A BCH code-based error correction decoding method

Abstract

The present invention belongs to the technical field of BCH code decoding, and specifically relates to an error correction decoding method based on BCH codes. The steps include constructing a neural network model suitable for UDE detection. If the output result is approval, decoding ends; otherwise, it is determined to be an undetectable decoding error (UDE), triggering an ordered statistical decoder (OSD) for further decoding; constructing a DIA correction model to improve the bit reliability metric of the received sequence before OSD decoding; using the ALMLT algorithm to obtain the order of test error patterns as the initial value of the OSD decoding path, and then obtaining the frequency distribution characteristics of the actual error pattern or estimated error pattern corresponding to the decoded codeword, continuously fine-tuning the order of the test error patterns, obtaining an optimized decoding path, and performing OSD decoding on the BCH code. The present invention significantly improves the reliability and efficiency of BCH codes in NMS decoding, while reducing computational complexity and latency.

Description

Technical Field

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

[0002] Information transmission is ubiquitous in our daily lives. Whether through telephones, the internet, or satellite communications, information undergoes a process of encoding, transmission, and decoding. During this process, the presence of noise can cause errors at the receiving end. Therefore, reliably transmitting information in noisy environments is a critical issue in the communications field.

[0003] In communication systems, information is usually represented in binary form. Assume a binary message row vector (message m) , encoded into codewords in the Galois field GF(2) through the encoding matrix (generator matrix) G , where K and N are the lengths of the message and codeword respectively, 、 Then, each bit is modulated by simple binary phase shift keying (BPSK). Map to a symbol However, during the transmission process, channel noise will interfere with the signal. Assume that the noise has a mean of zero and a variance of Additive white Gaussian noise (AWGN) , the final sequence obtained by the receiver is satisfy , To receive an element in the sequence y, the decoder's task is to estimate the possible transmitted codewords based on the received sequence y.

[0004] To improve decoding reliability, various decoding algorithms have been proposed. Among them, ordered statistical decoding (OSD) and its variants use the log-likelihood ratio (LLR) to determine bit reliability, while the normalized minimum sum (NMS) algorithm is favored for its channel invariance. However, these algorithms still face challenges in practical applications. For example, the NMS algorithm performs poorly when processing high-density codes, and while the OSD algorithm performs well, its high computational complexity makes it difficult to meet real-time requirements. Summary of the Invention

[0005] In view of the above shortcomings in the prior art, 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 reducing the computational complexity and latency.

[0006] To achieve the above objectives, the present invention provides an error correction decoding method based on BCH code, comprising the following steps:

[0007] S1. Construct a neural network model suitable for UDE detection. Its input is a weighted iterative distance sequence containing the distance information obtained in each iteration of the NMS decoding process of the BCH code. The output is a binary probability distribution. If the output result is approved, the decoding ends. Otherwise, it is determined to be an undetectable decoding error (UDE), triggering the ordered statistical decoder (OSD) for further decoding.

[0008] S2, construct a DIA correction model to improve the bit reliability metric of the received sequence before OSD decoding;

[0009] S3. Using the ALMLT algorithm to obtain the order of the test error patterns as the initial value of the OSD decoding path, then obtaining the frequency distribution characteristics of the actual error patterns or estimated error patterns corresponding to the decoded codewords in an offline or online manner. Based on the actual error patterns and frequency distribution characteristics, the order of the test error patterns is continuously fine-tuned to obtain an optimized decoding path.

[0010] S4. Based on the optimized decoding path, perform OSD decoding on the BCH code.

[0011] As a preferred solution of the present invention, the process of constructing a neural network model suitable for UDE detection is as follows: assuming that the message m forms a transmission codeword c=mG under the action of the generator matrix G, c is modulated by BPSK to obtain a signal s, and s is interfered by AWGN noise during the channel transmission process, and the received sequence obtained at the receiving end is y. At the same time, the standard check matrix H of the BCH code is optimized to obtain the extended matrix H o , taking y as the o Iterative decoding of the NMS decoding input;

[0012] Assuming that the maximum number of iterations set by the NMS decoding algorithm is I, 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 convolution layer, a flattening layer, and a softmax layer.

