A short code length LDPC decoding method based on gradient guided gibbs sampling

Abstract

This invention discloses a short-code-length LDPC decoding method based on gradient-guided Gibbs sampling, belonging to the field of wireless communication and channel coding technology. Addressing the performance degradation of traditional belief propagation decoding and the excessively high complexity of maximum likelihood decoding caused by short-code-length LDPC codes due to short loops, this invention constructs an objective function including cross-correlation terms and checksum synthesis terms; calculates the flip function values ​​of each bit using gradient information, and determines the sampling update order in ascending order; constructs a log-likelihood ratio surrogate value based on the difference in the objective function, performs Gibbs sampling in conjunction with temperature parameters, and mixes uniform random sampling to enhance global exploration; employs multiple parallel samplers for independent iteration, selecting the result with the largest objective function value as the decoding output. This invention achieves near-optimal decoding performance with significantly lower complexity than maximum likelihood decoding, and is particularly suitable for short-code-length and medium-code-length regular / irregular LDPC codes, exhibiting good scalability and hardware friendliness.

Description

Technical Field

[0001] This invention relates to the fields of wireless communication and channel coding technology, specifically to a short-code-length LDPC decoding method based on gradient-guided Gibbs sampling. This method achieves high-performance, low-complexity decoding of short-code-length LDPC codes by fusing the parity substructure information and gradient sorting information of the LDPC code. Background Technology

[0002] With the rapid development of industrial automation, intelligent transportation, and machine-type communication services, ultra-reliable low-latency communication (ULLP) places higher demands on channel coding and decoding algorithms. Low-density parity-check (LDPC) codes, due to their strong error correction capabilities and sparse structure, are widely regarded as one of the important coding techniques for meeting the requirements of ULLP. To meet the low-latency requirements, short-code-length LDPC codes are often used in practical systems.

[0003] However, existing decoding methods still have significant shortcomings in scenarios involving short-code-length LDPC codes. Traditional belief propagation decoding achieves approximate posterior probability calculation by iteratively passing messages on a Tanner graph, which performs well in long-code-length scenarios. However, for short-code-length LDPC codes, the Tanner graph typically contains many short cycles, increasing message correlation and causing belief propagation decoding performance to deviate significantly from optimality. On the other hand, maximum likelihood decoding can achieve optimal decoding performance, but its complexity increases exponentially with code length, making it difficult to implement in practical systems.

[0004] To reduce complexity, existing research has proposed low-complexity methods such as gradient descent and bit flipping, but these methods still lag significantly behind optimal decoding performance. In recent years, deep learning-based decoding schemes have also emerged, including neural belief propagation based on model expansion and end-to-end model-free decoding schemes. However, the former is limited by the original backpropagation framework, while the latter faces problems such as the curse of dimensionality and rapidly increasing training complexity.

[0005] Gibbs sampling in Markov chain Monte Carlo methods can approximate the target distribution by sampling from the conditional distribution step by step, thus providing a new approach for constructing near-optimal decoders. However, existing LDPC decoding methods based on Gibbs sampling do not fully utilize the check structure of LDPC codes when calculating conditional probabilities, resulting in low sampling efficiency. They often require a large number of samples to approach near-optimal performance, resulting in high computational overhead, and their performance degrades significantly with increasing code length.

[0006] Therefore, there is an urgent need for a new short-code-length LDPC decoding method that can fully utilize the structural features of LDPC codes while balancing decoding performance and computational complexity. Summary of the Invention

[0007] Technical challenges: Traditional backpropagation (BP) decoding exhibits significant performance degradation in scenarios with short-code, long LDPC codes containing numerous short loops. Machine-based (ML) decoding suffers from excessive complexity, making it difficult to implement in engineering. Existing Gibbs sampling-based decoding schemes fail to fully utilize the LDPC code check structure, resulting in low sampling efficiency and high near-optimal performance costs. In summary, existing methods struggle to simultaneously balance performance, complexity, and scalability in both regular and irregular code scenarios.

