Quasi-belief propagation decoding method for BCH codes based on neural networks

Abstract

This invention belongs to the field of BCH code decoding technology, specifically involving a quasi-belief propagation decoding method for BCH codes based on neural networks. The steps include: determining the redundancy of the BCH code; expanding and optimizing the parity-check matrix (PCM) of the BCH code using the redundancy to obtain a preprocessed PCM; performing quasi-belief propagation iterative decoding (QBP-SF) based on neural networks on the BCH code based on the preprocessed PCM; constructing a hybrid decoding architecture of QBP-SF and an ordered statistical decoder (OSD); during the iterative decoding process, the decoding convergence state is judged in real time; if the convergence condition is met during the iteration, the decoding result is directly output; if convergence is not achieved after the preset maximum number of decoding iterations, the OSD is triggered to perform secondary decoding, and finally, the codewords and information sequence obtained by the OSD decoding are output. This invention balances decoding accuracy, computational complexity, and hardware implementation cost, and can achieve high-probability recovery of the original information from noisy received sequences.

Description

Technical Field

[0001] This invention belongs to the field of BCH code decoding technology, specifically relating to a quasi-belief propagation decoding method for BCH codes based on neural networks. Background Technology

[0002] In communication systems, reliable information transmission is one of their core functions. From everyday wireless calls and internet access to critical fields such as industrial automation and intelligent transportation, data transmission involves encoding, modulation, channel propagation, and decoding. During this process, signals are inevitably affected by factors such as channel noise and interference, leading to bit errors at the receiving end. Therefore, how to achieve efficient and reliable information transmission over noisy physical channels has always been a fundamental problem in communication technology research.

[0003] From the perspective of information theory and coding theory, a typical digital communication link can be modeled as follows. Let the sequence of binary information to be transmitted be a row vector. K is the information bit length. This is the i-th original information bit. This sequence is encoded in the Galois field. Based on the generating matrix Perform a linear transformation to obtain the codeword. N is the code length ( ), Let be the i-th bit in the codeword. Subsequently, the codeword is modulated using Binary Phase Shift Keying (BPSK), which modulates each bit... Mapped to send symbols The signal is affected by additive white Gaussian noise (AWGN) during transmission. The interference, the noise follows a pattern with a mean of zero and a variance of . The normal distribution. The observation sequence obtained by the receiver is... Among them, single-bit observations The core task of the decoder is to decode based on a noisy sequence of observations. To recover the original transmitted codewords with the highest probability. To restore the binary information sequence .

[0004] To improve decoding reliability, the industry has developed various decoding algorithms. Early algebra-based hard-decision decoding algorithms, while simple in structure, had limited error correction capabilities due to quantization loss in the channel output. Subsequently, soft-decision iterative decoding algorithms, represented by Belief Propagation (BP), emerged. By iteratively transmitting probability information between variable nodes and check nodes, they can approximate optimal Maximum A Posteriori (MAP) decoding performance. These algorithms have achieved great success, especially when combined with Low-Density Parity-Check (LDPC) codes with sparse parity-check matrices, and have become the mainstream solution for long code decoding in modern communication standards such as 5G and Wi-Fi.

[0005] However, traditional backpropagation (BP) algorithms face significant challenges when processing high-density parity-check (HDPC) codes like BCH codes, which have dense parity-check matrices. The dense matrix results in numerous short cycles in the corresponding Tanner graph, violating the message-passing independence assumption upon which the BP algorithm relies, leading to poorer convergence, performance degradation, and even divergence. This limitation severely restricts the application potential of BCH codes (classic codes with excellent algebraic structure, strict minimum distance guarantees, and particularly suitable for short to medium code lengths) within modern iterative decoding frameworks.

[0006] To overcome this bottleneck, academia and industry have conducted numerous explorations, such as using weighted bit-flipping (WBF), subspace-based soft decoding, or hybrid methods combining ordered statistical decoding (OSD). However, these methods often struggle to achieve a balance between error correction performance, computational complexity, processing latency, and hardware parallelization friendliness, and in particular, lack a high-performance iterative decoding scheme that can fully leverage the advantages of modern parallel processors (such as GPUs and FPGAs). Therefore, developing a practical soft iterative decoding algorithm that efficiently supports parallel computing architectures for HDPC codes such as BCH codes has become a key technical problem urgently needing to be solved in the field of communication decoding. Summary of the Invention

[0007] In view of the shortcomings of the prior art, the purpose of this invention is to provide a quasi-belief propagation decoding method for BCH codes based on neural networks, which balances decoding accuracy, computational complexity and hardware implementation cost, and can achieve high-probability recovery of the original information of noisy received sequences.