[0013] As a preferred solution of the present invention, the input of the neural network model suitable for UDE detection is: o The amplitude of the received sequence corresponding to the decoding result of NMS is recorded as the reliability measure of each bit. , obtain the H-based o The hard decision result of the last iteration of the NMS decoding algorithm , and the intermediate results of the iteration including the received sequence are compared with For comparison, we obtain the weighted iterative distance sequence:

[0014] ;

[0015] Where, The i-th element of the weighted iterative distance sequence represents the difference between the hard decision result after the i-th iteration and the result of the last iteration; is the jth component of the received sequence y, represents the amplitude of the jth bit in the received sequence, which is used as a measure of the reliability of the bit; represents the hard decision of the i-th iteration The jth component of ; express The jth component of ; is the indicator function, when The value is 1 when , otherwise it is 0; N is the length of the codeword;

[0016] 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 suitable for UDE detection is the binary probability distribution of the decoding results of the current received sequence, including approval and denial.

[0017] As a preferred solution of the present invention, if the probability difference of the approval minus the rejection of the binary probability distribution is greater than the pre-set probability threshold , it declares approval, otherwise it is judged as UDE, triggering OSD for further decoding.

[0018] As a preferred solution of the present invention, a neural network model suitable for UDE detection is trained, and the training data used is, when the H-based o The frame error rate corresponding to the NMS is between 0.08 and 0.12 SNR points, generate computer simulation data, and then call the H-based o The NMS decoding algorithm sets the corresponding weighted iterative distance sequence when the decoding result of each received sequence matches the actual transmitted codeword. The label is '0', otherwise, it is set to '1', and all samples of supervised learning are obtained. The binary interaction entropy loss function is used in the training process.

[0019] As a preferred embodiment of the present invention, in S2, the DIA correction model includes two one-dimensional convolutional layers, a flattening layer, and an output layer;

[0020] For NMS decoding with a maximum number of iterations I>5, only the first five iterations of the codeword posterior information 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.

[0021] 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.

[0022] As a preferred solution of the present invention, in said S3, the optimized decoding path is the priority ranking of the test error patterns TEPs obtained by running the updated ALMLT algorithm offline, online, or a combination of both, wherein:

[0023] In the offline update phase, assuming that the TEPs decoding path length is , the extended path length is ,in is the expansion factor, and the loss function is defined as the sum of the serial numbers of each TEP, where TEP represents a single test error pattern, then:

[0024] Step 1: Determine based on the calculation results of the ALMLT algorithm The priority order of each TEP is used as the starting point of the current extended decoding path, and the respective counters are initialized to zero;

[0025] Step 2: Collect the number of occurrences of the real error pattern EP corresponding to the first batch of NMS decoding failure cases, sort them from high to low, and intercept the first occurrence of the EP in the EP list. elements; add the count of each EP in the list to the counter of the corresponding TEP of the current extended decoding path;

[0026] Step 3: Similarly, after processing the last batch of NMS decoding failure cases, the counters of the final TEPs are arranged from high to low, and the intercepted length is The decoding path is the optimized result;

[0027] Online update phase: OSD obtains a batch of decoding results under the current decoding path. Assuming that the estimated TEPs corresponding to the decoding results are consistent with the actual ones, the estimated TEPs count is used to update the existing decoding path according to step 2 of the offline phase. Then, the updated decoding path is used to decode the next batch of data and the decoding path is continued to be updated, and so on.

[0028] As a preferred solution of the present invention, in the above S4, based on the optimized decoding path, a sliding window assisted arbitration model SWA is introduced, setting Threshold ,if , then directly use the optimized decoding path, if , the SWA model is used to divide the decoding path into blocks, and the sliding window mechanism is used for dynamic detection and arbitration to decide whether to terminate the decoding early.

[0029] The algorithm involved in the present invention can be executed by an electronic device, which includes a memory, a processor, and a computer program stored in the memory and capable of running on the processor. The above-mentioned algorithm calculation is realized by executing the software through the processor.

[0030] The beneficial effects of the present invention are:

[0031] This paper improves the reliability and efficiency of NMS decoding results 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 low and medium signal-to-noise ratio conditions, triggering OSD decoding in a timely manner to avoid the degradation of decoding performance caused by UDE. At the same time, the DIA correction model improves the bit reliability metric after NMS decoding failures, providing more accurate input information for subsequent OSD decoding, thereby improving overall decoding performance.