[0008] Technical Solution: To solve the above-mentioned technical problems, this invention proposes a short code-length LDPC decoding method based on gradient-guided Gibbs sampling, comprising the following steps:

[0009] S1. Obtain the received signal vector, LDPC code generation matrix, noise power, and decoding iteration parameters, and initialize the bit vector to be decoded;

[0010] S2. Construct a comprehensive objective function based on the current candidate codewords, the received signal, and the LDPC code parity-check matrix;

[0011] S3. For the bit position to be updated, construct a log-likelihood ratio surrogate value based on the difference of the comprehensive objective function when the bit takes different values;

[0012] S4. Calculate the flip function value for each symbol position, and determine the bit update order in the current outer iteration according to the ascending order of the flip function values;

[0013] S5. Perform Gibbs sampling updates sequentially according to the update order, and perform uniform random sampling with a predetermined probability when necessary to enhance the search space exploration capability;

[0014] S6. Repeat steps S3 to S5 until the preset number of outer iterations is reached to obtain candidate decoding results; further, use multiple parallel samplers to independently execute the above process, and select the result with the largest comprehensive objective function value from multiple candidate results as the final decoding output.

[0015] Preferably, the comprehensive objective function in step S2 includes a cross-correlation term and a check term, wherein the cross-correlation term is used to characterize the consistency between the candidate codeword and the received signal, and the check term is used to characterize the degree to which the candidate codeword satisfies the parity check constraint of the LDPC code.

[0016] Preferably, the comprehensive objective function is expressed as:

[0017]

[0018] in, For candidate bipolar codeword vectors, The first candidate bipolar codeword One portion, For receiving the signal One portion, To verify the number of equations, For code length, This represents the set of variable nodes connected to the i-th check node. This represents the candidate bipolar codeword component corresponding to the variable node belonging to the variable node set.

[0019] Preferably, the log-likelihood ratio proxy value in step S3 is expressed as:

[0020]

[0021] in, and These are the candidate bipolar codewords corresponding to the k-th bit being 1 and 0 respectively in the t-th iteration. For temperature parameters, This represents noise power.

[0022] Preferably, the first surrogate value is calculated based on the log-likelihood ratio. The conditional probability that each bit is 1 at the current update time:

[0023]

[0024] in, Let y be the k-th information bit in the t-th iteration, and y be the received signal vector. To generate the matrix, Represents all bits except the k-th bit. This represents the log-likelihood ratio proxy value for the k-th position.

[0025] Preferably, the flip function value in step S4 is expressed as:

[0026]

[0027] in, For the first The flip function value at each symbol position, For candidate bipolar codeword vectors, The first candidate bipolar codeword vector One portion, For receiving the signal One portion, Indicates the first The set of verification nodes associated with each variable node. Indicates the first The set of variable nodes connected to each verification node. Belongs to The candidate bipolar codeword components corresponding to the variable nodes.

[0028] Preferably, in step S4, determining the sampling update order based on the flip function value specifically involves: calculating the flip function value for all bit positions, sorting each bit position in ascending order of the flip function value, and obtaining the sampling update order in the current outer iteration.

[0029] Preferably, step S5 further includes: performing uniform random sampling with a predetermined probability instead of Gibbs sampling to enhance the global exploration capability of the search space.

[0030] Preferably, after step S6, the method further includes: using multiple parallel samplers to independently execute steps S3 to S6, and selecting the result with the largest comprehensive objective function value from the candidate decoding results obtained by each sampler as the final decoding output.

[0031] Preferably, the temperature parameter The value is 2, and the predetermined probability is 1 / K, where K is the information bit length.

