Normalization minimum sum decoding method and system based on dynamic oscillation factor

Abstract

The application discloses a kind of normalization minimum and decoding method and system based on dynamic oscillation factor, method includes the following steps: step S1: initialization module stores input information, input information includes LDPC code word sequence and corresponding check matrix H;Step S2: influence parameter calculation module is calculated in turn to obtain double normalization factor α1 And α2, and according to the dynamic oscillation factor of iteration number k variation and the external probability message that correction check node transmits to variable node;Step S3: decoding module uses the influence parameter of influence parameter calculation module input, implements decoding algorithm to input LDPC code word sequence, obtains the last output code word sequence.The application can improve iteration message accuracy, reduce the influence of iteration message oscillation on decoding efficiency, enhance the reliability and convergence of LDPC decoding algorithm for the difference between variable node message minimum and second minimum.

Description

Technical Field

[0001] This invention belongs to the field of communication technology, specifically relating to a normalized minimum sum decoding method and system based on dynamic oscillation factor. Background Technology

[0002] Low-density parity-check (LDPC) codes are a type of forward error-correcting code based on a parity-check matrix. They possess superior performance characteristics such as high coding gain, low complexity, and low error level. Theoretically, their decoding performance can approach the Shannon limit. They are widely used in various communication standards and have promising application prospects in the field of reliable information transmission.

[0003] LDPC decoding algorithms are essentially message-iterative decoding algorithms based on the LDPC parity-check matrix represented by a Tanner graph. They are mainly divided into hard-decision and soft-decision algorithms. Hard-decision algorithms have low computational complexity but poor decoding performance. Soft-decision algorithms have excellent performance; their basic algorithm is the belief propagation (BP) algorithm, which uses posterior probability information to determine the decoding. Node probability messages are passed between variable nodes and check nodes through edges on the Tanner graph, iterating and updating to a stable value after multiple iterations. The decoding reliability is improved by the constraints of the check equation represented by the parity-check matrix. The min-sum algorithm is a standard improved BP algorithm. It simplifies the check node update rules of the logarithmic field BP algorithm through minimum value operations and sign operations, reducing computational complexity and making it easy to implement in hardware. To compensate for the loss caused by the min-sum algorithm's overestimation of the magnitude using approximations, correction factors and offset factors are used to further correct the node message magnitude, effectively improving decoding performance with almost no increase in complexity.

[0004] Traditional improved min-sum algorithms enhance decoding performance by correcting message amplitude, but they neglect message transmission accuracy and reliability. Using a single correction factor, based on the difference between the minimum and second-minimum values ​​of variable node messages, suffers from insufficient accuracy in verifying node message updates. Furthermore, under high signal-to-noise ratio conditions, the cycles on the Tanner graph corresponding to the parity-check matrix, especially short cycles, can cause oscillations in external information transmitted between nodes, significantly impacting message independence and reliability, and reducing the convergence of the decoding algorithm. Therefore, optimization of the improved min-sum algorithm is necessary to further enhance the accuracy and reliability of iterative messages. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a normalized minimum sum decoding method and system based on dynamic oscillation factors, so as to improve the decoding performance of the decoding algorithm, such as convergence and bit error rate.

[0006] The present invention adopts the following technical solution:

[0007] The normalized minimum sum decoding method based on dynamic oscillation factors specifically includes the following steps:

[0008] Step S1: Initialize the module to store input information, which includes a certain type of LDPC codeword sequence y and the corresponding parity check matrix H;

[0009] Step S2: To address the issue of node message update accuracy caused by the difference between the minimum and second minimum external probability messages passed from the dependent variable node to the verification node in the iterative decoding process, the parameter calculation module sequentially calculates and obtains the double normalization factors α1 and α2, as well as the dynamic double oscillation factor that changes according to the iteration number k. and Correct the external probability message passed from the verification node to the variable node;

[0010] Step S3: The decoding module uses the influence parameters input by the influence parameter calculation module to perform a decoding algorithm on the input LDPC codeword sequence y to obtain the final output codeword sequence x.