[0032] This paper utilizes the ALMLT algorithm and the SWA model to optimize the OSD decoding path, significantly reducing the computational complexity and latency of OSD decoding. The ALMLT algorithm optimizes the decoding path based on actual error distribution characteristics, making the decoding process more efficient. The SWA model further reduces the decoding computational complexity and improves data throughput and decoding efficiency through dynamic decoding path management and early termination mechanisms. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a schematic diagram of the process of the present invention;

[0034] Figure 2 is a graph showing the relationship between the probability threshold and the recognition rate of the neural network model suitable for UDE detection in the verification process of the present invention;

[0035] Figure 3 It is a reliable measurement deviation value curve of BCH (63, 45) at SNR=2.0dB during the verification process of the present invention;

[0036] Figure 4 This is a graph showing the reliability measurement deviation value of BCH (63, 45) at SNR=3.5dB during the verification process of the present invention;

[0037] Figure 5 It is a schematic diagram of improving bit metrics without the DIA correction model in the verification process of the present invention;

[0038] Figure 6 It is a schematic diagram of the DIA correction model participating in improving the bit metric during the verification process of the present invention. DETAILED DESCRIPTION

[0039] The embodiments of the present invention are further described below with reference to the accompanying drawings:

[0040] like Figure 1 As shown, a BCH code-based error correction decoding method includes the following steps:

[0041] S1. Construct a neural network model suitable for UDE detection. Its input is a weighted iterative distance sequence containing the distance information obtained in each iteration of the NMS decoding process of the BCH code. The output is a binary probability distribution. If the output result is approved, the decoding ends. Otherwise, it is determined to be an undetectable decoding error (UDE), triggering the ordered statistical decoder (OSD) for further decoding.

[0042] S2, construct a DIA correction model to improve the bit reliability metric of the received sequence before OSD decoding;

[0043] S3. Using the ALMLT algorithm to obtain the order of the test error patterns as the initial value of the OSD decoding path, then obtaining the frequency distribution characteristics of the actual error patterns or estimated error patterns corresponding to the decoded codewords in an offline or online manner. Based on the actual error patterns and frequency distribution characteristics, the order of the test error patterns is continuously fine-tuned to obtain an optimized decoding path.

[0044] S4. Based on the optimized decoding path, perform OSD decoding on the BCH code.

[0045] The error correction decoding method of this embodiment is mainly aimed at BCH codes with high code rate and ultra-short code. For BCH codes with low code rate or medium-long code, considering that cases of UDE are very rare, a model for detecting UDE may not be introduced.

[0046] The ALMLT algorithm (Arranged List of the Most a Priori Likely Tests) is a well-known reliable soft-decision decoding algorithm based on ordered statistics, primarily used for decoding long linear block codes. Its core concept is to pre-generate a list of weighted test vectors and leverage the statistical characteristics of the channel signal-to-noise ratio (SNR) to optimize the test order during decoding, thereby ensuring performance while reducing computational complexity. The ALMLT algorithm described in the open paper "New approach to order statistics decoding of long linear block codes" can be used.

[0047] Normalized min-sum decoding (NMS) is an improved min-sum decoding algorithm that improves decoding performance through normalization, offering high throughput and low complexity. By simplifying the calculation of check nodes, the NMS algorithm is suitable for decoding sparse check matrices. Ordered statistics decoding (OSD) is a universal decoding method whose core concept is to approximate maximum likelihood decoding by generating and testing possible error patterns. The NMS and OSD methods used in this embodiment are based on the NMS and OSD methods disclosed in CN119154894B.

[0048] Undetected Decoding Errors (UDE) are errors in which the decoder outputs an erroneous codeword but is not detected by the verification mechanism.

