Error correction decoding method based on BCH code

Abstract

The invention belongs to the technical field of BCH code decoding, and particularly relates to an error correction decoding method based on a BCH code, which comprises the following steps: constructing a neural network model suitable for UDE detection, if an output result is approved, ending decoding, otherwise, judging that decoding error UDE cannot be detected, and triggering an ordered statistical decoder OSD for further decoding; constructing a DIA correction model, and improving the bit reliability measurement of a received sequence before OSD decoding; an ALMLT algorithm is utilized to obtain a sequence of test error modes, the sequence is used as an initial value of a decoding path of the OSD, then frequency distribution characteristics of a real error mode or an estimated error mode corresponding to a decoding code word are obtained, the sequence of the test error modes is continuously finely adjusted, an optimized decoding path is obtained, and OSD decoding is carried out on a BCH code. According to the method, the reliability and the efficiency of the BCH code in NMS decoding are remarkably improved, and meanwhile, the calculation complexity and the time delay are reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of BCH code decoding, and specifically relates to an error correction decoding method based on BCH code. Background Art

[0002] In daily life, information transmission is everywhere. Whether it is through telephone, network or satellite communication, information needs to go through the processes of encoding, transmission and decoding. In this process, due to the existence of noise, the receiving end may receive incorrect information. Therefore, how to reliably transmit information in a noisy environment is an important issue in the field of communication.

[0003] In a communication system, information is usually represented in binary form. Assume a binary message row vector (message m) , which is encoded into a codeword in the Galois field GF(2) through an encoding matrix (generator matrix) G, where K and N are the lengths of the message and the codeword respectively, , represent the bits in m and c respectively. Then, through simple binary phase shift keying (BPSK) modulation, each bit is mapped to a symbol . However, during the transmission process, channel noise will interfere with the signal. Assume the noise is additive white Gaussian noise (AWGN) with a mean of zero and a variance of , and the sequence finally obtained by the receiving end satisfies , , being the elements in the received sequence y. The task of the decoder is to estimate the possibly transmitted codeword based on the received sequence y.

[0004] In order to improve the reliability of decoding, various decoding algorithms have been proposed in existing research. Among them, ordered statistic decoding (OSD) and its variants use the magnitude of the log-likelihood ratio (LLR) to judge the reliability of bits, while the normalized min-sum (NMS) algorithm is favored for its channel invariance. However, these algorithms still face some challenges in practical applications. For example, the NMS algorithm performs poorly when dealing with high-density codes, while the OSD algorithm, although having excellent performance, has a high computational complexity and is difficult to meet the real-time requirements. Summary of the Invention

[0005] According to the deficiencies in the above existing technologies, the purpose of the present invention is to provide an error correction decoding method based on BCH code. By constructing a UDE detection and DIA correction model and optimizing the OSD decoding path, the reliability and efficiency of BCH code in NMS decoding are significantly improved, while the computational complexity and latency are reduced.

[0006] To achieve the above object, the present invention provides an error correction decoding method based on BCH code, comprising the following steps: S1. Construct a neural network model suitable for UDE detection, the input of which is a weighted iterative distance sequence containing the distance information obtained in each iteration during the NMS decoding process of the BCH code, and the output is a binary probability distribution. If the output result is recognized, the decoding ends; otherwise, it is determined as an undetectable decoding error UDE, and an ordered statistics decoder OSD is triggered for further decoding; S2. Construct a DIA correction model to improve the bit reliability metric of the received sequence before OSD decoding; S3. Use the ALMLT algorithm to obtain the sorting of the test error patterns as the initial value of the decoding path of the OSD, and then obtain the frequency distribution characteristics of the true error pattern or the estimated error pattern corresponding to the decoded codeword in an offline or online manner. Based on the true error pattern and the frequency distribution characteristics, continuously fine-tune the sorting of the test error patterns to obtain an optimized decoding path; S4. Perform OSD decoding on the BCH code based on the optimized decoding path.