[0011] Preferably, step S2 includes:

[0012] Step S21: First, based on the logarithmic field BP algorithm and the minimum sum decoding algorithm, and according to the mean of the first iteration message, the double normalization factors α1 and α2 are obtained to correct the minimum value min and the second smallest value min2 of the variable node message, respectively.

[0013] Step S22: Next, apply the Monte Carlo method to randomly obtain multiple sets of double oscillation factors in the range (0,1) to further correct the verification node messages corresponding to the minimum and second smallest values ​​min2 of the variable node messages, and obtain oscillation factors with different weights according to the iteration number k. and To determine whether the message symbols of the preceding and following check nodes have been flipped, different message update strategies are adopted to reduce the oscillation of the check node's iterative messages, thereby further improving the reliability and accuracy of the check node's message updates.

[0014] Preferably, step S3 includes:

[0015] Step S31: The variable node message initialization process does not perform channel estimation. The log-likelihood ratio probability message is simplified into a channel received information sequence y, which is used as the initial message received by the variable node.

[0016] Step S32: Use double normalization factors α1 and α2 to correct the original check node update messages corresponding to the minimum and second smallest external probability messages of the variable nodes, respectively, thereby improving the accuracy of the normalized minimum sum decoding algorithm using a single normalization factor.

[0017] Step S33: Based on the dual-normalized factor minimum sum decoding algorithm, considering the impact of node message oscillation on decoding convergence, and also for the difference analysis of minimum and second-minimum value messages, an oscillation factor with different weights varying according to the iteration number k is used. and Correct the check node message under the condition that the message symbol is flipped, and optimize the reliability and convergence of the decoding algorithm;

[0018] Step S34: Based on the verification node message, calculate the external probability message that the variable node passes to the verification node in the k-th iteration, and use it as the input variable node message for the next iteration; at the same time, calculate the posterior probability of the variable node.

[0019] Step S35 uses the posterior probability information of the variable nodes to perform hard-decision decoding to obtain the codeword vector x for the k-th iteration. k ;

[0020] Step S36: If the checksum x is satisfied k ·H T =0 or the number of iterations I reaches the set maximum number of iterations I. max If the output codeword sequence is obtained after decoding, the decoding process ends; otherwise, I is incremented by 1, and the process returns to step S32 to continue the iterative update decoding step.

[0021] This invention also discloses a normalized minimum sum decoding system based on a dynamic oscillation factor, which includes the following modules:

[0022] Initialization module: Stores input information, including LDPC codeword sequences and corresponding parity check matrices H;

[0023] The parameter calculation module calculates the double normalization factors α1 and α2, and the dynamic oscillation factor that varies with the iteration number k. and Correct the external probability message passed from the verification node to the variable node;

[0024] Decoding module: Using the influence parameters input by the influence parameter calculation module, the module performs a decoding algorithm on the input LDPC codeword sequence to obtain the final output codeword sequence.

[0025] Preferably, the parameter calculation module is as follows:

[0026] Based on the logarithmic field BP algorithm and the minimum sum decoding algorithm, and calculated according to the mean of the first iteration message, the double normalization factors α1 and α2 are obtained to correct the minimum value min and the second smallest value min2 of the variable node message, respectively.

[0027] Multiple codeword sequences within the range [0,1] are randomly constructed. The Monte Carlo method is applied to obtain the check node messages corresponding to the minimum and second minimum values ​​(min2) of the further modified variable node messages, as well as the oscillation factor γ with different weights varying according to the iteration number k. k 1 and γ k 2. Determine whether the message symbols of the preceding and following check nodes have been flipped, and adopt different message update strategies: If the message symbols are consistent, use a fixed value of the double normalization factor to correct the check node update message based on the original double normalization factor minimum sum algorithm steps; if the message symbols have been flipped, use a dynamic double oscillation factor based on the difference between the check node messages corresponding to the minimum value min and the second smallest value min2 of the variable node message, and improve the accuracy of the check node update message under different iteration numbers.

[0028] Preferably, the decoding module is as follows:

[0029] The log-likelihood ratio probability message is simplified into a channel received information sequence y, which serves as the initial message received by the variable node.