[0008] To achieve the above objectives, this invention provides a quasi-belief propagation decoding method for BCH codes based on neural networks, comprising the following steps: S1. Determine the redundancy of the BCH code, expand the parity check matrix of the BCH code using the redundancy, and optimize the parity check matrix to obtain the preprocessed parity check matrix. S2. Based on the preprocessed parity-check matrix, perform quasi-belief propagation iterative decoding (QBP-SF) on the BCH code using a neural network. The single iteration process is as follows: S2.1. Combine the expansion factor to complete the expansion preprocessing of the input information, and perform variable node information distribution operation based on the expanded input information; S2.2 Extract the input messages related to the current verification node to construct the input vector, input the input vector into the pre-trained neural network, and output the message vector transmitted by the verification node to each variable node; S2.3. Perform inverse transformation on each component of the output message vector according to the automorphism mapping during input dilation. After block alignment, sum and summarize the messages in all message blocks. Multiply the total message obtained by the sum by the aggregation coefficient to complete the weighted merging. Update the log-likelihood ratio sequence using the weighted merged messages. S2.4 Perform normalization on the updated log-likelihood ratio message vector, and output the hard decision result based on the normalized log-likelihood ratio sequence to complete a single iteration; S3. Construct a hybrid decoding architecture of QBP-SF and ordered statistical decoder OSD. During the iterative decoding process, the decoding convergence status is judged in real time. If the QBP-SF meets the convergence judgment condition during the iteration, the decoding result is directly output. If the QBP-SF fails to converge after iterating to the preset maximum number of decoding times, the OSD is triggered to perform secondary decoding, and finally the codeword and information sequence obtained by OSD decoding are output.

[0009] As a preferred embodiment of the present invention, the specific implementation process of step S2.1 is as follows: Define the row weight of the preprocessed parity-check matrix as Iterative index of QBP-SF ,in Set the expansion factor to the preset maximum number of iterations. and redundancy ; According to the received signal ,calculate The corresponding initial log-likelihood ratio ,in This represents the i-th input message bit, where N is the code length. As input message; for Preprocessing is performed using the automorphism property of BCH codes to obtain the dilated... The input information is doubled; The log-likelihood ratio corresponding to each variable node v in the expanded input information is used as a message to be distributed to the connected verification node c. The message passing formula is: ; In the formula, Indicates the time at the (t-1)th iteration The corresponding log-likelihood ratio; , The set of verification nodes connected to variable node v; This represents the message distributed from variable node v to verification node c.

[0010] As a preferred embodiment of the present invention, the specific implementation process of step S2.2 is as follows: Extract all nodes associated with the current verification node c. Each variable node distributes messages. The input vector is constructed. ,right Each group of messages undergoes a symbol-amplitude separation operation to obtain independent symbol information and amplitude information. The amplitude values ​​after separation are sorted in descending order. The one-to-one mapping relationship between the original index and the sorted position is recorded simultaneously. The sorted amplitude sequence is fed into a pre-trained neural network. After the pre-trained neural network performs the operation, it outputs the non-negative amplitude result in the sorted state. Based on the index mapping relationship of the records, the non-negative amplitude values ​​output by the neural network are backfilled into the original corresponding positions of the message. According to the sign update rule of the check node update equation, the backfilled amplitude values ​​are matched with corresponding positive and negative signs. Finally, the output vectors sent by check node c to each connected variable node v are generated. .

[0011] As a preferred embodiment of the present invention, the specific implementation process of step S2.3 is as follows: Will Each component undergoes an inverse transformation according to the automorphism mapping during input dilation, and after block alignment, they are merged to obtain... For each message block, update the log-likelihood ratio sequence as follows: ; In the formula, This indicates a message originating from the w-th message block; Indicates the time of the t-th iteration The corresponding log-likelihood ratio; The polymerization coefficient is denoted as .

[0012] As a preferred embodiment of the present invention, the specific implementation process of step S2.4 is as follows: Define message vectors ,right The normalization operation is performed as follows: ; In the formula, This represents the variance of additive white Gaussian noise; express The mean of the amplitude values ​​of each component; This represents the assignment operator; According to the normalized Output the hard decision result. If the hard decision result satisfies all the parity check matrix equations, terminate the iteration early and output the result; otherwise, the iteration count is zero. Return to S2.1 and continue iterating until the maximum number of iterations is reached. .

[0013] As a preferred embodiment of the present invention, the EXIT analysis tool of the scatter-type external information transfer graph is introduced for parameter optimization. The optimized parameters include the maximum number of iterations of QBP-SF, the expansion factor, and the redundancy.

[0014] As a preferred embodiment of the present invention, the process of obtaining the pre-trained neural network is as follows: The model structure of the neural network is determined. The neural network integrates a complete set of operational logic for performing sign-amplitude separation, amplitude descending order sorting, establishing the mapping between the original index and the sorting position, amplitude inference output, index backfilling, and sign assignment on the input vector. Obtain the training sample set of the neural network, collect BCH code decoding samples covering the entire target signal-to-noise ratio range, the sample input is the input vector constructed based on the preprocessed parity-check matrix and after dilation preprocessing, and the sample label is the standard ideal output vector of the corresponding parity-check node; The loss function, optimization strategy, and parameters for training are determined with the goal of minimizing the error between the network output and the standard ideal output vector. The Adam optimizer is used to perform gradient descent to complete the global basic pre-training. After training, a pre-trained neural network adapted to the full signal-to-noise ratio range is obtained. The basic optimized values ​​of the aggregation coefficient adapted to the full signal-to-noise ratio range are solved simultaneously.

