CN110784232B - A Sliding Window Decoding Method for Space-Coupled LDPC Codes - Google Patents

Abstract

The invention provides a sliding window decoding method of a space coupling LDPC code in the technical field of communication, which comprises the following steps: step (b)S10, setting a value range of a window W according to the coupling width W and the coupling length L of the (J, K, L) SC-LDPC code; s20, determining the number of variable nodes and check nodes contained in the window W; s30, defining the leftmost original model diagram in the window W as a target symbol and executing belief propagation decoding on the target symbol; s40, setting a threshold value theta and the maximum iterative decoding times, iteratively decoding the target symbol in the window W, and calculating the average log-likelihood ratio of the target symbol in the window W

According to the threshold value theta and the average log-likelihood ratio

The size of the extended window W; and S50, after the iterative decoding of the current target symbol is finished, sliding the window W to the next position for decoding. The invention has the advantages that: the delay of belief propagation decoding of the SC-LDPC code is reduced, and meanwhile, the decoding performance is greatly improved.

Description

A Sliding Window Decoding Method for Space-Coupled LDPC Codes

technical field

The invention relates to the technical field of communication, in particular to a sliding window decoding method of a spatially coupled LDPC code.

Background technique

When the SC-LDPC code (spatially coupled LDPC code) is decoded using the belief-propagation (BP) decoding algorithm, it only starts decoding after receiving a complete codeword. When the code of the SC-LDPC code When the length is large, BP decoding will cause a higher delay.

In order to solve the problem of high delay in BP decoding, the following method is traditionally adopted: since the SC-LDPC code is a convolutional LDPC code (LDPC convolutional code, LDPC-CC), its parity check matrix is the same as that of the LDPC convolutional code. The structure of the parity check matrix is similar, showing a diagonal band structure with non-zero entries, which makes it possible to run BP decoding in a W-dimensional window (the W-dimensional window refers to the size of the window, and W is a positive integer), This iterative decoding scheme with a sliding window structure is called sliding window decoding (window decoding, WD). After receiving part of the codeword, the WD uses part of the parity check matrix of the codeword to perform BP decoding within a window. The decoding window slides along the diagonal strip of the parity-check matrix, and codewords are estimated group by group, which effectively reduces decoding delay, decoding complexity and memory requirements.

However, the traditional method has the following disadvantages: because WD limits BP decoding to a W-dimensional window, although WD reduces the delay and decoding complexity of BP decoding, it loses decoding performance.

Contents of the invention

The technical problem to be solved by the present invention is to provide a sliding-window decoding method for spatially coupled LDPC codes, which reduces the delay in belief propagation decoding of SC-LDPC codes and improves decoding performance.

The present invention is achieved in that a kind of spatially coupled LDPC code sliding window decoding method comprises the following steps:

Step S10: Coupling the original model graphs with L degree distributions of (J, K) to obtain (J, K, L) SC-LDPC codes, according to the coupling width of the (J, K, L) SC-LDPC codes w and the coupling length L set the value range of the window W: w+1≤W≤L; where J represents the degree of the variable node, K represents the degree of the check node, and both J and K are positive integers, and both w and L are is a positive number;

Step S20, determining the number of variable nodes and check nodes included in the window W;

Step S30, defining the leftmost protograph in the window W as the target symbol, and performing belief propagation decoding on the target symbol in the window W;

Step S40, setting a threshold θ and a maximum number of iterative decoding, iteratively decoding the target symbol according to the maximum number of iterative decoding in the window W, and calculating the window based on the number of variable nodes and check nodes The average log likelihood ratio L ^j of the target symbol in W, expand the size of the window W according to the threshold θ and the average log likelihood ratio L ^j ; where θ is a positive number;

Step S50 , after the iterative decoding of the current target symbol is completed, slide the window W to the next position, and redefine the target symbol for decoding until all target symbols are decoded.

Further, in the step S10, the coupling width w represents that the variable nodes of the original model graph are connected to the check nodes of the adjacent w original model graphs; the coupling length L represents that the SC-LDPC code consists of L original model graphs Graph construction is generated.

Further, the step S20 is specifically:

Let a=gcd(J,K), a represents the greatest common divisor of J and K, there are positive integers J' and K' respectively satisfying J=aJ', K=aK', and gcd(J',K')= 1, then there are K'W variable nodes and J'W check nodes in the window W.