[0030] Using double normalization factors α1 and α2, the original verification node update messages corresponding to the minimum and second smallest external probability messages of variable nodes min and min2 are corrected respectively.

[0031] Based on the dual-normalized factor minimum sum decoding algorithm, and for the analysis of the difference between the minimum and second-minimum value messages, an oscillation factor with different weights varying according to the iteration number k is used. and Differential correction is applied to check node messages under conditions where message symbols are flipped.

[0032] Based on the verification node message, calculate the external probability message that the variable node passes to the verification node in the k-th iteration, and use it as the input variable node message for the next iteration; at the same time, calculate the posterior probability of the variable node.

[0033] Based on the posterior probability information of the variable nodes, hard-decision decoding obtains the codeword vector x for the k-th iteration. k ;

[0034] If the checksum x is satisfied k ·H T =0 or the number of iterations I reaches the set maximum number of iterations I. max If the output codeword sequence is obtained after decoding, the decoding process ends; otherwise, the count I is incremented by 1, and the process returns to continue iteratively updating the decoding process.

[0035] Compared with existing technologies, this invention takes into account the message update accuracy problem caused by the difference between the minimum and second minimum values ​​of variable node messages in the verification node message update step. Based on the use of double normalization factors to correct message amplitude, it further optimizes the process by using oscillation factors with different weights according to the iteration number. This can effectively improve the reliability and accuracy of verification node message updates, and enhance the decoding performance such as convergence and error rate of the decoding algorithm. Attached Figure Description

[0036] Figure 1 This is the overall flowchart of the normalized minimum sum decoding method based on dynamic oscillation factor in Embodiment 1 of the present invention.

[0037] Figure 2 This is a flowchart of the parameter calculation module of the present invention.

[0038] Figure 3 This is a flowchart of the decoding module algorithm of the present invention.

[0039] Figure 4 This is a block diagram of the normalized minimum sum decoding system based on the dynamic oscillation factor in Embodiment 2 of the present invention. Detailed Implementation

[0040] The preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0041] The LDPC decoding algorithm is a confidence message propagation algorithm based on the parity-check matrix. The min-sum algorithm estimates the magnitude of the number-domain message by taking the minimum value and performing sign operations, significantly reducing computational complexity. The normalized min-sum algorithm selects a single, fixed normalization factor, effectively compensating for the performance loss caused by overestimation of the magnitude. However, existing decoding methods suffer from reliability and convergence issues due to the potential for message oscillation in parity-check node messages caused by cycles in the Tanner graph corresponding to the parity-check matrix, and the impact of the difference between the minimum and second-smallest values ​​on the accuracy of node message updates. Therefore, this invention provides the following embodiments to address these issues.

[0042] Example 1

[0043] like Figure 1 As shown in the figure, this embodiment of a normalized minimum sum decoding method based on dynamic dual oscillation factors specifically includes the following steps:

[0044] Step S1: The initialization module stores the input LDPC codeword sequence y of a certain type and the corresponding parity-check matrix H, which also serves as the input for subsequent modules. Different parity-check matrix structures correspond to different decoding systems.

[0045] Step S2: To address the issue of the difference between the minimum and second minimum external probability messages passed from the dependent variable node to the verification node in the iterative decoding process, which affects the accuracy of node message updates, the parameter calculation module calculates and obtains the double normalization factors α1 and α2 sequentially, as well as the dynamic oscillation factor that changes according to the iteration number k. and Correct the external probability message passed from the verification node to the variable node;

[0046] Step S3: The decoding module uses the influence parameters input by the influence parameter calculation module to implement the improved decoding algorithm process on the input LDPC codeword sequence y, and obtains the final output codeword sequence x.

[0047] In this embodiment, for example, Figure 2 As shown, the specific processing flow of the parameter calculation module includes:

[0048] Step S21: First, based on the logarithmic field BP algorithm and the minimum sum decoding algorithm, and according to the mean of the first iteration message, the double normalization factors α1 and α2 are obtained to correct the minimum value min and the second smallest value min2 of the variable node message, respectively.

[0049] By traversing and comparing the message magnitudes of all variable nodes passed to the nth verification node in the kth iteration, the minimum message value min and the second smallest message value min2 of the variable node set are obtained.