[0049] In S1, the process of constructing a neural network model suitable for UDE detection is as follows: assume that the message m forms a transmission codeword c=mG under the action of the generator matrix G, c is modulated by BPSK to obtain the signal s, and s is interfered by AWGN noise during the channel transmission process, and the received sequence obtained at the receiving end is y. At the same time, the standard check matrix H of the BCH code is optimized to obtain the extended matrix H o , taking y as the o Iterative decoding of the NMS decoding input;

[0050] Assuming that the maximum number of iterations set by the NMS decoding algorithm is I, 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 convolution layer (convolution kernel size is 3×1×2), a flattening layer, and a softmax layer (weight matrix size is 4×2, bias vector size is 2).

[0051] Among them, based on the process of obtaining the best check matrix disclosed in CN119154894B, the expanded matrix H is obtained o .

[0052] The input of the neural network model suitable for UDE detection is, for all o The amplitude of the received sequence corresponding to the decoding result of NMS is recorded as the reliability measure of each bit. , obtain the H-based o The hard decision result of the last iteration of the NMS decoding algorithm , and the intermediate results of the iteration including the received sequence are compared with For comparison, we obtain the weighted iterative distance sequence:

[0053] ;

[0054] Where, The i-th element of the weighted iterative distance sequence represents the difference between the hard decision result after the i-th iteration and the result of the last iteration; is the jth component of the received sequence y, represents the amplitude of the jth bit in the received sequence, which is used as a measure of the reliability of the bit; represents the hard decision of the i-th iteration The jth component of ; express The jth component of ; is the indicator function, when The value is 1 when , otherwise it is 0; N is the length of the codeword;

[0055] 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 suitable for UDE detection is the binary probability distribution of the decoding results of the current received sequence, including approval and denial.

[0056] If the probability difference of approval minus rejection in the binary probability distribution is greater than the pre-set probability threshold , it declares approval, otherwise it is judged as UDE, triggering OSD for further decoding.

[0057] The neural network model suitable for UDE detection is trained with the data used to make the H-based o The frame error rate corresponding to the NMS is between 0.08 and 0.12 SNR points, generate computer simulation data, and then call the H-based o The NMS decoding algorithm sets the corresponding weighted iterative distance sequence when the decoding result of each received sequence matches the actual transmitted codeword. The label is '0', otherwise, it is set to '1', and all samples of supervised learning are obtained. The binary interaction entropy loss function is used in the training process.

[0058] In S2, the DIA correction model includes two one-dimensional convolutional layers (the convolution kernel size is 3×1×2), a flattening layer, and an output layer;

[0059] For NMS decoding with a maximum number of iterations I>5, only the first five iterations of the codeword posterior information 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.

[0060] 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.

[0061] When the ALMLT algorithm sorts TEPs, it estimates the sorting statistics of each bit of the received sequence under the AWGN assumption (channel noise is modeled as additive white Gaussian noise). In the process of designing the NMS+OSD hybrid algorithm, this embodiment uses the results of the ALMLT algorithm as the starting point when determining the optimal decoding path of OSD, and then uses the actual H-based o The frequency distribution characteristics of sequences corresponding to NMS decoding failures are continuously fine-tuned to obtain a decoding path that can be continuously optimized offline or online. Furthermore, after introducing the DIA correction model to improve bit reliability, the actual reliability distribution of each bit deviates further from the AWGN assumption, objectively requiring a decoding path that is more realistic.

[0062] In S3, the optimized decoding path is the priority ranking of the test error patterns TEPs obtained by running the updated ALMLT algorithm offline, online, or a combination of both, where:

[0063] In the offline update phase, assuming that the TEPs decoding path length is , the extended path length is ,in is the expansion factor, and the loss function is defined as the sum of the serial numbers of each TEP, where TEP represents a single test error pattern, then:

[0064] Step 1: Determine based on the calculation results of the ALMLT algorithm The priority order of each TEP is used as the starting point of the current extended decoding path, and the respective counters are initialized to zero;

[0065] Step 2: Collect the number of occurrences of the real error pattern EP corresponding to the first batch of NMS decoding failure cases, sort them from high to low, and intercept the first occurrence of the EP in the EP list. elements; add the count of each EP in the list to the counter of the corresponding TEP of the current extended decoding path;

[0066] Step 3: Similarly, after processing the last batch of NMS decoding failure cases, the counters of the final TEPs are arranged from high to low, and the intercepted length is The decoding path is taken as the optimized result;

[0067] Online update phase: OSD obtains a batch of decoding results under the current decoding path. Assuming that the estimated TEPs corresponding to the decoding results are consistent with the actual ones, the estimated TEPs count is used to update the existing decoding path according to step 2 of the offline phase. Then, the updated decoding path is used to decode the next batch of data and the decoding path is continued to be updated, and so on.