Further, the step S40 specifically includes:

Step S41, setting a threshold θ and a maximum number of iterative decoding;

Step S42, iteratively decoding the target symbol within the window W;

Step S43, judging whether the number of times of iterative decoding is equal to the maximum number of times of iterative decoding, if so, then enter step S44; if not, then enter step S42;

Step S44, calculating the average log-likelihood ratio L ^j of the target symbol in the window W, and judging whether the average log-likelihood ratio L ^j is smaller than the threshold θ, and if so, adding 1 to the size of the window W, And go to step S30; if not, go to step S50.

Further, the threshold θ is specifically:

其中W_f表示窗口W的初始大小，W_max表示窗口的最大值，W_s表示当前窗口W的大小，inc＝W_max-W_f；

Where W _f represents the initial size of the window W, W _max represents the maximum value of the window, W _s represents the size of the current window W, inc=W _max -W _f ;

具体为：The mean log-likelihood ratio

Specifically:

其中

表示当前窗口目标符号的第i个信息位第j次迭代后的似然比,

表示目标符号总共包含的K′M个信息位第j次迭代后的平均对数似然比；K′为正整数；M表示(J,K,L)SC-LDPC码的扩展因子，即原模图中一个变量节点或者校验节点对应Tanner图中节点的个数。

in

Indicates the likelihood ratio of the i-th information bit of the target symbol in the current window after the j-th iteration,

Indicates the average log-likelihood ratio of the K′M information bits contained in the target symbol after the jth iteration; K′ is a positive integer; M represents the expansion factor of the (J, K, L) SC-LDPC code, that is, the original A variable node or check node in the model graph corresponds to the number of nodes in the Tanner graph.

Further, the step S50 is specifically:

After the iterative decoding of the current target symbol is completed, slide the window W to the next position, and redefine the target symbol for decoding, and judge whether the decoding of all target symbols is completed, if not, then enter step S30; if so, then End the process.

进行扩展，使得不必在接收到完整的码字后才开始译码，降低对SC-LDPC码进行置信传播译码的延迟，而所述窗口W的大小是变化的，提升了置信传播译码的性能。The advantage of the present invention is: by setting the window W, and performing iterative belief propagation decoding on the target symbol in the window W, and the size of the window W is based on the threshold θ and the average log likelihood ratio

Extending, so that it is not necessary to start decoding after receiving a complete codeword, reducing the delay of belief propagation decoding for SC-LDPC codes, and the size of the window W is variable, which improves the performance of belief propagation decoding performance.

Description of drawings

The present invention will be further described below in conjunction with the embodiments with reference to the accompanying drawings.

FIG. 1 is a flowchart of a sliding window decoding method for a spatially coupled LDPC code according to the present invention.

Fig. 2 is a schematic diagram of the construction process of the (3,6,10) SC-LDPC code.

FIG. 3 is a schematic diagram of size expansion of a window W in the present invention.

Fig. 4 is a simulation diagram of the present invention and traditional sliding window decoding.

FIG. 5 is a schematic diagram of conventional sliding window decoding that slides along the diagonal bands of the parity check matrix.

Fig. 6 is a schematic diagram of traditional sliding window decoding where the decoding window slides along the original model graph of the spatially coupled LDPC code.

Detailed ways

Please refer to Fig. 1 to shown in Fig. 6, one of the preferred embodiments of a kind of spatially coupled LDPC code sliding window decoding method of the present invention, comprises the following steps:

Step S10, perform edge extension coupling on L original model graphs with degree distribution (J, K) to obtain (J, K, L) SC-LDPC code, according to the (J, K, L) SC-LDPC code The coupling width w and the coupling length L set the value range of the window W: w+1≤W≤L; where J represents the degree of the variable node, K represents the degree of the check node, and J and K are both positive integers, w and L are all positive numbers;

Step S20, determining the number of variable nodes and check nodes included in the window W;

Step S30, define the leftmost protograph in the window W as the target symbol, and perform belief propagation decoding on the target symbol in the window W;

Step S40, setting a threshold θ and a maximum number of iterative decoding, iteratively decoding the target symbol according to the maximum number of iterative decoding in the window W, and calculating the window based on the number of variable nodes and check nodes The average log likelihood ratio L ^j of the target symbol in W, expand the size of the window W according to the threshold θ and the average log likelihood ratio L ^j ; where θ is a positive number; the log likelihood ratio is the log -likelihood ratios, LLR;

Step S50 , after the iterative decoding of the current target symbol is completed, slide the window W to the next position, and redefine the target symbol for decoding until all target symbols are decoded.