[0050]

[0051] Where m is the variable node index and n is the check node index. Vn\m is the set of all variable nodes connected to the nth check node, excluding the mth variable node, and index n This is the index of the variable node corresponding to the minimum value of the variable node message amplitude; `min` is used for minimum value calculation. This refers to the external probability message passed from the verification node to the variable node in the k-th iteration.

[0052] Original logarithmic field BP algorithm check node update message It can be obtained from the following formula:

[0053]

[0054] Where tanh represents the hyperbolic function operation. and The indexes of the second smallest and smallest values ​​of the variable node messages correspond to the check node messages.

[0055] The minimum sum algorithm is based on an approximation of the number field BP algorithm, reducing computational complexity by estimating the magnitude through minimum value operations. Its verification node updates messages. It can be obtained from the following formula:

[0056]

[0057] Where sign represents symbolic operation. and The indexes of the second smallest and smallest values ​​of the variable node messages correspond to the check node messages.

[0058] The double normalization factors α1 and α2 are fixed values ​​across all iterations, calculated based on the mean of the first iteration message, and can be obtained using the following formula.

[0059]

[0060]

[0061] Step S22: Next, apply the Monte Carlo method to randomly obtain multiple sets of double oscillation factors in the range (0,1) to further correct the check node messages corresponding to the minimum value min and the second smallest value min2 of the variable node messages. Substitute each set of oscillation factors into the normalized minimum sum algorithm of the improved fixed double normalization factor, determine whether the symbols of the check node messages before and after are flipped, adopt different message update strategies, obtain the relationship between each set of oscillation factors and the bit error rate at each iteration, and thus determine the optimal set of oscillation factors corresponding to the number of iterations in each iteration.

[0062] The calculation method for the check node update step of the original minimum sum decoding algorithm is as follows:

[0063]

[0064] in, This refers to the external probability message passed from the verification node to the variable node in the k-th iteration.

[0065] Improved inspection node update message As shown in the following formula:

[0066]

[0067] in, and To adjust the minimum and second minimum values ​​of the variable node messages min and min2 respectively, based on the oscillation factors with different weights according to the iteration number k, the values ​​range from (0,1).

[0068] The Monte Carlo method is a computational method that uses random sampling to obtain statistical values ​​and deduce numerical solutions. Applying the Monte Carlo method allows for accurate determination of the relationship between the oscillation factor and the bit error rate for each iteration.

[0069] The Tanner graph corresponds one-to-one with the parity-check matrix, representing the connection relationship between the parity-check nodes and the variable nodes. When a cycle exists in the Tanner graph corresponding to the parity-check matrix, error node messages in the iterative decoding process will be passed cyclically through the cycle structure, resulting in oscillation of the parity-check nodes. This causes the parity-check node message updates to originate from nodes within the cycle, weakening the stability and independence of messages in previous and subsequent iterations, and significantly impacting decoding efficiency and convergence.

[0070] like Figure 3 As shown, the specific processing flow of the decoding module includes:

[0071] Step S31: The variable node message initialization process does not perform channel estimation. The log-likelihood ratio probability message is simplified into a channel received information sequence y, which is used as the initial message received by the variable node.

[0072]

[0073] Among them, P m This is the channel initial probability message.

[0074] Step S32: Use double normalization factors α1 and α2 to correct the original check node update messages corresponding to the minimum and second smallest external probability messages of the variable nodes, respectively, thereby improving the accuracy of the normalized minimum sum decoding algorithm using a single normalization factor; the calculation method is the same as in step S22. As shown.

[0075] Step S33: Based on the dual-normalized factor minimum sum decoding algorithm, considering the impact of node message oscillation on decoding convergence, and also for the difference analysis of minimum and second-minimum value messages, an oscillation factor with different weights varying according to the iteration number k is used. and Correcting the check node message under the condition of message symbol flipping further optimizes reliability and convergence; the calculation method is the same as in step S22. As shown.

[0076] Step S34: Based on the verification node message, calculate the external probability message passed from the variable node to the verification node in the k-th iteration. The variable node message is used as input for the next iteration. The posterior probability of the variable node is also calculated.