[0015] As a preferred embodiment of the present invention, the neural network consists of two one-dimensional convolutional layers, a flattening layer, two fully connected layers, and a scale parameter arranged sequentially. The scale parameter is used to accelerate training and fitting, and can be merged with the aggregation coefficient into a single factor during the online inference stage. The activation function configuration of the neural network is as follows: the first two one-dimensional convolutional layers and the first fully connected layer both use the HardSwish activation function, and the last fully connected layer uses a linear activation function.

[0016] As a preferred embodiment of the present invention, the training loss function adopts a combination of distance loss, ranking loss and positive loss, wherein the distance loss supervises the closeness of the predicted value to the true label, the ranking loss forces the output vector to satisfy the ascending order constraint, and the positive loss forces all output values ​​to be non-negative.

[0017] As a preferred embodiment of the present invention, after completing the global basic pre-training of the neural network, the basic values ​​of the aggregation coefficients adapted to the entire signal-to-noise ratio range are first solved by a bisection linear search method, and then QBP-SF fine-tuning optimization is performed: the network parameters of the pre-trained neural network and the basic values ​​of the universal aggregation coefficients for the entire range obtained by the bisection search are loaded; each specific signal-to-noise ratio test point in the communication scenario is traversed, and the general pre-trained network parameters and the basic values ​​of the aggregation coefficients obtained by the bisection method are used as initial values ​​to carry out fine parameter fine-tuning. The network weights and aggregation coefficients are iteratively updated under the training samples corresponding to the current signal-to-noise ratio, and the optimal values ​​of the neural network parameters and the optimal values ​​of the aggregation coefficients adapted to the channel conditions of that signal-to-noise ratio are solved respectively; the optimal network parameters and the optimal aggregation coefficients corresponding to each group of signal-to-noise ratios are stored and archived for matching and calling in the subsequent online QBP-SF iterative decoding stage.

[0018] The beneficial effects of this invention are: This invention employs a neural network to completely replace the complex nonlinear update equations of the check nodes in traditional BP decoding, eliminating highly complex iterative operations such as hyperbolic tangent and multiplication. The neural network is pre-trained with a triple-constraint loss function of distance, sorting, and positivity, which can better match the processing logic of amplitude sorting and non-negative output in the decoding stage, significantly improving the short-loop interference and poor convergence problems caused by the dense check matrix of BCH. At the same time, it combines BCH code automorphic expansion preprocessing and check matrix redundancy expansion to improve the utilization rate of decoding redundancy information. It uses a scatter-type EXIT graph tool to quantitatively optimize parameters such as the maximum number of iterations, expansion factor, and redundancy, getting rid of the traditional rough design mode of manual trial and error. The iterative convergence speed is faster, the frame error rate (FER) performance is significantly improved, and the performance gap with LDPC layered BP decoding of the same code rate is greatly narrowed.

[0019] This invention designs a two-stage joint optimization mechanism combining binary coarse search and signal-to-noise ratio gradient fine-tuning to obtain the optimal aggregation coefficient. First, the initial value of the universal aggregation coefficient with full signal-to-noise ratio is obtained through binary search. Then, the network weights and aggregation coefficients are simultaneously fine-tuned for each channel's SNR scenario, solving the defect that fixed aggregation coefficients cannot adapt to multi-channel conditions. At the same time, a QBP-SF and OSD concatenated hybrid decoding architecture is constructed. The serial OSD secondary decoding is only called when the neural network iteration reaches the maximum number of iterations and still has not converged, reducing the frequency of OSD calls to reduce the overall decoding latency. The entire iterative process supports hardware parallel computing, taking into account decoding reliability, computational complexity, and real-time processing performance, and is suitable for 5G / 6G URLLC high-reliability low-latency communication scenarios. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating the principle of this invention; Figure 2 This is a performance comparison chart of the FER decoding algorithm for the BCH(127,64) code in Embodiment 1 of the present invention; Figure 3 This is a performance comparison chart of the FER decoding algorithm for the BCH(127, 99) code in Embodiment 1 of the present invention; Figure 4 This is a comparison chart of the BER performance of the decoding algorithm for the BCH(127, 99) code in Embodiment 1 of the present invention; Figure 5 This is a performance comparison chart of the FER decoding algorithm for CCSDS (128, 64) codes in Embodiment 2 of the present invention. Detailed Implementation