[0007] As a preferred solution of the present invention, in the process of constructing a neural network model suitable for UDE detection, it is assumed that the message m forms the transmitted codeword c = mG under the action of the generator matrix G. After BPSK modulation, c obtains the signal s, and s is interfered by AWGN noise during the channel transmission process and the received sequence y is obtained at the receiving end. At the same time, the standard parity-check matrix H of the BCH code is optimized to obtain the extended matrix H o , and y is used as the input for iterative decoding of NMS based on H o ; It is assumed that the maximum number of iterations set by the NMS decoding algorithm is I. Then, the input dimension of the neural network model suitable for UDE detection is I×1, and the output dimension is 2×1. Its architecture includes a one-dimensional convolutional layer, a flattening layer, and a Softmax layer.

[0008] As a preferred solution of the present invention, the input of the neural network model suitable for UDE detection is, for any received sequence corresponding to the decoding result of all NMSs based on H o , the amplitude of the received sequence is recorded as the metric of the reliability of each bit , and the hard decision of the last iteration result of the NMS decoding algorithm based on H o is obtained , and the intermediate results of the iteration including the received sequence are compared with to obtain a weighted iterative distance sequence: ; In the formula, represents the i-th element of the weighted iterative distance sequence, indicating the difference between the hard decision result after the i-th iteration and the result of the last iteration; is the j-th component of the received sequence y, represents the amplitude of the j-th bit in the received sequence, serving as a measure of the reliability of this bit; represents the hard decision of the i-th iteration of the j-th component; represents of the j-th component; is an indicator function, taking the value of 1 when , and 0 otherwise; N is the length of the codeword; After passing through a one-dimensional convolutional layer, a flattening layer, and a fully connected layer with a Softmax activation function, the input of the neural network model applicable to UDE detection is the binary probability distribution of the decoding result of the current received sequence, including approval and denial.

[0009] As a preferred solution of the present invention, if the probability difference between the approval and the denial of the binary probability distribution is greater than a pre-set probability threshold , then approval is announced, otherwise it is determined as UDE, triggering OSD for further decoding.

[0010] As a preferred solution of the present invention, the neural network model applicable to UDE detection is trained, and the data used for training is to generate computer simulation data at the SNR points where the frame error rate corresponding to NMS based on H o is between 0.08 and 0.12, and then call the NMS decoding algorithm based on H o . When the decoding result of each received sequence matches the true transmitted codeword, set the label of the corresponding weighted iterative distance sequence to '0', otherwise, set it to '1' to obtain all samples for supervised learning, and use the binary cross-entropy loss function during the training process.

[0011] As a preferred solution of the present invention, in the S2, the DIA correction model includes two one-dimensional convolutional layers, a flattening layer, and an output layer; For NMS decoding with the maximum number of iterations I > 5, only the posterior information of the first 5 iterations of the codeword is retained as the input of the DIA correction model. If I ≤ 5, then all NMS decoding information is retained as the input of the DIA correction model; The absolute value of the sum of the output of the DIA correction model and the log-likelihood ratio of the received sequence is used as a further correction to the reliability measure of the received sequence.

[0012] As a preferred embodiment of the present invention, in step S3, the optimized decoding path is the priority sorting of the test error patterns (TEPs) obtained by the ALMLT algorithm operating offline, online, or in a hybrid of both, where: In the offline update phase, assume the decoding path length of the TEPs is , and the extended path length is , where is the extension factor, and the loss function is defined as the sum of the sequence numbers where each TEP is located. Here, TEP represents a single test error pattern, then: Step 1. Determine the sorting of the priorities of the TEPs as the starting point of the current extended decoding path according to the calculation results of the ALMLT algorithm, and initialize their respective counters to zero; Step 2. Collect the number of occurrences of the true error patterns (EPs) corresponding to the first batch of NMS decoding failure cases, arrange them from high to low, and intercept the first elements in this EP list; add the counts of each EP in the list to the counters of the TEPs in the corresponding current extended decoding path; Step 3. By analogy, when all the last batch of NMS decoding failure cases are processed, sort the counters of the final TEPs from high to low, and intercept the decoding path with a length of as the optimized result; In the online update phase: The OSD obtains a batch of decoding results under the current decoding path. Assume that the decoding results correspond to the estimated TEPs and are consistent with the actual ones. Update the existing decoding path according to step 2 of the offline phase using the counts of the estimated TEPs, and then use this updated decoding path to decode the next batch of data and continue to update the decoding path, and so on.