[0077]

[0078]

[0079] Among them, C m \n represents the set of all check nodes connected to the m-th variable node, excluding the n-th check node.

[0080] Step S35: Based on the posterior probability information of the variable nodes, hard-decode to obtain the codeword vector for this iteration;

[0081]

[0082] in, Let m be the code element corresponding to the node index m of the codeword vector variable in the k-th iteration.

[0083] Step S36: Determine if the checksum x is satisfied. k ·H T =0 or the number of iterations I reaches the set maximum number of iterations I. max .

[0084] If the conditions are met, the decoding process ends, and the codeword sequence result after decoding is output. Otherwise, increment I by 1 and return to step S32 to continue the iterative update decoding process.

[0085] By studying the accuracy of the check node update messages corresponding to the minimum and second-smallest values ​​(min2) of the variable node messages, and using a dual oscillation factor with different weights varying according to the number of iterations, the normalized minimum sum algorithm with dual normalization factors is further optimized to obtain the final decoded codeword output. This invention can effectively reduce the impact of the possible loop structure in the Tanner graph corresponding to the LDPC check matrix on the decoding convergence, and can more accurately improve the reliability and accuracy of the check node update messages, resulting in superior decoding performance.

[0086] Example 2

[0087] like Figure 4 As shown, this embodiment discloses a system based on Embodiment 1, including the following modules:

[0088] Initialization module: Stores input information, including LDPC codeword sequences and corresponding parity check matrices H;

[0089] The parameter calculation module calculates the double normalization factors α1 and α2, and the dynamic oscillation factor that varies with the iteration number k. and Correct the external probability message passed from the verification node to the variable node;

[0090] Decoding module: Using the influence parameters input by the influence parameter calculation module, the module performs a decoding algorithm on the input LDPC codeword sequence to obtain the final output codeword sequence.

[0091] This invention discloses a normalized minimum sum decoding method and system based on a dynamic oscillation factor. The method includes: an initialization module storing input information, including a certain type of LDPC codeword sequence and the corresponding parity-check matrix; an influence parameter calculation module sequentially calculating a double normalization factor and an oscillation factor, calculating the double normalization factor based on the mean of the first iteration message, determining the dynamic oscillation factor under different iteration numbers using the Monte Carlo method, and updating the node external probability message with weights; and a decoding module using the input influence parameters to implement an improved decoding algorithm on the input sequence to obtain the output codeword result. This invention addresses the difference between the minimum and second minimum values ​​of variable node messages, improving the accuracy of iterative messages, reducing the impact of iterative message oscillations on decoding efficiency, and enhancing the reliability and convergence of the LDPC decoding algorithm.

[0092] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope of the present invention.