[0021] The embodiments of the present invention will be further described below with reference to the accompanying drawings: Example 1: As Figure 1 As shown, the quasi-belief propagation decoding method for BCH codes based on neural networks includes the following steps: S1. Determine the redundancy of the BCH code, expand the parity check matrix of the BCH code using the redundancy, and optimize the parity check matrix to obtain the preprocessed parity check matrix. S2. Based on the preprocessed parity-check matrix, perform quasi-belief propagation iterative decoding (QBP-SF) on the BCH code using a neural network. The single iteration process is as follows: S2.1. Combine the expansion factor to complete the expansion preprocessing of the input information, and perform variable node information distribution operation based on the expanded input information; S2.2 Extract the input messages related to the current verification node to construct the input vector, input the input vector into the pre-trained neural network, and output the message vector transmitted by the verification node to each variable node; S2.3. Perform inverse transformation on each component of the output message vector according to the automorphism mapping during input dilation. After block alignment, sum and summarize the messages in all message blocks. Multiply the total message obtained by the sum by the aggregation coefficient to complete the weighted merging. Update the log-likelihood ratio sequence using the weighted merged messages. S2.4 Perform normalization on the updated log-likelihood ratio message vector, and output the hard decision result based on the normalized log-likelihood ratio sequence to complete a single iteration; S3. Construct a hybrid decoding architecture of QBP-SF and ordered statistical decoder OSD. During the iterative decoding process, the decoding convergence status is judged in real time. If the QBP-SF meets the convergence judgment condition during the iteration, the decoding result is directly output. If the QBP-SF fails to converge after iterating to the preset maximum number of decoding times, the OSD is triggered to perform secondary decoding, and finally the codeword and information sequence obtained by OSD decoding are output.

[0022] The specific implementation process of step S2.1 is as follows: Define the row weight of the preprocessed parity-check matrix as Iterative index of QBP-SF ,in Set the expansion factor to the preset maximum number of iterations. and redundancy ; where row weight is the total number of elements with a value of 1 in any row of the matrix.

[0023] According to the received signal ,calculate The corresponding initial log-likelihood ratio ,in This represents the i-th input message bit. That is, the Nth input message bit, and so on, where N is the code length. As input message; for Preprocessing is performed using the automorphism property of BCH codes to obtain the dilated... The input information is multiplied: first, the original permutation, the interleaved permutation, and the Frobenius map permutation are generated, and then the three permutations are subjected to... An arbitrary cyclic shift forms the final expanded input sequence, where . A larger value results in better decoding performance, but also higher computational complexity. It is the preferred choice for lightweight, high-speed scenarios. Preferred for conventional communication scenarios Suitable for low signal-to-noise ratio, high-reliability decoding scenarios. For compromise scenarios with limited hardware resources, the following can be used: .

[0024] The log-likelihood ratio corresponding to each variable node v in the expanded input information is used as a message to be distributed to the connected verification node c. The message passing formula is: ; In the formula, Indicates the time at the (t-1)th iteration The corresponding log-likelihood ratio; , The set of verification nodes connected to variable node v; This represents the message distributed from variable node v to verification node c.

[0025] The specific implementation process of step S2.2 is as follows: Extract all nodes associated with the current verification node c. Each variable node distributes messages. The input vector is constructed. ,right Each group of messages undergoes a symbol-amplitude separation operation to obtain independent symbol information and amplitude information. The amplitude values ​​after separation are sorted in descending order. The one-to-one mapping relationship between the original index and the sorted position is recorded simultaneously. The sorted amplitude sequence is fed into a pre-trained neural network. After the pre-trained neural network performs the operation, it outputs the non-negative amplitude result in the sorted state. Based on the index mapping relationship of the records, the non-negative amplitude values ​​output by the neural network are backfilled into the original corresponding positions of the message. According to the sign update rule of the check node update equation, the backfilled amplitude values ​​are matched with corresponding positive and negative signs. Finally, the output vectors sent by check node c to each connected variable node v are generated. .

[0026] The sign update rule of the verification node update equation refers to extracting the signs of all other input messages of the verification node for the message output by the verification node to any variable node, performing a multiplication operation, and using the multiplication result as the positive or negative sign of the output message, which is then combined with the non-negative amplitude value output by the neural network to form a complete verification node message.

[0027] The specific implementation process of step S2.3 is as follows: Will Each component undergoes an inverse transformation according to the automorphism mapping during input dilation, and after block alignment, they are merged to obtain... For each message block, update the log-likelihood ratio sequence as follows: ; In the formula, This indicates a message originating from the w-th message block; Indicates the time of the t-th iteration The corresponding log-likelihood ratio; The polymerization coefficient is denoted as .

[0028] Through the inner layer Sum the messages of all expanding branches with equal weight, then multiply the sum by a unified factor. Finally, it is superimposed on the previous log-likelihood ratio to complete the update of the log-likelihood ratio.

[0029] The specific implementation process of step S2.4 is as follows: Define message vectors ,right The normalization operation is performed as follows: ; In the formula, This represents the variance of additive white Gaussian noise; express The mean of the amplitude values ​​of each component; This represents the assignment operator; Indicates the time of the t-th iteration The corresponding log-likelihood ratio, and the same applies to the others.

[0030] According to the normalized Output the hard decision result. If the hard decision result satisfies all the parity check matrix equations, terminate the iteration early and output the result; otherwise, the iteration count is zero. Return to S2.1 and continue iterating until the maximum number of iterations is reached. .

[0031] Let the hard decision codeword obtained from the decoding be... , This is the preprocessed parity-check matrix. The parity-check matrix equation refers to the binary field equation. The superscript T indicates transpose. This represents a column vector of all zeros.

[0032] The EXIT analysis tool for scatter plot external information transfer graphs was introduced to optimize parameters, including the maximum number of iterations of QBP-SF, the expansion factor, and the redundancy.