[0013] As a preferred embodiment of the present invention, in step S4, on the basis of the optimized decoding path, a sliding window assisted arbitration model (SWA) is introduced, and a threshold is set. If , then directly adopt the optimized decoding path. If , then use the SWA model to block-process the decoding path, and dynamically detect and arbitrate through the sliding window mechanism to decide whether to terminate the decoding in advance.

[0014] The algorithms involved in the present invention can be executed by an electronic device. The electronic device includes a memory, a processor, and a computer program stored on the memory and executable on the processor. The above algorithm calculations are realized by the processor executing software.

[0015] The beneficial effects of the present invention are: The present invention realizes the improvement of the reliability and efficiency of the NMS decoding result by constructing a neural network model for UDE detection and a DIA correction model. The UDE detection model can effectively identify undetectable errors in NMS decoding under medium and low signal-to-noise ratio conditions, trigger OSD decoding in a timely manner, avoid the degradation of decoding performance caused by UDE, and at the same time, the DIA correction model improves the bit reliability metric after NMS decoding fails, providing more accurate input information for subsequent OSD decoding, thereby improving the overall decoding performance.

[0016] The present invention optimizes the OSD decoding path by using the ALMLT algorithm and the SWA model, significantly reducing the computational complexity and latency of OSD decoding. The ALMLT algorithm optimizes the decoding path in combination with the actual error distribution characteristics, making the decoding process more efficient, while the SWA model further reduces the decoding computation amount and improves the data throughput and decoding efficiency through dynamic management of the decoding path and an early termination mechanism. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 is the flow schematic diagram of the present invention; Figure 2 is the relationship diagram between the probability threshold and the recognition rate of the neural network model applicable to UDE detection during the verification process of the present invention; Figure 3 is the curve diagram of the reliable metric deviation value of BCH(63, 45) at SNR = 2.0dB during the verification process of the present invention; Figure 4 is the curve diagram of the reliable metric deviation value of BCH(63, 45) at SNR = 3.5dB during the verification process of the present invention; Figure 5 is the schematic diagram of the improvement of bit metric without the participation of the DIA correction model during the verification process of the present invention; Figure 6 is the schematic diagram of the improvement of bit metric with the participation of the DIA correction model during the verification process of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0018] The following further describes the embodiments of the present invention with reference to the drawings: As Figure 1 shown, an error correction decoding method based on BCH code includes the following steps: S1. Construct a neural network model applicable to UDE detection, whose input is a weighted iterative distance sequence containing the distance information obtained in each iteration during the NMS decoding process of BCH code, and the output is a binary probability distribution. If the output result is recognized, the decoding ends; otherwise, it is determined as an undetectable decoding error UDE, and an ordered statistic decoder OSD is triggered for further decoding; S2. Construct a DIA correction model to improve the bit reliability metric of the received sequence before OSD decoding; S3. Use the ALMLT algorithm to obtain the sorting of the test error patterns as the initial value of the decoding path of the OSD. Then, obtain the frequency distribution characteristics of the true error pattern or the estimated error pattern corresponding to the decoded codeword in an offline or online manner. Continuously fine-tune the sorting of the test error patterns based on the true error pattern and the frequency distribution characteristics to obtain an optimized decoding path; S4. Perform OSD decoding on the BCH code based on the optimized decoding path.

[0019] The error correction decoding method of this embodiment is mainly aimed at the BCH code of high code rate and ultra-short code. For the BCH code of low code rate or medium-long code, considering that the cases of UDE are very rare, the model for detecting UDE can be not introduced.