[0068] In S4, based on the optimized decoding path, the sliding window assisted arbitration model SWA is introduced, setting Threshold ,if , then directly use the optimized decoding path, if , the SWA model is used to divide the decoding path into blocks, and the sliding window mechanism is used for dynamic detection and arbitration to decide whether to terminate the decoding early.

[0069] The Sliding Window Assistance (SWA) model is a lightweight binary classifier neural network model, a two-layer fully connected network FCN, used to dynamically manage the early termination mechanism of OSD. The window width of SWA is , then its input dimension , the output dimension is 2×1, where the current window position occupies one dimension of the input.

[0070] SWA uses a weighted cross entropy loss function, where input generation and model decision are:

[0071] Input generation: For each TEP block on the decoding path (sorted by error statistics priority), calculate their weighted Hamming distance ; Use width Sliding window traversal Sequence, generate input samples.

[0072] Model decision: output probability distribution ,in Indicates the confidence level for terminating decoding, Indicates the confidence level for continuing decoding; if (soft threshold, such as 0.8), terminate OSD and return the current optimal codeword.

[0073] The verification process of this embodiment includes:

[0074] Case Study on the Effectiveness of Neural Network Models for UDE Detection, Setting Probability Thresholds , by adjusting The ratio of false positive rate to missed positive rate can be flexibly configured according to the actual scenario. First, the neural network model suitable for UDE detection is trained. After training, the probability of the model outputting '0' and the probability difference of '1' are compared with the model (the model in this part is the neural network model suitable for UDE detection). The values ​​are compared. Based on the pairing of the model output and the actual codeword sent, there are three possibilities:

[0075] The two are consistent;

[0076] The model output does not recognize the NMS decoding result, but the actual codeword is the same as the sent codeword, which is a misjudgment.

[0077] The model output recognizes the NMS decoding result, but the actual codeword is different from the sent codeword, which is a missed judgment.

[0078] 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, causing the hybrid decoding performance to be seriously affected by UDE.

[0079] For BCH high-rate ultra-short codes, for example (63, 45), the minimum code distance is 7, which can only correct up to 3 bits of received sequence errors. In the low to medium SNR region (e.g., below 2.6dB), the maximum number of iterations I of the NMS decoding algorithm is set to 4, and the number of verified UDEs accounts for up to one-third of the frame error rate. In other words, all H-based codes that pass the check matrix detection are o In the NMS decoding results, only two-thirds of the probability is consistent with the sent codeword. All samples are input into the trained model. Probability threshold The relationship with the recognition rate of the model (frame error rate FER) is as follows Figure 2 shown.

[0080] In the case study of OSD decoding path optimization, the ALMLT algorithm estimates the statistics of the bit order of the received sequence under the AWGN assumption when sorting TEPs. Still taking (63, 45) as an example, the reliability metric values ​​calculated based on the ALMLT theory at the selected SNR = 2.0dB and 3.5dB are estimated based on the reliability metric deviation curve introduced by various factors such as experimental simulation, bit swapping of Gaussian elimination, and the case of being limited to the output of the UDE model (a neural network model suitable for UDE detection). Figure 3 and Figure 4 shown.

[0081] Depend on Figure 3 and Figure 4As can be seen, the experimental simulation results closely match the ALMLT theoretical calculations, as evidenced by the small fluctuations in the blue curve corresponding to the deviation values ​​of the reliability metrics for each bit near the horizontal line at zero on the y-axis. When the effect of bit swapping caused by Gaussian elimination is additionally considered, the orange curve exhibits a spike in the deviation of the reliability metrics around the 18th bit (63 - 45 = 18). By counting only sequences corresponding to NMS decoding failures, i.e., the output of the UDE model, the green and red curves show that the data deviates significantly from the ALMLT theoretical calculations, regardless of whether bit swapping caused by Gaussian elimination is considered or not. These observations strongly emphasize the necessity of fine-tuning the TEP sorting based on the ALMLT calculation results after applying the UDE model.