[0032] Beneficial effects: Compared with the prior art, the technical solution provided by the present invention has the following beneficial effects:

[0033] By combining cross-correlation terms with checksum synthesis terms, a comprehensive objective function highly matched to the LDPC code structure is constructed, enabling the sampling probability to more accurately reflect the effectiveness of candidate codewords. A flip function is constructed using the gradient information of the objective function with respect to the symbolic components of the candidate codewords, and bit positions are updated in ascending order of flip function values, prioritizing bits more likely to improve the objective function, thereby significantly improving sampling efficiency. In short-code-length regular LDPC codes and 5G NR irregular LDPC code scenarios, this invention achieves a significantly better bit error rate performance than traditional BP decoding, approaching the benchmark performance of OSD or ML. Regarding computational complexity, compared to ML decoding and higher-order OSD decoding, this invention significantly reduces multiplication complexity while achieving near-optimal performance, and can further reduce redundant computations through incremental updates of the objective function. This invention is applicable to different code lengths and regular / irregular LDPC code structures, supports parallel implementation, and has good hardware friendliness. Attached Figure Description

[0034] Figure 1 The flowchart of the gradient descent-based Gibbs decoding algorithm for implementing this invention is shown below.

[0035] Figure 2 This is a comparison chart of the bit error rate performance of the method of the present invention and the comparative method under (3,6) regular LDPC code (N=48, K=24);

[0036] Figure 3This is a comparison chart of the bit error rate performance of the method of the present invention and the comparative method under (3,6) regular LDPC code (N=96, K=48);

[0037] Figure 4 This is a comparison chart of the bit error rate performance of the method of the present invention and the comparative method under 5G NR irregular LDPC code (N=90, K=60). Detailed Implementation

[0038] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0039] I. System Model Used in This Embodiment

[0040] Consider the binary information bit vector:

[0041]

[0042] in, Represents a binary field, Indicates the length of information bits. A matrix is ​​generated using LDPC. Encode the information bit vector to obtain the codeword:

[0043]

[0044] in, The codeword is then subjected to binary phase-shift keying modulation to obtain a bipolar transmit symbol vector. The signal vector received by the receiver is represented as:

[0045]

[0046] in, Indicates BPSK modulation mapping, With a mean of 0 and a variance of A Gaussian white noise vector. For each valid codeword. All satisfy ,in For the verification matrix, .make Indicates the first The set of variable nodes associated with each verification node. Indicates the first The set of check nodes associated with each variable node. Regular LDPC codes correspond to the case where each column weight and each row weight are fixed, while the column weights and row weights of irregular LDPC codes are not exactly the same.

[0047] II. Specific Steps of This Embodiment

[0048] like Figure 1As shown in the figure, this embodiment of the invention provides a gradient-guided Gibbs sampling flowchart, including the following steps:

[0049] S1. Initialize decoding parameters and candidate vectors;

[0050] Acquire received signal Generating matrix Noise variance Number of outer iterations Number of parallel samplers Mixed sampling ratio and temperature parameters Initialize the bit estimation vector. And obtain the corresponding candidate bipolar codewords through BPSK mapping. The initial vector It can be generated by random bits or provided by the output of an existing decoder, preferably a BP decoder.

[0051] S2. Construct the comprehensive objective function;

[0052] To simultaneously characterize the consistency between the candidate codeword and the received signal, as well as the degree to which the candidate codeword satisfies the LDPC check constraint, the following comprehensive objective function is constructed:

[0053]

[0054] The first term is the cross-correlation term, used to enhance the candidate codewords that match the received signal; the second term is the parity subsynthesis term, which reaches its maximum value if and only if the candidate codewords satisfy all parity check constraints. Therefore, the larger the overall objective function value, the more likely the candidate codeword is to be the correct decoding result.

[0055] S3. Construct a log-likelihood ratio surrogate value;

[0056] In the In the next outer iteration, for the ... For each bit position to be updated, consider the two cases where its value is 1 and 0, and obtain the corresponding candidate bipolar codeword accordingly. and Based on the difference in the objective function values ​​of the two, a surrogate value for the log-likelihood ratio is constructed:

[0057]

[0058] in, This is a temperature parameter used to adjust the mixing rate of the sampled Markov chain. A larger value... This is beneficial for improving the ability to explore sampled states and reducing the number of iterations required to reach the correct solution; however, if If the value is too large, it will weaken the preference for high-probability states, causing the sampling process to tend towards a random walk. Preferably, the value can be determined based on numerical experiments. Furthermore, the proxy value can be used to calculate the first... The sampling probability of each bit under the current conditions:

[0059]

[0060] S4. Calculate the flip function and determine the update order;

[0061] To improve sampling efficiency, this invention does not employ the fixed-order bit-by-bit update method used in traditional Gibbs sampling. Instead, it introduces gradient information from the objective function to determine a better variable update order. It should be noted that although the candidate codeword components... Only discrete values ​​are taken Here, the partial derivative calculation is a pseudo-gradient obtained by treating it as a real-valued variable. It indicates the trend of the objective function at this position and does not affect the actual execution of the algorithm. The comprehensive objective function with respect to the ... Symbolic components The partial derivatives are:

[0062]

[0063] When the When a sign is flipped, a first-order approximation can be used to characterize the changing trend of the objective function. Based on this, the flipping function is defined as follows:

[0064]

[0065] when Furthermore, a larger absolute value indicates that flipping that position is more likely to improve the overall objective function, and therefore should be updated first. A vector is formed from the flip function values ​​corresponding to all bit positions. The vector is sorted in ascending order to obtain the sampling update order in the current outer iteration.

[0066] S5, Perform hybrid sampling update.

[0067] After determining the bit update order, the update is performed on each bit position sequentially. For each position to be updated, a uniformly random number is first generated. .when At that time, Gibbs sampling was performed; when At this point, uniform random sampling is performed, setting the flip probability to 1 / 2. Specifically, uniform random sampling involves setting the current bit to either 0 or 1 with equal probability (i.e., directly reassigning a random value regardless of the current value). This enhances the global exploration capability of the search under conditions of suboptimal initialization or low signal-to-noise ratio, reducing the risk of getting trapped in unfavorable local regions. Gibbs sampling involves using the conditional probability calculated in step S3... Generate a uniformly distributed random number in the interval [0,1]. ,like Then set the bit to 1; otherwise set it to 0. Preferably, the bit can be set to... ,in The length of the information bits.

[0068] S6. Perform multiple rounds of outer layer iterations and parallel sampling.

[0069] Repeat steps S3 to S5 until the preset number of outer iterations is completed. In actual deployment, it can be set... Each parallel sampler independently executes the above process to explore the sample space more fully. Finally, from the candidate results obtained by all parallel samplers, the candidate result with the largest comprehensive objective function value is selected as the final decoding output. The parallel sampling mechanism can improve resource utilization efficiency and enhance the hardware implementation friendliness of the algorithm.

[0070] III. Implementation Results

[0071] To enable those skilled in the art to better understand the present invention, the performance advantages of the present invention are explained below in conjunction with numerical experimental results.

[0072] Example 1: As Figure 2 As shown, for the (3,6) regular LDPC code, in , In scenarios where a GWG(32,24) configuration is used, the bit error rate performance of the method of this invention is comparable to that of OSD-2 and close to that of ML decoding, while significantly outperforming BP decoding and the ORBGRAND scheme with a query budget of 1024.

[0073] Example 2: As Figure 3 As shown, in , In the (3,6) rule LDPC code scenario, although the search space is relatively smaller than... The error rate increases significantly, but after adopting GWG(256,128), the method of the present invention can still approach the performance of OSD-3 and ML benchmarks, and maintain a significant bit error rate gain relative to BP decoding, indicating that the present invention still has good scalability when the code length increases.

[0074] Example 3: As Figure 4 As shown, in irregular LDPC code scenarios conforming to the 5G NR standard, the following is adopted: , The code configuration of this invention. Under different row and column weight distributions and non-uniform Tanner graph connection structures, the method of this invention can still achieve a significantly better bit error rate performance than BP decoding and approach the OSD-3 / ML benchmark, indicating that this invention does not depend on a fixed regular code structure, but can maintain good adaptability to different LDPC code structures.