[0020] The ALMLT algorithm (Arranged List of the Most a priori Likely Tests) is a well-known technology and is a reliability soft decision decoding algorithm based on ordered statistics, mainly used for the decoding of long linear block codes. Its core idea is to pre-generate a list of test vectors sorted by weight, utilize the statistical characteristics of the channel signal-to-noise ratio (SNR), optimize the test order in the decoding process, so as to reduce the computational complexity while ensuring the performance. The ALMLT algorithm described in the public literature "New approach to order statistics decoding of long linear block codes" can be adopted.

[0021] Normalized Min-Sum (NMS) is an improved Min-Sum decoding algorithm, which improves the decoding performance through normalization and has the characteristics of high throughput and low complexity. The NMS algorithm simplifies the calculation of the check nodes and is applicable to the decoding of sparse check matrices. Ordered Statistics Decoding (OSD) is a general decoding method, and its core idea is to approximate the maximum likelihood decoding by generating and testing possible error patterns. The NMS and OSD involved in this embodiment are based on the NMS and OSD disclosed in CN119154894B.

[0022] Undetected Decoding Errors (UDE) is an error type in which the decoder outputs an incorrect codeword but is not detected by the checking mechanism.

[0023] In S1, the process of constructing a neural network model suitable for UDE detection is as follows. Assume that the message m forms the transmitted codeword c under the action of the generating matrix G, i.e., c = mG. After BPSK modulation, the signal s is obtained from c. During the channel transmission, the signal s is interfered by AWGN noise and the received sequence y is obtained at the receiving end. At the same time, the standard parity-check matrix H of the BCH code is optimized to obtain the extended matrix H. o , and y is used as the input for iterative decoding of NMS decoding based on H o . Assume that the maximum number of iterations set by the NMS decoding algorithm is I. Then, the input dimension of the neural network model suitable for UDE detection is I×1, and the output dimension is 2×1. Its architecture includes a one-dimensional convolutional layer (with a convolutional kernel size of 3×1×2), a flattening layer, and a Softmax layer (with a weight matrix size of 4×2 and a bias vector size of 2).

[0024] Among them, based on the process of obtaining the optimal parity-check matrix disclosed in CN119154894B, the extended matrix H is obtained. o .

[0025] The input of the neural network model suitable for UDE detection is as follows. For any received sequence corresponding to the decoding result of all NMS based on H o , the amplitude of the received sequence is recorded as a measure of the reliability of each bit. , and the hard decision of the last iteration result of the NMS decoding algorithm based on H o is obtained. , and the intermediate results of the iteration including the received sequence are compared with to obtain a weighted iterative distance sequence: ; In the formula, represents the i-th element of the weighted iterative distance sequence, indicating the difference between the hard decision result after the i-th iteration and the last iteration result; is the j-th component of the received sequence y, represents the amplitude of the j-th bit in the received sequence, serving as a measure of the reliability of this bit; represents the hard decision of the i-th iteration of the j-th component; represents of the j-th component; is an indicator function, taking the value of 1 when and 0 otherwise; N is the length of the codeword; After passing through the one-dimensional convolutional layer, the flattening layer, and the fully connected layer with the Softmax activation function, the input of the neural network model suitable for UDE detection is the binary probability distribution of the decoding result of the current received sequence, including approval and denial.

[0026] If the probability difference between the recognition and the denial of the binary probability distribution is greater than a pre-set probability threshold , recognition is declared, otherwise it is determined as UDE, triggering OSD for further decoding.

[0027] Train the neural network model applicable to UDE detection. The data used for training is to generate computer simulation data at the SNR points where the frame error rate corresponding to NMS based on H o is between 0.08 and 0.12, and then call the NMS decoding algorithm based on H o . When the decoding result of each received sequence matches the true transmitted codeword, set the label of the corresponding weighted iteration distance sequence to '0', otherwise, set it to '1' to obtain all samples for supervised learning. The binary cross-entropy loss function is used during the training process.

