index and the symbol product of each input information. The third step is to update the feedback output information for each input variable node according to the minimum sum algorithm rule, and perform selective annealing on the output information according to the value of the symbol s _m .

图3是校验节点单元第二步过程的详细描述。首先输入的信号符号和当前的校验式符号相乘更新校验式符号，接着将输入数据的绝对值和当前的次小值做比较，如果输入数据绝对值小于次小值则更新次小值，最后将更新的次小值数据和当前的最小值数据做比较，按照输入数据大小，分别更新次小值和最小值或维持不变，若发生最小值的更新，则将最小值索引记为当前输入数据的节点序号。Fig. 3 is a detailed description of the second step process of the check node unit. First, the input signal symbol is multiplied by the current check formula symbol to update the check formula symbol, and then the absolute value of the input data is compared with the current second minimum value. If the absolute value of the input data is less than the second minimum value, the second minimum value is updated. , and finally compare the updated sub-minimum value data with the current minimum value data, update the sub-minimum value and the minimum value respectively or keep them unchanged according to the size of the input data, if the update of the minimum value occurs, record the minimum value index as The node number of the current input data.

图4是校验节点单元第三步计算，向各个变量节点更新输出信息的详细描述。首先将对应的变量节点输入信息符号和校验式总的输出符号相乘，作为向该节点输出的信息符号，如果该变量节点序号等于最小值索引，则输出信息的绝对值为次小值，若果不等则输出信息的绝对值为最小值。其后，根据符号s_m的取值对输出信息进行选择性退火：如果s_m＝-1，则输出信息乘一小于1的参数进行退火处理。Fig. 4 is a detailed description of the third step calculation of the check node unit, updating output information to each variable node. First, multiply the input information symbol of the corresponding variable node and the total output symbol of the verification formula as the information symbol output to the node. If the variable node serial number is equal to the minimum value index, the absolute value of the output information is the second smallest value. If they are not equal, the absolute value of the output information is the minimum value. Thereafter, selective annealing is performed on the output information according to the value of the symbol s _m : if s _m =-1, the output information is multiplied by a parameter less than 1 for annealing.

图5是变量节点单元计算当前输出和向校验节点更新输出信息的方法流程。首先变量节点单元将各个校验节点输入信息相加，作为该变量节点当前迭代的输出，该输出直接作硬判决得到当前的译码输出，并用校验式检验输出是否正确。如果本次迭代没有得到正确的译码输出，则变量节点单元将总的输出分别减去原先各个校验节点的输入，更新向对应校验节点的输出信息。Fig. 5 is a flow chart of a variable node unit calculating current output and updating output information to a check node. Firstly, the variable node unit adds the input information of each check node as the output of the current iteration of the variable node. The output is directly made a hard decision to obtain the current decoding output, and the check formula is used to check whether the output is correct. If the correct decoding output is not obtained in this iteration, the variable node unit subtracts the input of each check node from the total output, and updates the output information to the corresponding check node.

图6是AWGN信道下，总长8064，信息长度4032，1/2码率的非规则LDPC码在NMSA方法，AN-MSA方法下的误比特码率性能比较。非规则LDPC码的变量节点分布为λ(x)＝4032x+2688x²+1344x⁸，校验节点分布为ρ(x)＝4032x⁶。其中，x^d-1前的系数表示度数为d的节点个数。从图中可以看出，AN-MSA方法的性能(退火系数β＝0.75)比NMSA方法(优化的乘性修正因子0.85)提高了约0.1-0.2dB，优于其他的改进方法。Fig. 6 is an AWGN channel, the total length is 8064, the information length is 4032, and the irregular LDPC code of 1/2 code rate compares the bit error rate performance under the NMSA method and the AN-MSA method. The variable node distribution of the irregular LDPC code is λ(x)=4032x+2688x ² +1344x ⁸ , and the check node distribution is ρ(x)=4032x ⁶ . Among them, the coefficient before x ^d-1 represents the number of nodes with degree d. It can be seen from the figure that the performance of AN-MSA method (annealing coefficient β=0.75) is about 0.1-0.2dB higher than that of NMSA method (optimized multiplicative correction factor 0.85), which is better than other improved methods.