In the step S10, the coupling width w represents that the variable nodes of the protograph are connected to the check nodes of the adjacent w protographs; the coupling length L represents that the SC-LDPC code is generated by constructing L protographs .

The step S20 is specifically:

Let a=gcd(J,K), a represents the greatest common divisor of J and K, there are positive integers J' and K' respectively satisfying J=aJ', K=aK', and gcd(J',K')= 1, then there are K'W variable nodes and J'W check nodes in the window W.

The step S40 specifically includes:

Step S41, setting a threshold θ and a maximum number of iterative decoding;

Step S42, iteratively decoding the target symbol within the window W;

Step S43, judging whether the number of times of iterative decoding is equal to the maximum number of times of iterative decoding, if so, then enter step S44; if not, then enter step S42;

判断所述平均对数似然比

是否小于阈值θ，若是，则将所述窗口W的大小加1，并进入步骤S30；若否，则进入步骤S50。若虽然平均对数似然比

小于阈值θ，但所述窗口W的大小已经扩展到最大值，则进入步骤S50。Step S44, calculating the average log likelihood ratio of the target symbols in the window W

Judging the mean log-likelihood ratio

Whether it is smaller than the threshold θ, if yes, add 1 to the size of the window W, and enter step S30; if not, enter step S50. If although the mean log-likelihood ratio

is smaller than the threshold θ, but the size of the window W has expanded to the maximum value, then enter step S50.

The threshold θ is specifically:

其中W_f表示窗口W的初始大小，W_max表示窗口的最大值，W_s表示当前窗口W的大小，inc＝W_max-W_f；

Where W _f represents the initial size of the window W, W _max represents the maximum value of the window, W _s represents the size of the current window W, inc=W _max -W _f ;

具体为：The mean log-likelihood ratio

Specifically:

其中

表示当前窗口目标符号的第i个信息位第j次迭代后的似然比,

表示目标符号总共包含的K′M个信息位第j次迭代后的平均对数似然比；K′为正整数；M表示(J,K,L)SC-LDPC码的扩展因子，即原模图中一个变量节点或者校验节点对应Tanner图中节点的个数。

in

Indicates the likelihood ratio of the i-th information bit of the target symbol in the current window after the j-th iteration,

Indicates the average log-likelihood ratio of the K′M information bits contained in the target symbol after the jth iteration; K′ is a positive integer; M represents the expansion factor of the (J, K, L) SC-LDPC code, that is, the original A variable node or check node in the model graph corresponds to the number of nodes in the Tanner graph.

The step S50 is specifically:

After the iterative decoding of the current target symbol is completed, slide the window W to the next position, and redefine the target symbol for decoding, and judge whether the decoding of all target symbols is completed, if not, then enter step S30; if so, then End the process.

Two of the preferred embodiments of a kind of spatially coupled LDPC code sliding window decoding method of the present invention comprise the following steps:

Step S10, performing edge extension coupling on 10 protographs with degree distributions of (3,6) to obtain (3,6,10) SC-LDPC codes, according to the (3,6,10) SC-LDPC codes Coupling width 2 and coupling length 10 set the value range of the window W: 3≤W≤10; where J represents the degree of variable nodes, and K represents the degree of check nodes;

Step S20, let a=gcd(3,6), a represents the greatest common divisor of 3 and 6, there are positive integers J' and K' respectively satisfying 3=aJ', 6=aK', and gcd(J', K ')=1, then there are K'W variable nodes and J'W check nodes in the window W, J'=1, K'=2;

Step S30, define the leftmost protograph in the initial window W with a size of 3 as the target symbol, and perform belief propagation decoding on the target symbol in the window W;

Step S40, setting a threshold θ, a maximum window size W _max and a maximum number of iterative decoding, and performing iterative decoding on the target symbol in the window W according to the maximum number of iterative decoding, based on the variable nodes and The number of check nodes calculates the average log-likelihood ratio L ^j of the target symbol in the window W, and expands the size of the window W according to the threshold θ and the average log-likelihood ratio L ^j until the average log-likelihood ratio L ^j is not less than the threshold θ or the window size is extended to W _max ; where θ is a positive number;

Step S50, after the iterative decoding of the current target symbol is completed, slide the window W to the next position, and redefine the target symbol for decoding, and judge whether the decoding of all target symbols is completed, if not, proceed to step S30; If so, end the process.