[0082] Assume that the TEPs decoding path length , , then the extended path length If the actual EP is not of length When the TEP list is determined by the ALMLT algorithm, its sequence number is ;like Figure 5 and Figure 6 As shown in Figure 2, at SNR=3.5dB, we collected cases where NMS failed to decode the BCH (127, 99) code, used the DIA correction model to enhance the bit reliability metric, and compared it with the results without using the correction model.

[0083] We also compared the traditional OSD permutation of TEPs (CVT curve), its permutation optimized after offline fine-tuning (CVT_MS curve), and the ALMLT permutation of TEPs (ALMLT curve) and its offline fine-tuning optimization (ALMLT_MS curve). The Train_bound curve represents the ideal curve obtained by sorting all collected NMS decoding failure cases from highest to lowest number of occurrences, serving as a reference. The asymptotic frame error rate (AER) on the vertical axis represents the ideal OSD FER (Frequency Error Rate) for all values ​​up to the nth TEP in the decoding path (assuming that the true error pattern EP corresponding to the most reliable base MRB can always be identified). We then used the TEP priority determined by SNR = 3.5dB to generalize and verify the SNRs of 3.0dB, 3.5dB, 4.0dB, and 4.5dB, resulting in Tables 1 and 2.

[0084] Table 1 Comparison of the average TEP consumed per received sequence when no DIA is involved

[0085]

[0086] Table 2 Comparison of the average TEP consumed per received sequence when DIA is involved

[0087]

[0088] By observing the curves and tables, we can draw the following conclusions:

[0089] DIA can slightly improve the bit reliability metric, so that the EP corresponding to the received sequence can appear earlier in the decoded sequence, thereby reducing the average TEP consumed by each received sequence.

[0090] The order of TEPs sorted by order using the traditional OSD is significantly inferior to the ordering using the ALMLT algorithm. Both the graph and table show that the ALMLT sorting algorithm for offline updates can further improve, and we anticipate even greater improvements with more offline or online data.

[0091] From the slopes of the curves, we can see that the effect of each TEP on reducing FER is getting weaker and weaker. Figure 5 and Figure 6 As shown in the ALMLT_MS curve, the FER of the 400th TEP is approximately 0.02 (equivalent to a contribution of approximately 1-0.02=0.98 from the first 400 TEPs). However, the contribution of the 600 TEPs between the 400th and 1000th TEPs is only 0.013 (reducing the FER from approximately 0.02 for the 400th TEP to approximately 0.007 for the 1000th TEP). This indirectly demonstrates the necessity of prioritizing TEPs in the decoding path.

[0092] Tables 1 and 2 show that the decoding paths obtained at an SNR of 3.5dB generalize well. All sorting methods with DIA outperform those without DIA. The fine-tuned ALMLT algorithm also slightly outperforms the theoretical ALMLT calculation. As the SNR increases, fine-tuning ALMLT becomes less necessary. As shown in the last row of Tables 1 and 2, at 4.5dB, ALMLT_MS fails to outperform the theoretical ALMLT calculation.