Claims

1. A normalized minimum sum decoding method based on dynamic oscillation factor, characterized in that, Specifically, the following steps are included: Step S1: Initialize the module to store input information, including the LDPC codeword sequence and the corresponding parity check matrix H; Step S2: To address the issue of the difference between the minimum and second minimum external probability messages passed from the dependent variable node to the verification node in the iterative decoding process, which affects the accuracy of node message updates, the parameter calculation module calculates and obtains the double normalization factors α1 and α2 sequentially, as well as the dynamic oscillation factor that changes according to the iteration number k. and Correct the external probability message passed from the verification node to the variable node; the specific steps are as follows: Step S21: Based on the logarithmic field BP algorithm and the minimum sum decoding algorithm, calculate the double normalization factors α1 and α2 of the minimum value min and the second smallest value min2 of the variable node message according to the mean of the first iteration message; Step S22: Apply the Monte Carlo method to randomly obtain multiple sets of double oscillation factors in the range (0,1) to further correct the check node messages corresponding to the minimum value min and the second smallest value min2 of the variable node messages. Substitute each set of oscillation factors into the improved normalized minimum sum algorithm of fixed double normalization factors, determine whether the symbols of the check node messages before and after are flipped, adopt different message update strategies, obtain the relationship between each set of oscillation factors and the bit error rate at each iteration, and thus determine the optimal set of oscillation factors corresponding to the number of iterations in each iteration. Step S3: The decoding module uses the influence parameters input by the influence parameter calculation module to implement an improved decoding algorithm on the input LDPC codeword sequence y, obtaining the final output codeword sequence x; this step is detailed as follows: Step S31: The variable node message initialization process does not perform channel estimation. The log-likelihood ratio probability message is simplified into a channel received information sequence y, which is used as the initial message received by the variable node. ; Step S32: Use double normalization factors α1 and α2 to correct the original check node update messages corresponding to the minimum and second smallest values ​​min2 of the external probability messages of the variable nodes, respectively; Step S33: Based on the dual-normalized factor minimum sum decoding algorithm, considering the impact of node message oscillation on decoding convergence, for the difference analysis of minimum and second-minimum value messages, an oscillation factor with different weights varying according to the iteration number k is used. and Correct the check node message under the condition that the message symbol is flipped; Step S34: Based on the verification node message, calculate the external probability message passed from the variable node to the verification node in the k-th iteration. , as the input variable node message for the next iteration; Step S35: Based on the posterior probability information of the variable nodes, hard-decode to obtain the codeword vector for this iteration; Step S36: judging whether the check sum x is satisfied k ·H T = 0 or the iteration number I reaches the set maximum iteration number I max ; If the conditions are met, the decoding process ends, and the codeword sequence result after decoding is output. Otherwise, increment I by 1 and return to step S32 to continue the iterative update decoding step.

2. A normalized minimum sum decoding system based on a dynamic oscillation factor, characterized in that, Includes the following modules: Initialization module: Stores input information, including LDPC codeword sequences and corresponding parity check matrices H; The parameter calculation module addresses the issue of inconsistent external probability messages (minimum and second smallest values) passed from the dependent variable node to the verification node during the iterative decoding process, which affects the accuracy of node message updates. It calculates and obtains the double normalization factors α1 and α2, as well as a dynamic oscillation factor that varies with the iteration number k. and Correct the external probability message passed from the verification node to the variable node; specifically as follows: Based on the logarithmic field BP algorithm and the minimum sum decoding algorithm, and calculated according to the mean of the first iteration message, the double normalization factors α1 and α2 are obtained to correct the minimum value min and the second smallest value min2 of the variable node message, respectively. The Monte Carlo method is applied to randomly obtain multiple sets of double oscillation factors in the range (0,1) to further correct the check node messages corresponding to the minimum value min and the second smallest value min2 of the variable node messages. Each set of oscillation factors is brought into the improved normalized minimum sum algorithm of fixed double normalization factors to determine whether the symbols of the check node messages before and after are flipped. Different message update strategies are adopted to obtain the relationship between each set of oscillation factors and the bit error rate at each iteration, thereby determining the optimal set of oscillation factors corresponding to the number of iterations in each iteration. Decoding module: Utilizing the influence parameters input from the influence parameter calculation module, the module applies an improved decoding algorithm to the input LDPC codeword sequence y to obtain the final output codeword sequence x; specifically as follows: The variable node message initialization process does not perform channel estimation. Instead, it simplifies the log-likelihood ratio probability message into a channel received information sequence y, which serves as the initial message received by the variable node. ; Using double normalization factors α1 and α2, the original verification node update messages corresponding to the minimum and second smallest external probability messages of variable nodes min and min2 are corrected respectively. Based on the dual-normalized factor minimum sum decoding algorithm, and considering the impact of node message oscillations on decoding convergence, this paper analyzes the differences between the minimum and second-minimum value messages and uses oscillation factors with different weights that vary according to the iteration number k. and Correct the check node message under the condition that the message symbol is flipped; Based on the verification node message, calculate the external probability message passed from the variable node to the verification node in the k-th iteration. , as the input variable node message for the next iteration; Based on the posterior probability information of the variable nodes, hard-decision decoding obtains the codeword vector for this iteration. Determine if the checksum x is satisfied. k ·H T =0 or the iteration count I reaches the set maximum iteration count I. max ; If the conditions are met, the decoding process ends, and the codeword sequence result after decoding is output. Otherwise, increment I by 1 and return to continue iteratively updating the decoding.

Images