[0033] In this embodiment, the expansion and optimization of the standard parity-check matrix of the BCH code using redundancy, the introduction of the EXIT analysis tool for parameter optimization using a scattered external information transfer graph, and the parity node update equation can all be implemented using the technical solutions disclosed in the inventor's prior application CN121864106B. The ordered statistical decoder OSD adopts the OSD architecture disclosed in the inventor's prior application CN120342407B (corresponding to the OSD II decoding algorithm in the verification process).

[0034] The process of obtaining a pre-trained neural network is as follows: The model structure of the neural network is determined. The neural network integrates a complete set of operational logic for performing sign-amplitude separation, amplitude descending order sorting, establishing the mapping between the original index and the sorting position, amplitude inference output, index backfilling, and sign assignment on the input vector. Obtain the training sample set for the neural network, collecting BCH code decoding samples covering the entire target signal-to-noise ratio (SNR) range. The sample input is an input vector constructed based on the preprocessed parity-check matrix and after dilation preprocessing, and the sample label is the standard ideal output vector of the corresponding parity-check node. Merge samples from all SNR regions into a single set greater than 10. 6 The training dataset of samples.

[0035] The loss function, optimization strategy, and parameters for training are determined with the goal of minimizing the error between the network output and the standard ideal output vector. The Adam optimizer is used to perform gradient descent to complete the global basic pre-training. After training, a pre-trained neural network adapted to the full signal-to-noise ratio range is obtained. The basic optimized values ​​of the aggregation coefficient adapted to the full signal-to-noise ratio range are solved simultaneously.

[0036] The neural network consists of two one-dimensional convolutional layers, a flattening layer, two fully connected layers, and a scale parameter set sequentially. The scale parameter is used to accelerate training and fitting, and can be merged with the aggregation coefficients into a single factor during the online inference stage. The activation function configuration of the neural network is as follows: the first two one-dimensional convolutional layers and the first fully connected layer both use the HardSwish activation function, and the last fully connected layer uses the linear activation function.

[0037] Taking the BCH(127,64) code as an example, an exemplary convolutional layer parameter and fully connected layer parameter are shown in Table 1 and Table 2.

[0038] Table 1 Examples of Convolutional Layer Parameters

[0039] Table 2 Examples of Fully Connected Layer Parameters

[0040] The training loss function can be either cross-entropy loss or distance loss. Ranking loss and positive loss Combination loss function ,Right now ,in Supervise the degree of closeness between the predicted value and the true label. Force the output vectors to satisfy the ascending order constraint. Force all output values ​​to be non-negative.

[0041] ; In the formula, Indicates the training batch size; i is the index of an element within the output magnitude vector; This represents the i-th predicted value of the sorted magnitude vector output by the neural network. The standard truth label corresponding to the same position is constructed from the output message of the standard verification node. This loss term ensures that the neural network output can accurately fit the target value of the training data.

[0042] ; In the formula, ReLU represents the ReLU activation function; This represents the (i+1)th predicted value of the sorted magnitude vector output by the neural network. when (When ascending order is satisfied) ReLU outputs 0, incurring no loss; when When the ascending order is violated, the difference is positive, and ReLU outputs this difference, resulting in a positive loss. This loss term forces the neural network output vector to satisfy... To ensure consistency between the training and amplitude ranking inference processes, This represents the first value of the sorted magnitude vector of the neural network output. One predicted value, and the rest are calculated similarly.

[0043] ; when hour, ReLU outputs 0, incurring no loss; when hour, ReLU outputs this positive value, generating a positive loss; this loss term ensures that the neural network tends to output non-negative values ​​during training.

[0044] The training process uses the Adam optimizer to optimize the neural network parameters using gradient descent. The initial learning rate is 0.001, and the learning rate decays by 0.995 every 200 steps, accumulating to 10 steps. 5 The global pre-training process ends after one iteration.

[0045] After completing the global pre-training of the neural network, the basic values ​​of the aggregation coefficients adapted to the entire signal-to-noise ratio (SNR) range are first solved using a bisection linear search method. Then, QBP-SF fine-tuning optimization is performed: the network parameters of the pre-trained neural network and the basic values ​​of the universal aggregation coefficients obtained from the bisection search are loaded; for each specific SNR test point in the communication scenario, fine-tuning of parameters is carried out using the universal pre-trained network parameters and the basic values ​​of the aggregation coefficients obtained by the bisection method (bisection linear search method) as initial values. The network weights and aggregation coefficients are iteratively updated under the training samples corresponding to the current SNR, and the optimal values ​​of the neural network parameters and the optimal values ​​of the aggregation coefficients adapted to the channel conditions of that SNR are solved respectively; the optimal network parameters and the optimal aggregation coefficients corresponding to each group of SNRs are stored and archived for matching and calling in the subsequent online QBP-SF iterative decoding stage.

[0046] The process of finding the basic values ​​of the aggregation coefficients that fit the entire signal-to-noise ratio range using a binary linear search method is as follows: Step 1: Settings e is the natural constant, x is the variable to be optimized, and an initial optimization interval is selected. Let a and b be the lower and upper limits of the initial optimization interval, respectively, and take the midpoint of the interval. ; Step 2: Select a value , To find the minimum value, calculate separately. , The corresponding frame error rate (FER) index , ; Step 3, if If the interval is not equal, then update the upper limit of the interval b=d; otherwise, update the lower limit of the interval a=d. Repeat steps one through three until the interval length is reduced to the preset threshold, and take the d at this point as the optimal x value.