图7：是AWGN信道下，总长8064，信息长度6048，3/4码率的非规则LDPC码λ(x)＝1008x+6048x²+1008x⁷，ρ(x)＝2016x²⁷在NMSA方法，AN-MSA方法(退火系数β＝0.75)下的误帧率性能比较。我们给出的修正方案使得译码性能比NMSA方法(优化的乘性修正因子0.85)提高了约0.1-0.2dB。Fig. 7: Under the AWGN channel, the total length is 8064, the information length is 6048, the irregular LDPC code λ(x)=1008x+6048x ² +1008x ⁷ of 3/4 code rate, ρ(x)=2016x ²⁷ in NMSA method, AN - Frame error rate performance comparison under MSA method (annealing coefficient β=0.75). The correction scheme we give improves the decoding performance by about 0.1-0.2dB compared with the NMSA method (optimized multiplicative correction factor 0.85).

Claims

1. A minimum-sum decoding method for low-density parity-check codes based on selective annealing, characterized in that: in the minimum-sum iterative decoding process of low-density parity-check codes, variable nodes and check nodes perform soft values successively Update; in an iteration process, the variable node makes a hard judgment on the total amount of information to judge whether each check-type check is successful; if the check-type checks are all successful, the iterative decoding will automatically stop, otherwise the subsequent check When the soft value of the verification node is updated, the verification node whose verification is successful is updated according to the original minimum sum principle, and the verification node whose verification is unsuccessful is updated based on the soft value of the minimum sum principle and multiplied by a value less than The coefficient β of 1 completes the annealing treatment;

The soft value update at the verification node performs selective annealing according to whether the verification formula satisfies the verification, and executes the bipartite graph representation based on the low-density parity-check code. The specific expression is several steps executed in the following order:

Definition: check matrix H _M×N of low-density parity-check code = [h _{m, n} ], where M is the number of rows of the check matrix, N is the number of columns of the check matrix, h _{m, n} represent the check matrix The element in the mth row and nth column of the verification matrix, m ranges from 1 to M, and n ranges from 1 to N; the corresponding bipartite graph variable node and check node set is V={v _n , n∈[ 1, N]}, C={c _m , m∈[1, M]}; define the check node set A(n)={m, h _{m, n} =1} that variable node v _n participates in, contained in The variable node set B(m) of the check node c _m ={n, h _m,n =1}; define the node set A(n)\m in which the check node c _m is removed from the check node set A(n) , define the node set B(m)\n that removes the variable node v _n from the variable node set B(m), and the code sequence u=(u ₁ , u ₂ ,..., u _n ,..., u _N ) of length N ;

Step 1: Initialization: binary shift keying BPSK modulation x _n =1-2u _n , n∈[1,N] passes through the Gaussian white noise channel, and the received signal sequence Y={y _n |y _n =x _n + w _n , n∈[1,N]}, where w _n is Gaussian white noise with zero mean variance σ ² ; the initial variable node v _n , n∈[1,N] is sent to the check node c _m , m∈A (n) output side information

The number of iterations k=0;

Step 2: variable node calculation: each variable node v _n will output edge information of all participating check nodes c _m , m∈A(n)

Add, as the total output of the variable node for the kth iteration of the current iteration

{L L}_{n no}^{k k} = = {y the y}_{n no} + + \underset{m m &Element; &Element; A A ((n no))}{Σ Σ} {L L}_{mn mn}^{k k}

According to the total output information of each variable node in the current iteration

According to the following formula to make a hard judgment of the symbol to obtain the output sequence

z^{k} = (z_{1}^{k}, z_{2}^{k}, &Center Dot; &Center Dot; &Center Dot;, z_{no}^{k}, &Center Dot; &Center Dot; &Center Dot;, z_{N}^{k})