[0075] Complexity comparison results show that, when achieving near-ML performance, the numerical complexity of the method in this invention is significantly lower than that of OSD in multiple scenarios. For example, in In the context of rule-based codes, the complexity of this invention is approximately 57.96% of that of OSD; Rule code scenarios and In irregular code scenarios, this proportion further decreases to 7.74% and 4.72%. Meanwhile, although BP has fewer multiplications, its performance tends to saturate at a given number of iterations, and further increasing the number of iterations is unlikely to significantly improve the bit error rate performance. Therefore, this invention achieves a more reasonable trade-off between performance and complexity.

Claims

1. A short code-length LDPC decoding method based on gradient-guided Gibbs sampling, characterized in that, Includes the following steps: S1. Obtain the received signal vector, LDPC code generation matrix, noise power, and decoding iteration parameters, and initialize the bit vector to be decoded; S2. Based on the bit vector to be decoded, the received signal vector, and the parity check matrix of the LDPC code, construct a comprehensive objective function to characterize the effectiveness of the candidate codeword; S3. For the bit position to be updated in the current iteration, use the comprehensive objective function to calculate the difference of the objective function value corresponding to the bit taking different binary states, and construct the log-likelihood ratio surrogate value of the bit position accordingly. S4. Based on the gradient information of the candidate code character component by the comprehensive objective function, calculate the flip function value of each symbol position, and determine the sampling update order of each bit position according to the flip function value. S5. Perform Gibbs sampling update according to the sampling update order and in combination with the log-likelihood ratio proxy value to obtain a new candidate bit vector; S6. Repeat steps S3 to S5 until the preset number of iterations is reached, and output the decoding result.

2. The decoding method according to claim 1, characterized in that, The comprehensive objective function in step S2 includes a cross-correlation term and a check term. The cross-correlation term is used to characterize the consistency between the candidate codeword and the received signal, and the check term is used to characterize the degree to which the candidate codeword satisfies the parity check constraint of the LDPC code.

3. The decoding method according to claim 2, characterized in that, The comprehensive objective function is expressed as follows: ； in, For candidate bipolar codeword vectors, The first candidate bipolar codeword One portion, For receiving the signal One portion, To verify the number of equations, For code length, This represents the set of variable nodes connected to the i-th check node. This represents the candidate bipolar codeword component corresponding to the variable node belonging to the variable node set.

4. The decoding method according to claim 1, characterized in that, The log-likelihood ratio proxy value in step S3 is expressed as: ； in, and These are the candidate bipolar codewords corresponding to the k-th bit being 1 and 0 respectively in the t-th iteration. For temperature parameters, This represents noise power.

5. The decoding method according to claim 4, characterized in that, Calculate the first value based on the log-likelihood ratio proxy value. The conditional probability that each bit is 1 at the current update time: ； in, Let y be the k-th information bit in the t-th iteration, and y be the received signal vector. To generate the matrix, Represents all bits except the k-th bit. This represents the log-likelihood ratio proxy value for the k-th position.

6. The decoding method according to claim 1, characterized in that, The flip function value in step S4 is expressed as: ； in, For the first The flip function value at each symbol position. For candidate bipolar codeword vectors, The first candidate bipolar codeword vector One portion, For receiving the signal One portion, Indicates the first The set of verification nodes associated with each variable node. Indicates the first The set of variable nodes connected to each verification node. Belonging to The candidate bipolar codeword components corresponding to the variable nodes.

7. The decoding method according to claim 1, characterized in that, In step S4, determining the sampling update order based on the flip function value specifically involves: calculating the flip function value for all bit positions, sorting each bit position in ascending order of the flip function value, and obtaining the sampling update order in the current outer iteration.

8. The decoding method according to claim 1, characterized in that, Step S5 also includes: performing uniform random sampling with a predetermined probability instead of Gibbs sampling to enhance the global exploration capability of the search space.

9. The decoding method according to claim 1, characterized in that, Step S6 is followed by: using multiple parallel samplers to independently execute steps S3 to S6, and selecting the result with the largest comprehensive objective function value from the candidate decoding results obtained by each sampler as the final decoding output.

10. The decoding method according to claim 8, characterized in that, The predetermined probability is 1 / K, where K is the information bit length.

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