[0047] The effectiveness of the method in this embodiment is verified under AWGN channel conditions for BCH codes and LDPC codes with different code rates. Figures 2-5 In the Chinese: QBP is the quasi-BP decoding algorithm; QBP-SF is the neural network-based quasi-belief propagation iterative decoding algorithm in this embodiment; DDS1 is based on an optimal decoding path length of 10. 3 The OSD II decoding algorithm; DDS2 is based on an optimal decoding path length of 10. 4 OSD II decoding algorithm; ISD+Dual (10 4 The TEP (Generate Test Error Pattern) proposed in the paper "On hard and soft decision decoding of BCH codes" has a length of 10. 4 The OSD variant; NMS is the improved NMS disclosed in CN119154894B, ML-LB is the theoretically calculated lower bound of the maximum likelihood decoding FER; ML is the maximum likelihood decoding FER value obtained from experimental simulation; BP-RNN is the BP algorithm based on recurrent neural network RNN. This represents the power spectral density of the signal energy / noise per bit, i.e., the signal-to-noise ratio, measured in dB (decibels). The numbers in parentheses correspond to... The value of , for example, QBP-SF(18) corresponds to .

[0048] For BCH(127, 64) code, set , The FER performance of each iterative algorithm is as follows: Figure 2 As shown.

[0049] The FER of all algorithms follows The increase shows an exponential decreasing trend. The decoding performance of NMS lags behind QBP-SF(18) by more than 0.5 dB, even when it is reduced. Increasing the FER from 8 to 18 still results in very limited improvement, with the performance gap compared to QBP-SF (18) remaining above 0.5 dB. Compared to QBP with a similar number of iterations, QBP-SF suffers a slight FER performance loss of less than 0.1 dB due to errors caused by neural network fitting and check node updates. Hybrid decoding using QBP-SF superimposed with DDS1 or DDS2 can significantly improve decoding performance, with the QBP-SF (18) + DDS2 combination reducing the performance gap with ML to within 0.4 dB. Compared to ISD + Dual (10... 4 Compared to the former, the difference is only about 0.2dB. The latter is a pure OSD variant based on a customized decoding strategy for the received sequence, which has a significant bottleneck in data throughput.

[0050] In this embodiment, QBP-SF is used instead of QBP, and the improved OSD is used as an auxiliary decoder. While maintaining the hybrid decoding architecture's performance close to the maximum likelihood FER, the computational and implementation complexity are further improved.

[0051] For BCH(127, 99) code, set , The FER and BER performance of each iterative decoding algorithm are as follows: Figure 3 and Figure 4 As shown.

[0052] Regarding FER, such as Figure 3 As shown, QBP-SF(12) outperforms the NMS algorithm by more than 0.4 dB; after increasing the number of iterations to 30, the lead gap is reduced to FER=10. -2 The FER is increased to over 0.6 dB. Furthermore, the FER performance of the finely tuned QBP-SF(30) is slightly ahead of QBP(30), indicating that the potential accuracy loss caused by the tanh function multiplication can be compensated by the neural network portion. Compared to the maximum likelihood ML performance, QBP-SF(30) still has an FER gap of about 1 dB, but this gap can be made up by the hybrid decoding of QBP-SF and DDS1 (inferred from the fact that the NMS and OSD hybrid decoding architecture of CN120342407B can approach ML performance; to keep the charts neat, Figure 3 (No relevant curves were plotted).

[0053] Regarding BER, such as Figure 4As shown, BP-RNN performance lags significantly behind NMS, while NMS still lags behind the QBP-SF proposed in this invention by more than 0.5 dB. In the same... Under these conditions, QBP-SF still outperforms QBP in terms of BER performance.

[0054] Example 2: The difference between this example and Example 1 is that a neural network is used to replace the original check node update equation in the belief propagation decoding, which is applicable to both BCH codes and LDPC codes; the standard version of the neural network (the pre-trained neural network in Example 1) has a dimension equal to the row weight of the check matrix. The magnitude vector is used as input, and the preprocessing rules of sign-magnitude separation and descending order of input magnitude are followed. Through a network structure consisting of two one-dimensional convolutional layers, a flattening layer, and two fully connected layers, the output of the current verification node to all associated variable nodes is fitted in parallel at one time. The path updates the amplitude, thus directly replacing the traditional calculation process of iteratively solving the nonlinear update formula at the check node; A simplified one-dimensional output neural network variant can also be constructed to achieve a lightweight alternative, where the input dimension of the simplified network is... Only the single-path update magnitude passed from the verification node to the single target variable node is fitted; the original 3D training samples can be decomposed into One-dimensional sample reuse simplifies network fitting, reduces model parameters and computational cost, and allows for reduction in network depth and number of filters. ReLU can be used as the activation function. In this embodiment, both types of neural networks are trained by using distance loss to supervise the fitting of the output with the update amplitude of the ideal check node and positive loss to constrain the output amplitude to be non-negative. The standard version of the neural network adds an additional sorting loss to force the output amplitude to remain in ascending order. After training, the online decoding stage directly outputs the check node update message by forward inference from the neural network, saving the complex nonlinear iterative solution calculation of the traditional check node. For LDPC codes, because Generally smaller, the number of layers, parameters, and computational overhead required for neural networks can be further reduced, resulting in a more significant lightweight alternative.