[0028] In S2, the DIA correction model includes two one-dimensional convolutional layers (the kernel size of both is 3×1×2), a flattening layer, and an output layer; For the NMS decoding with the maximum number of iterations I > 5, only the posterior information of the first 5 iteration codewords is retained as the input of the DIA correction model. If I ≤ 5, all NMS decoding information is retained as the input of the DIA correction model; The absolute value of the sum of the output of the DIA correction model and the log-likelihood ratio of the received sequence is used as a further correction to the reliability measure of the received sequence.

[0029] When the ALMLT algorithm sorts the TEPs, it is estimated based on the bit sorting statistics of the received sequence under the AWGN hypothesis (the channel noise is modeled as additive white Gaussian noise). During the design of the hybrid algorithm of NMS + OSD, in this embodiment, when determining the optimal decoding path of OSD, the result of the ALMLT algorithm is used as the starting point, and then it is continuously fine-tuned with the frequency distribution characteristics of the sequences corresponding to the NMS decoding failure based on H o to obtain a decoding path that is continuously optimized offline or online. Moreover, after introducing the DIA correction model to improve the bit reliability measure, the actual reliability measure distribution of each bit deviates more from the AWGN hypothesis, which objectively requires a more practical decoding path.

[0030] In S3, the optimized decoding path is the priority sorting of the test error patterns TEPs obtained by the ALMLT algorithm that runs offline, online, or a combination of both for update, where: In the offline update stage, assume that the decoding path length of the TEPs is , and the extended path length is , where Let \(\alpha\) be the expansion factor, and the loss function is defined as the sum of the sequence numbers of each TEP, where TEP represents a single test error pattern. Then: Step 1: Determine the sorting of the priorities of the TEP as the starting point of the current expansion decoding path according to the calculation results of the ALMLT algorithm, and initialize their respective counters to zero; Step 2: Collect the number of occurrences of the true error pattern EP corresponding to the first batch of NMS decoding failure cases, and after arranging them from high to low, intercept the first elements in this EP list; add the counts of each EP in the list to the counters of the corresponding TEPs in the current expansion decoding path; Step 3: By analogy, when the last batch of NMS decoding failure cases is processed, sort the counters of each final TEP from high to low, and intercept the decoding path with a length of as the optimized result; Online update stage: The OSD obtains a batch of decoding results under the current decoding path. Assuming that the decoding results correspond to the estimated TEPs and are consistent with the actual ones, update the existing decoding path according to the steps in the offline stage using the counts of the estimated TEPs, and then use this updated decoding path to decode the next batch of data and continue to update the decoding path, and so on.

[0031] In S4, based on the optimized decoding path, introduce the sliding window assistance arbitration model SWA, and set the threshold of , if , then directly adopt the optimized decoding path. If , then use the SWA model to perform block processing on the decoding path, and dynamically detect and arbitrate through the sliding window mechanism to decide whether to terminate the decoding in advance.

[0032] The sliding window assistance arbitration model (Sliding Window Assistance, SWA) is a lightweight binary classification neural network model, which is a two-layer fully connected network FCN, used to dynamically manage the early termination mechanism of the OSD. The window width of SWA is , then its input dimension , and the output dimension is 2×1, where the position of the current window occupies one dimension of the input.

[0033] SWA adopts a weighted cross-entropy loss function, and its input generation and model decision are respectively: Input generation: For each TEP block on the decoding path (sorted according to the error statistics priority), calculate its weighted Hamming distance ; use the sliding window with a width of to traverse Generate input samples from the sequence.

[0034] Model decision: Output probability distribution , where represents the confidence for terminating decoding, represents the confidence for continuing decoding; if (soft threshold, such as 0.8), then terminate OSD and return the current optimal codeword.