To sum up, the advantages of the present invention are: by setting the window W, and performing iterative belief propagation decoding on the target symbol in the window W, and the size of the window W is based on the threshold θ and the average logarithmic likelihood However, the ratio L ^j is extended, so that it is not necessary to start decoding after receiving a complete codeword, reducing the delay in belief propagation decoding of SC-LDPC codes, and the size of the window W is variable, which improves the confidence Spread decoding performance.

Although the specific embodiments of the present invention have been described above, those skilled in the art should understand that the specific embodiments we have described are only illustrative, rather than used to limit the scope of the present invention. Equivalent modifications and changes made by skilled personnel in accordance with the spirit of the present invention shall fall within the protection scope of the claims of the present invention.

Claims (4)

1. A space coupling LDPC code sliding window decoding method is characterized in that: the method comprises the following steps:

step S10, coupling the original pattern diagram with L degree distribution of (J, K) to obtain a (J, K, L) SC-LDPC code, and setting a value range of a window W according to the coupling width W and the coupling length L of the (J, K, L) SC-LDPC code: w is more than or equal to W +1 and less than or equal to L; j represents the degree of a variable node, K represents the degree of a check node, both J and K are positive integers, and both w and L are positive numbers;

s20, determining the number of variable nodes and check nodes contained in the window W;

step S30, defining the leftmost original model diagram in the window W as a target symbol, and performing belief propagation decoding on the target symbol in the window W;

s40, setting a threshold value theta and a maximum iterative decoding frequency, carrying out iterative decoding on the target symbol in the window W according to the maximum iterative decoding frequency, and calculating the average log-likelihood ratio of the target symbol in the window W based on the number of the variable nodes and the check nodes

According to the threshold value theta and the average log-likelihood ratio

The size of the extended window W; wherein θ is a positive number;

s50, after the iterative decoding of the current target symbol is finished, sliding the window W to the next position, and redefining the target symbol for decoding until the decoding of all the target symbols is finished;

the step S40 specifically includes:

step S41, setting a threshold value theta and a maximum iterative decoding frequency;

step S42, carrying out iterative decoding on the target symbol in the window W;

step S43, judging whether the iterative decoding times are equal to the maximum iterative decoding times, if so, entering step S44; if not, the step S42 is carried out;

step S44, calculating the average log-likelihood ratio of the target symbol in the window W

Determining the average log-likelihood ratio

Whether the window size is smaller than the threshold value theta or not, if so, adding 1 to the size of the window W, and entering the step S30; if not, the step S50 is carried out;

the threshold θ is specifically:

wherein W _f Represents the initial size of the window W, W _max Represents the maximum value of the window, W _s Denotes the size of the current window W, inc = W _max -W _f ；

The average log-likelihood ratio

The method specifically comprises the following steps:

wherein

Representing the likelihood ratio of the ith information bit of the current window target symbol after the jth iteration,

representing the average log-likelihood ratio of K' M information bits contained in the target symbol after the j iteration; k' is a positive integer; m represents the spreading factor of the (J, K, L) SC-LDPC code, namely the number of nodes in the Tanner graph corresponding to one variable node or check node in the original graph.

2. The sliding-window decoding method of spatial-coupled LDPC codes according to claim 1, wherein: in the step S10, the coupling width w represents that the variable node of the master graph is connected to the check nodes of w adjacent master graphs; the coupling length L represents that the SC-LDPC code is generated by L master graph constructions.

3. The sliding-window decoding method of spatial-coupled LDPC codes according to claim 1, wherein: the step S20 is specifically:

let a = gcd (J, K), a represents the greatest common divisor of J and K, and if there are positive integers J 'and K' satisfying J = aJ ', K = aK', and gcd (J ', K') =1, then there are K 'W variable nodes and J' W check nodes within the window W.

4. The sliding-window decoding method of spatial-coupled LDPC codes according to claim 1, wherein: the step S50 is specifically:

after the iterative decoding of the current target symbol is finished, sliding the window W to the next position, redefining the target symbol for decoding, judging whether the decoding of all the target symbols is finished or not, and if not, entering the step S30; if yes, the flow is ended.

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