[0055] In this embodiment, the verification node update method is changed from strict explicit mathematical tangent function operation to implicit neural network replacement. From the perspective of data input and output relationship, this operation of changing from hard connection to soft connection makes the quasi-belief propagation decoding based on neural network easily applicable to decoding tasks of non-AWGN channel models (such as more complex mobile communication scenarios such as Rayleigh fading) through transfer learning.

[0056] For the CCSDS(128,64) code in LDPC codes, its parity-check matrix row weights When the update equation of its check node is replaced by a neural network, the SPA-SF decoding algorithm is formed. Because The smaller size allows for halving the number of convolutional layer filters and the dimension of the fully connected layer before the output layer, thus effectively reducing the neural network size while maintaining fitting accuracy. The FER performance of each iterative decoding algorithm is as follows: Figure 5 As shown.

[0057] Depend on Figure 5 It can be seen that, in the same Under these conditions, SPA-SF is always slightly better than NMS. At this time, SPA-SF lags slightly behind Layered-BP because SPA-SF uses a flooding method for message updates, while Layered-BP sacrifices some parallelism for faster message updates. Therefore, this performance difference is not due to neural network fitting errors. Considering the significantly reduced computational complexity of NMS, the advantage of choosing SPA-SF for this code rate of LDPC codes is not significant. However, for low code rate LDPC codes, NMS has a significant FER performance gap compared to BP. In this case, introducing SPA-SF as an alternative can maintain the decoding performance of BP while being simpler and more efficient in terms of computation and implementation complexity.

[0058] Example 3: A quasi-belief propagation decoding device for BCH codes based on neural networks, comprising: One or more processors; Memory, used to store one or more computer programs; When one or more programs are executed by one or more processors, the one or more processors perform the method in Embodiment 1 or Embodiment 2.

[0059] Example 4: A computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, cause the processor to perform the method in Example 1 or Example 2.

[0060] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can make equivalent substitutions or modifications based on the technical solution and concept of the present invention within the scope of the technology disclosed in the present invention, and such modifications should also be considered to fall within the scope of protection of the present invention.

Claims

1. A quasi-belief propagation decoding method for BCH codes based on neural networks, characterized in that, Includes the following steps: S1. Determine the redundancy of the BCH code, expand the parity check matrix of the BCH code using the redundancy, and optimize the parity check matrix to obtain the preprocessed parity check matrix. S2. Based on the preprocessed parity-check matrix, perform quasi-belief propagation iterative decoding (QBP-SF) on the BCH code using a neural network. The single iteration process is as follows: S2.

1. Combine the expansion factor to complete the expansion preprocessing of the input information, and perform variable node information distribution operation based on the expanded input information; S2.2 Extract the input messages related to the current verification node to construct the input vector, input the input vector into the pre-trained neural network, and output the message vector transmitted by the verification node to each variable node; S2.

3. Perform inverse transformation on each component of the output message vector according to the automorphism mapping during input dilation. After block alignment, sum and summarize the messages in all message blocks. Multiply the total message obtained by the sum by the aggregation coefficient to complete the weighted merging. Update the log-likelihood ratio sequence using the weighted merged messages. S2.4 Perform normalization on the updated log-likelihood ratio message vector, and output the hard decision result based on the normalized log-likelihood ratio sequence to complete a single iteration; S3. Construct a hybrid decoding architecture of QBP-SF and ordered statistical decoder OSD. During the iterative decoding process, the decoding convergence status is judged in real time. If the QBP-SF meets the convergence judgment condition during the iteration, the decoding result is directly output. If QBP-SF fails to converge after iterating to the preset maximum number of decoding iterations, OSD is triggered to perform secondary decoding, and finally outputs the codewords and information sequence obtained by OSD decoding.

2. The quasi-belief propagation decoding method for BCH codes based on neural networks according to claim 1, characterized in that, The specific implementation process of step S2.1 is as follows: Define the row weight of the preprocessed parity-check matrix as Iterative index of QBP-SF ,in Set the expansion factor to the preset maximum number of iterations. and redundancy ; According to the received signal ,calculate The corresponding initial log-likelihood ratio ,in This represents the i-th input message bit, where N is the code length. As input message; for Preprocessing is performed using the automorphism property of BCH codes to obtain the dilated... The input information is doubled; The log-likelihood ratio corresponding to each variable node v in the expanded input information is used as a message to be distributed to the connected verification node c. The message passing formula is: ； In the formula, Indicates the time at the (t-1)th iteration The corresponding log-likelihood ratio; , The set of verification nodes connected to variable node v; This represents the message distributed from variable node v to verification node c.