Claims

1. A BCH code-based error correction decoding method, characterized in that The following steps are involved: S1. Construct a neural network model suitable for UDE detection. Its input is a weighted iterative distance sequence containing the distance information obtained in each iteration of the NMS decoding process of the BCH code. The output is a binary probability distribution. If the output result is approved, the decoding ends. Otherwise, it is determined to be an undetectable decoding error (UDE), triggering the ordered statistical decoder (OSD) for further decoding. S2, construct a DIA correction model to improve the bit reliability metric of the received sequence before OSD decoding; S3. Using the ALMLT algorithm to obtain the order of the test error patterns as the initial value of the OSD decoding path, then obtaining the frequency distribution characteristics of the actual error patterns or estimated error patterns corresponding to the decoded codewords in an offline or online manner. Based on the actual error patterns and frequency distribution characteristics, the order of the test error patterns is continuously fine-tuned to obtain an optimized decoding path. S4. Based on the optimized decoding path, perform OSD decoding on the BCH code; In S1, the process of constructing a neural network model suitable for UDE detection is as follows: assume that the message m forms a transmission codeword c=mG under the action of the generator matrix G, c is modulated by BPSK to obtain the signal s, and s is interfered by AWGN noise during the channel transmission process, and the received sequence obtained at the receiving end is y. At the same time, the standard check matrix H of the BCH code is optimized to obtain the extended matrix H o , taking y as the o Iterative decoding of the NMS decoding input; Assuming that the maximum number of iterations set by the NMS decoding algorithm is I, 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 convolution layer, a flattening layer, and a softmax layer; In S3, the optimized decoding path is the priority ranking of the test error patterns TEPs obtained by running the updated ALMLT algorithm offline, online, or a combination of both, where: In the offline update phase, assuming that the TEPs decoding path length is , the extended path length is ,in is the expansion factor, and the loss function is defined as the sum of the serial numbers of each TEP, where TEP represents a single test error pattern, then: Step 1: Determine based on the calculation results of the ALMLT algorithm The priority order of each TEP is used as the starting point of the current extended decoding path, and the respective counters are initialized to zero; Step 2: Collect the number of occurrences of the real error pattern EP corresponding to the first batch of NMS decoding failure cases, sort them from high to low, and intercept the first occurrence of the EP in the EP list. elements; add the count of each EP in the list to the counter of the corresponding TEP of the current extended decoding path; Step 3: Similarly, after processing the last batch of NMS decoding failure cases, the counters of the final TEPs are arranged from high to low, and the intercepted length is The decoding path is taken as the optimized result; Online update phase: OSD obtains a batch of decoding results under the current decoding path. Assuming that the estimated TEPs corresponding to the decoding results are consistent with the actual ones, the estimated TEPs count is used to update the existing decoding path according to step 2 of the offline phase. Then, the updated decoding path is used to decode the next batch of data and the decoding path is continued to be updated, and so on.

2. The error correction decoding method based on BCH code according to claim 1, characterized in that: The input of the neural network model suitable for UDE detection is, for all o The amplitude of the received sequence corresponding to the decoding result of NMS is recorded as the reliability measure of each bit. , obtain the H-based o The hard decision result of the last iteration of the NMS decoding algorithm , and the intermediate results of the iteration including the received sequence are compared with For comparison, we obtain the weighted iterative distance sequence: ； Where, The i-th element of the weighted iterative distance sequence represents the difference between the hard decision result after the i-th iteration and the result of the last iteration; is the jth component of the received sequence y, represents the amplitude of the jth bit in the received sequence, which is used as a measure of the reliability of the bit; represents the hard decision of the i-th iteration The jth component of ; express The jth component of ; is the indicator function, when The value is 1 when , otherwise it is 0; 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 suitable for UDE detection is the binary probability distribution of the decoding results of the current received sequence, including approval and denial.

3. The error correction decoding method based on BCH code according to claim 2, characterized in that: If the probability difference of approval minus rejection in the binary probability distribution is greater than the pre-set probability threshold , it declares approval, otherwise it is judged as UDE, triggering OSD for further decoding.

4. The error correction decoding method based on BCH code according to claim 2, characterized in that: The neural network model suitable for UDE detection is trained with the data used to make the H-based o The frame error rate corresponding to the NMS is between 0.08 and 0.12 SNR points, generate computer simulation data, and then call the H-based o The NMS decoding algorithm sets the corresponding weighted iterative distance sequence when the decoding result of each received sequence matches the actual transmitted codeword. The label is '0', otherwise, it is set to '1', and all samples of supervised learning are obtained. The binary interaction entropy loss function is used in the training process.

5. The error correction decoding method based on BCH code according to claim 1, characterized in that: In S2, the DIA correction model includes two one-dimensional convolutional layers, a flattening layer, and an output layer; For NMS decoding with a maximum number of iterations I>5, only the first five iterations of the codeword posterior information 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.

6. The error correction decoding method based on BCH code according to claim 5, characterized in that: In the above S4, based on the optimized decoding path, the sliding window assisted arbitration model SWA is introduced, and the setting Threshold ,if , then directly use the optimized decoding path, if , the SWA model is used to divide the decoding path into blocks, and the sliding window mechanism is used for dynamic detection and arbitration to decide whether to terminate the decoding early.

Images