{z z}_{n no}^{k k} = = \{\begin{matrix} 00,, & if if & {L L}_{n no}^{k k} > > 00 \\ 11,, & if if & {L L}_{n no}^{k k} \leq \leq 00 \end{matrix};;

The check formula output information that each variable node v _n will participate in

Add, as the output edge information from variable node v _n to check node c _m :

{L L}_{nm nm}^{k k} = = \underset{{m m}^{' '} &Element; &Element; A A ((n no)) \ \ m m}{Σ Σ} {L L}_{{m m}^{' '} n no}^{k k} = = {L L}_{n no}^{k k} - - {L L}_{mn mn}^{k k};;

Different from the minimum sum algorithm, the likelihood ratio information of the variable node to the check node is transmitted

This information is in addition to the normal side information

In addition, it is necessary to add 1 bit of hard judgment information, that is, to pass along the edge v _n →c _m :

{\overset{&OverBar; &OverBar;}{L L}}_{nm nm}^{k k} = = (({L L}_{nm nm}^{k k},, {z z}_{n no}^{k k}));;

Step 3: check node calculation preprocessing: each check node s _m first checks the edge information

Hard judgment information in Perform processing to calculate whether the verification formula is successful:

{s the s}_{m m}^{k k} = = \underset{n no &Element; &Element; B B ((m m))}{Σ Σ} &CirclePlus; &CirclePlus; {z z}_{n no}^{k k},, m m &Element; &Element; [[11,, M m]]

Indicates XOR accumulation operation; write down the serial numbers of all check nodes that do not satisfy the check

u = {m | {the s}_{m}^{k} = 1, m &Element; [1, m]},

Simultaneous order

S = {m | {the s}_{m}^{k} = 0, m &Element; [1, m]}

Indicates the sequence number set of all verification nodes that satisfy the verification; if the number of nodes that do not satisfy the verification is 0, that is, |U|=0, the hard-judgment output result of step 2 will be used as the final decoding output

At the same time, the decoding is terminated. If it cannot be satisfied and the number of iterations k is equal to the maximum number of iterations, the decoding fails and the decoding is terminated. Otherwise, iterative decoding continues, k++;

Step 4: check node calculation: each check node c _m outputs side information according to the variable node of the k-1th iteration

According to the minimum sum principle, calculate the edge information output from the k-th iteration node c _m to the variable node v _n , if the check node m belongs to the set U, perform annealing processing, otherwise do not anneal, that is, perform the following operations:

\{\begin{matrix} {L L}_{mn mn}^{k k} = = β β \cdot \cdot ((\underset{{n no}^{' '} &Element; &Element; B B ((m m)) \ \ n no}{Π Π} sign sign (({L L}_{n no' ' m m}^{k k - - 11})))) \cdot &Center Dot; ((\underset{{n no}^{' '} &Element; &Element; B B ((m m)) \ \ n no}{min min} | | {L L}_{{n no}^{' '} m m}^{k k - - 11} | |)),, & if if & m m &Element; &Element; U u \\ {L L}_{mn mn}^{k k} = = ((\underset{{n no}^{' '} &Element; &Element; B B ((m m)) \ \ n no}{Π Π} sign sign (({L L}_{{n no}^{' '} m m}^{k k - - 11})))) \cdot &Center Dot; ((\underset{{n no}^{' '} &Element; &Element; B B ((m m)) \ \ n no}{min min} | | {L L}_{{n no}^{' '} m m}^{k k - - 11} | |)),, & if if & m m &Element; &Element; S S \end{matrix}

Among them, β<1 is the annealing coefficient,

sign (x) = \{\begin{matrix} 1, & if & x &Greater Equal; 0 \\ - 1, & if & x < 0 \end{matrix}

Indicates the sign function,

Indicates to take the minimum value of all x _n whose subscripts belong to B; jump to step 2 after execution.