[0035] The verification process of this embodiment includes: Case analysis of the effectiveness of the neural network model applicable to UDE detection, set the probability threshold , by adjusting , the ratio of the misjudgment rate and the missed judgment rate can be flexibly configured according to the actual scenario. First, train the neural network model applicable to UDE detection. After training, compare the difference between the probability of the model output being '0' and the probability of '1' with the value. According to the pairing of the model output and the actually transmitted codeword, there are three possibilities in total: They are the same; The model output does not recognize the NMS decoding result this time, but the actual and the transmitted codewords are actually the same, which belongs to misjudgment; The model output recognizes the NMS decoding result this time, but the actual and the transmitted codewords are not the same, which belongs to missed judgment.

[0036] In the hybrid decoding of NMS + OSD, special attention should be paid to the third scenario, because it does not trigger the subsequent OSD decoding, making the performance of the hybrid decoding seriously affected by UDE.

[0037] For BCH high-rate ultra-short codes, taking (63, 45) as an example, its minimum code distance is 7, and it can only correct the received sequence with at most 3 bits of error. In the medium and low SNR regions (such as below 2.6 dB), the maximum number of iterations I of the NMS decoding algorithm is set to 4, and the proportion of the number of verified UDEs in the frame error rate is as high as one-third. That is to say, among all the NMS decoding results based on H o detected by the parity-check matrix, in fact, only two-thirds of the probability is consistent with the transmitted codeword. Input all samples into the trained model. The relationship between the probability threshold and the recognition rate (frame error rate FER) of the model is as Figure 2 shown.

[0038] Case analysis of OSD decoding path optimization. When the ALMLT algorithm sorts TEPs, it is estimated based on the bit sorting statistics of the received sequence under the AWGN assumption. Still taking (63, 45) as an example, the reliability metric values calculated based on the ALMLT theory are at arbitrarily selected SNR = 2.0dB and 3.5dB. Considering experimental simulation, bit swapping in Gaussian elimination, and cases such as the output of the UDE model (neural network model applicable to UDE detection), the deviation value curves of the reliability metric introduced by various factors are estimated as follows Figure 3 and Figure 4 shown

[0039] From Figure 3 and Figure 4 it can be seen that the experimental simulation results are very close to the values calculated by the ALMLT theory, manifested in that the blue curve corresponding to the deviation value of each bit reliability metric fluctuates slightly near the horizontal line with a vertical coordinate of zero. When additionally considering the influence of bit swapping caused by Gaussian elimination, a spike in the deviation value of the reliability metric appears near the 18th bit (63 - 45 = 18) in the orange curve. Only counting the sequences corresponding to NMS decoding failures, that is, the output of the UDE model, the green curve and the red curve show that whether considering bit swapping caused by Gaussian elimination or not, the data significantly deviates from the values calculated by the ALMLT theory. These observed facts fully demonstrate the necessity of fine-tuning the TEP sorting based on the ALMLT calculation results after applying the UDE model.

[0040] Assume the decoding path length of TEPs , , then the extended path length . If the actual EP is not in the TEP list determined by the ALMLT algorithm with a length of , count its serial number as ; as Figure 5 and Figure 6 shown, at SNR = 3.5dB, cases where NMS decodes the BCH(127, 99) code unsuccessfully are collected, the DIA correction model is used to enhance the bit reliability metric, and a comparison is made with the results without using the correction model; At the same time, a comparison was made between the arrangement of TEPs by traditional OSD (CVT curve), its arrangement after offline fine-tuning optimization (CVT_MS curve), the arrangement of TEPs by ALMLT (ALMLT curve), and its offline fine-tuning optimization (ALMLT_MS curve). The curve Train_bound represents the ideal curve obtained by arranging all the collected NMS decoding failure cases in descending order of the number of occurrences as a reference. The ordinate asymptotic frame error rate represents the ideal FER value of the corresponding OSD when the abscissa value is up to the nth TEP in the decoding path (assuming that the true error pattern EP corresponding to the most reliable basis MRB can always be recognized). Then, the generalization verification of SNR = 3.0dB, 3.5dB, 4.0dB, and 4.5dB was carried out using the priority of TEPs determined by SNR = 3.5dB to obtain Tables 1 and 2.