3. The quasi-belief propagation decoding method for BCH codes based on neural networks according to claim 2, characterized in that, The specific implementation process of step S2.2 is as follows: Extract all nodes associated with the current verification node c. Each variable node distributes messages. The input vector is constructed. ,right Each group of messages undergoes a symbol-amplitude separation operation to obtain independent symbol information and amplitude information. The amplitude values ​​after separation are sorted in descending order. The one-to-one mapping relationship between the original index and the sorted position is recorded simultaneously. The sorted amplitude sequence is fed into a pre-trained neural network. After the pre-trained neural network performs the operation, it outputs the non-negative amplitude result in the sorted state. Based on the index mapping relationship of the records, the non-negative amplitude values ​​output by the neural network are backfilled into the original corresponding positions of the message. According to the sign update rule of the check node update equation, the backfilled amplitude values ​​are matched with corresponding positive and negative signs. Finally, the output vectors sent by check node c to each connected variable node v are generated. .

4. The quasi-belief propagation decoding method for BCH codes based on neural networks according to claim 3, characterized in that, The specific implementation process of step S2.3 is as follows: Will Each component undergoes an inverse transformation according to the automorphism mapping during input dilation, and after block alignment, they are merged to obtain... For each message block, update the log-likelihood ratio sequence as follows: ； In the formula, This indicates a message originating from the w-th message block; Indicates the time of the t-th iteration The corresponding log-likelihood ratio; The polymerization coefficient is denoted as .

5. The quasi-belief propagation decoding method for BCH codes based on neural networks according to claim 4, characterized in that, The specific implementation process of step S2.4 is as follows: Define message vectors ,right The normalization operation is performed as follows: ； In the formula, This represents the variance of additive white Gaussian noise; express The mean of the amplitude values ​​of each component; This represents the assignment operator; According to the normalized Output the hard decision result. If the hard decision result satisfies all the parity check matrix equations, terminate the iteration early and output the result; otherwise, the iteration count is zero. Return to S2.1 and continue iterating until the maximum number of iterations is reached. .

6. The quasi-belief propagation decoding method for BCH codes based on neural networks according to claim 1, characterized in that, The EXIT analysis tool for scatter plot external information transfer graphs was introduced to optimize parameters, including the maximum number of iterations of QBP-SF, the expansion factor, and the redundancy.

7. The quasi-belief propagation decoding method for BCH codes based on neural networks according to claim 3, characterized in that, The process of obtaining a pre-trained neural network is as follows: The model structure of the neural network is determined. The neural network integrates a complete set of operational logic for performing sign-amplitude separation, amplitude descending order sorting, establishing the mapping between the original index and the sorting position, amplitude inference output, index backfilling, and sign assignment on the input vector. Obtain the training sample set of the neural network, collect BCH code decoding samples covering the entire target signal-to-noise ratio range, the sample input is the input vector constructed based on the preprocessed parity-check matrix and after dilation preprocessing, and the sample label is the standard ideal output vector of the corresponding parity-check node; The loss function, optimization strategy, and parameters for training are determined with the goal of minimizing the error between the network output and the standard ideal output vector. The Adam optimizer is used to perform gradient descent to complete the global basic pre-training. After training, a pre-trained neural network adapted to the full signal-to-noise ratio range is obtained. The basic optimized values ​​of the aggregation coefficient adapted to the full signal-to-noise ratio range are solved simultaneously.

8. The quasi-belief propagation decoding method for BCH codes based on neural networks according to claim 7, characterized in that, The neural network consists of two one-dimensional convolutional layers, a flattening layer, two fully connected layers, and a scale parameter set sequentially. The scale parameter is used to accelerate training and fitting, and can be merged with the aggregation coefficients into a single factor during the online inference stage. The activation function configuration of the neural network is as follows: the first two one-dimensional convolutional layers and the first fully connected layer both use the HardSwish activation function, and the last fully connected layer uses the linear activation function.

9. The quasi-belief propagation decoding method for BCH codes based on neural networks according to claim 7, characterized in that, The training loss function is a combination of distance loss, ranking loss and positive loss. The distance loss supervises the closeness of the predicted value to the true label, the ranking loss forces the output vector to satisfy the ascending order constraint, and the positive loss forces all output values ​​to be non-negative.

10. The quasi-belief propagation decoding method for BCH codes based on neural networks according to claim 7, characterized in that, After completing the global pre-training of the neural network, the basic values ​​of the aggregation coefficients suitable for the entire signal-to-noise ratio (SNR) range are first solved using a binary linear search method. Then, QBP-SF fine-tuning optimization is performed: the network parameters of the pre-trained neural network and the universal basic values ​​of the aggregation coefficients obtained from the binary search are loaded; for each specific SNR test point in the communication scenario, fine-tuning of parameters is carried out using the universal pre-trained network parameters and the basic values ​​of the aggregation coefficients obtained by the binary search as initial values. The network weights and aggregation coefficients are iteratively updated under the training samples corresponding to the current SNR, and the optimal values ​​of the neural network parameters and the optimal values ​​of the aggregation coefficients suitable for the channel conditions of that SNR are solved respectively; the optimal network parameters and the optimal aggregation coefficients corresponding to each group of SNRs are stored and archived for matching and calling in the subsequent online QBP-SF iterative decoding stage.

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