[0041] Table 1 Comparison of the average value of TEPs consumed per received sequence without DIA participation

[0042] Table 2 Comparison of the average value of TEPs consumed per received sequence with DIA participation

[0043] Observing each curve and the table, the following conclusions can be obtained: DIA can slightly improve the bit reliability metric, enabling the EP corresponding to the received sequence to appear earlier at the forefront of the decoding sequence, thereby reducing the average value of TEPs consumed per received sequence.

[0044] The order of TEPs arranged by traditional OSD according to the order of magnitude is significantly inferior to the corresponding order of the ALMLT algorithm. Both the figure and the table show that the offline updated ALMLT sorting will have further improvement, and it can be expected that more offline or online data can obtain more improvement.

[0045] From the slopes of each curve, it can be seen that the role of each TEP in reducing FER becomes weaker and weaker. As Figure 5 and Figure 6 shown, for the ALMLT_MS curve, the FER of the 400th TEP is about 0.02 (equivalent to the contribution of the first 400 TEPs being about 1 - 0.02 = 0.98). And the contribution of the 600 TEPs between the 400th TEP and the 1000th TEP is only 0.013 (reducing the FER from about 0.02 corresponding to the 400th TEP to about 0.007 corresponding to the 1000th TEP), which indirectly proves the necessity of arranging the priority of TEPs in the decoding path.

[0046] As can be seen from Table 1 and Table 2, the decoding path obtained at SNR = 3.5 dB generalizes well, and all sorts of orderings with DIA participation are superior to the same type without DIA participation. Among them, the fine-tuned ALMLT algorithm is also slightly superior to the theoretical calculation of ALMLT. As the SNR increases, the fine-tuning of ALMLT loses its necessity. As shown in the last row of Table 1 and Table 2, at 4.5 dB, ALMLT_MS fails to outperform the theoretical calculation of ALMLT.

Claims

1. An error correction and decoding method based on BCH code, characterized in that It includes the following steps: S1. Construct a neural network model applicable to UDE detection. Its input is a weighted iterative distance sequence containing the distance information obtained in each iteration during the NMS decoding process of the BCH code, and the output is a binary probability distribution. If the output result is recognized, the decoding ends; otherwise, it is determined as an undetectable decoding error (UDE), and an ordered statistic decoder (OSD) is triggered for further decoding; S2. Construct a DIA correction model to improve the bit reliability metric of the received sequence before OSD decoding; S3. Use the ALMLT algorithm to obtain the ranking of the test error patterns, which serves as the initial value of the decoding path of the OSD. Then, obtain the frequency distribution characteristics of the true error pattern or the estimated error pattern corresponding to the decoded codeword in an offline or online manner. Continuously fine-tune the ranking of the test error patterns based on the true error pattern and the frequency distribution characteristics to obtain an optimized decoding path; S4. Perform OSD decoding on the BCH code based on the optimized decoding path.

2. The error correction and decoding method based on BCH code according to claim 1, characterized in that: In the above S1, the process of constructing a neural network model suitable for UDE detection is as follows: Assume that the message m forms the transmitted codeword c = mG under the action of the generation matrix G. After BPSK modulation, c becomes the signal s. During the channel transmission, s is affected by AWGN noise and the received sequence y is obtained at the receiving end. At the same time, the standard parity-check matrix H of the BCH code is optimized to obtain the extended matrix H o , and y is used as the input for iterative decoding of NMS decoding based on H o ; Assume that the maximum number of iterations set by the NMS decoding algorithm is I. Then, the input dimension of the neural network model applicable to UDE detection is I×1, and the output dimension is 2×1. Its architecture includes a one-dimensional convolutional layer, a flattening layer, and a Softmax layer.

3. The error correction decoding method based on BCH code according to claim 2, wherein, The input of the neural network model applicable to UDE detection is, for any received sequence corresponding to the decoding results of all NMSs that have passed the NMS based on H o Record the amplitude of the received sequence as a measure of the reliability of each bit , obtain the hard decision of the last iteration result of the NMS decoding algorithm based on H o , compare the intermediate results of the iteration including the received sequence with to obtain a weighted iterative distance sequence: ​ ； wherein, represents the i-th element of the weighted iterative distance sequence, representing the difference between the hard decision result after the i-th iteration and the result of the last iteration; is the j-th component of the received sequence y, represents the amplitude of the j-th bit in the received sequence, as a measure of the reliability of this bit; represents the hard decision of the i-th iteration of the j-th component; represents of the j-th component; is an indicator function, taking the value of 1 when and 0 otherwise; N is the length of the codeword; After passing through the one-dimensional convolutional layer, the flattening layer, and the fully connected layer containing the Softmax activation function, the input of the neural network model applicable to UDE detection is the binary probability distribution of the decoding result of the current received sequence, including recognition and denial.

4. The error correction and decoding method based on BCH code according to claim 3, characterized in that, If the probability difference between the recognition and the denial of the binary probability distribution is greater than a pre-set probability threshold , recognition is declared; otherwise, it is determined as UDE, triggering OSD for further decoding.

5. The error correction decoding method based on BCH code according to claim 3, characterized in that, Train a neural network model applicable to UDE detection. The data used for training is to generate computer simulation data at the SNR points where the false frame rate corresponding to NMS based on H o is between 0.08 and 0.12, and then call the NMS decoding algorithm based on H o . When the decoding result of each received sequence matches the true transmitted codeword, set the label of the corresponding weighted iterative distance sequence to '0', otherwise, set it to '1' to obtain all samples for supervised learning. The binary cross-entropy loss function is used during the training process.

6. A method for error correction decoding based on BCH code according to claim 2, characterized in that, In the S2 mentioned above, the DIA correction model includes two one-dimensional convolutional layers, a flattening layer, and an output layer; For NMS decoding with the maximum number of iterations I > 5, only the posterior information of the first 5 decoded codewords at the beginning is retained as the input of the DIA correction model. If I ≤ 5, all NMS decoding information is retained as the input of the DIA correction model; The absolute value of the sum of the output of the DIA correction model and the log-likelihood ratio of the received sequence is used as a further correction of the reliability metric of the received sequence.

7. A method for error correction decoding based on BCH code according to claim 1, characterized in that In the S3 mentioned above, the optimized decoding path is the priority ranking of the test error patterns (TEPs) obtained by the ALMLT algorithm updated offline, online, or in a hybrid manner of both, where: In the offline update stage, assume that the decoding path length of TEPs is , and the extended path length is , where is the extension factor, and the loss function is defined as the sum of the sequence numbers where each TEP is located. Here, TEP represents a single test error pattern. Then: Step 1. Determine the sorting of the TEP priorities as the starting point of the current extended decoding path, and initialize their respective counters to zero; Step 2. Collect the number of occurrences of the true error pattern EP corresponding to the first batch of NMS decoding failure cases, and after arranging them from high to low, intercept the first elements in this EP list; add the count of each EP in the list to the counter of the corresponding TEP of the current extended decoding path; Step 3. By analogy, after processing the last batch of cases with NMS decoding failures, sort the counters of each final TEP from high to low, and intercept the decoding path with a length of as the optimized result; Online update stage: The OSD obtains a batch of decoding results under the current decoding path. Assume that the decoding results correspond to the estimated TEPs and are consistent with the actual ones. Update the existing decoding path according to the count of the estimated TEPs based on the steps in the offline stage. Then, use this updated decoding path to decode the next batch of data and continue to update the decoding path, and so on.

8. A method for error correction decoding based on BCH code according to claim 7, characterized in that In S4 described above, based on the optimized decoding path, a sliding window assisted arbitration model SWA is introduced, and a threshold value is set. If , the optimized decoding path is directly adopted. If , the SWA model is used to perform block processing on the decoding path, and dynamic detection and arbitration are carried out through the sliding window mechanism to decide whether to terminate decoding in advance.

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