Spatial coupling LDPC (Low Density Parity Check) code sliding window decoding method based on jumping type backtracking retranslation

Abstract

The invention provides a space coupling LDPC (Low Density Parity Check) code sliding window decoding method based on jump type backtracking and redecoding. The method comprises the following steps: step 1, obtaining a space coupling LDPC code; 2, carrying out side information initialization on a decoding window according to a code word sequence of the space coupling low-density parity check code; step 3, carrying out iterative decoding; 4, calculating the output log-likelihood ratio of the target symbol after the iteration is completed, and carrying out decoding judgment; step 5, activating a jump type backtracking retranslation protocol; and step 6, after the decoding of the current judgment window is completed, the window slides to the next window position towards the lower right corner along the diagonal of the check matrix, and the steps 3-5 are repeated until the decoding window slides out of the matrix. According to the method, error information in a previous window can be prevented from being transmitted to a subsequent window through a coupling structure of the SC-LDPC code, the error propagation phenomenon is relieved, and the sliding window decoding performance is improved.

Description

Technical Field

[0001] This invention relates to the field of communication technology, and specifically to a sliding window decoding method for spatially coupled LDPC codes based on skip-backtracking re-decoding. Background Technology

[0002] Low-Density Parity-Check (LDPC) codes are high-performance error-correcting codes. Their core characteristic lies in the sparsity of their parity-check matrix, meaning the number of non-zero elements is far less than the number of zero elements. To further improve performance, Spatially-coupled Low-Density Parity-Check (SC-LDPC) codes were proposed. These codes are formed by coupling multiple regular LDPC code blocks together, exhibiting performance close to channel capacity at low signal-to-noise ratios. They have demonstrated superior error correction performance compared to traditional LDPC codes in next-generation communication standards and advanced optical communication systems.

[0003] The structural feature of SC-LDPC codes, with non-zero elements only on the diagonal, allows for decoding using the sliding window decoding (SWD) algorithm. This algorithm employs a fixed-length window to perform iterative belief propagation decoding on the information within the window. After the current window is completed, the window slides to the lower right corner until the entire sequence has been processed, significantly reducing decoding latency and memory usage. However, due to the coupled structure of SC-LDPC codes, decoding errors generated in the current window may affect the decoding of subsequent windows, ultimately leading to degraded decoding performance and error propagation. Summary of the Invention

[0004] Purpose of the invention: The technical problem to be solved by the present invention is to address the shortcomings of the prior art by providing a sliding window decoding method for Spatially Coupled Low Density Parity Check (SC-LDPC) codes based on skip-backtracking retranslation. The window position is determined by threshold comparison, and after decoding, the window jumps to the window position of the threshold comparison. This alleviates the error propagation problem caused by the coupling structure of SC-LDPC codes and improves the performance of sliding window decoding.

[0005] This method includes the following steps: Step 1, for L degree distributions The spatially coupled low-density parity-check (LDPC) code original model is coupled to obtain a spatially coupled LDPC code, where L is the coupling length, l is the degree of the variable node, and r is the degree of the parity node. Based on the received codeword sequence of the spatially coupled LDPC code, the following parameters are set: spread factor M, window size W, and maximum number of iterations. Minimum number of iterations Coupling length L, coupling width and state value flag, and M, W, , L Both `flag` and `flag` are positive integers; Step 2: Initialize the decoding window with side information according to the codeword sequence of the spatially coupled low-density parity-check code. The window slides from the upper left corner of the parity-check matrix along the diagonal to the lower right corner. Initialize the information of the newly entered lower right corner region of the window. The target symbol information bit receives the output log-likelihood ratio (LLR) of the previous window. Step 3, perform iterative decoding: within the decoding window of the spatially coupled low-density parity-check code, implement a multi-round iterative decoding strategy based on confidence propagation; if the number of iterations in the current decoding window accumulates to the preset minimum iteration threshold, start the decoding performance evaluation process: first, perform maximum a posteriori probability hard decision on the target symbol sequence, and then calculate the prediction bit error rate based on the decision result; Set a preset performance threshold (generally the predicted bit error rate calculated based on the traditional sliding window decoding process is used as the preset performance threshold), and compare it with the predicted bit error rate in the current window to achieve a binary determination of the decoding state: when the predicted bit error rate in the current window is greater than the threshold, it indicates that the current decoding convergence state has not met expectations, and the state identifier is assigned a value of 1, indicating that a jump-backtracking re-decoding optimization is needed, and step 5 is executed; otherwise, when the predicted bit error rate in the current window is less than or equal to the threshold requirement, the identifier is assigned a value of 0, indicating that the current window decoding has reached the reliability standard, and step 4 is executed; Step 4: Under the condition that the state identifier is detected as logic 0, calculate the output log-likelihood ratio of the target symbol after this iteration and make a decoding decision; after the decoding window completes the decoding of the current target symbol, it outputs the decoding result and slides down along the diagonal to decode the next target symbol. Step 5: When the state identifier is detected to be logic 1, the skip-backtracking re-decoding protocol is activated. The skip-backtracking re-decoding protocol first controls the decoding window to move backward along the diagonal trajectory, and the displacement is determined by the preset backtracking step size parameter. Within the window after backtracking positioning, message multiplexing technology is used to re-iterate the decoding process of the information within the window. After the re-iteration decoding is completed, the state identifier is reset to logic 0, indicating that the abnormal state has been effectively handled. Finally, the window skipping mechanism is used to reset to the initial judgment position and restore the standard sliding window decoding operation sequence. Step 6: After the current judgment window is decoded, the window slides along the diagonal of the parity check matrix to the lower right corner to the next window position, and repeats steps 3 to 5 until the decoding window slides out of the matrix.

[0006] In step 2, the calculation formula for initializing the edge information is: (1), (2), in, This represents the j-th variable node in the current window. This represents the initialization information received by the j-th variable node. Represented as the initial codeword sequence The j-th variable node in the verification matrix Indicates the received sequence In the j-th variable node of the verification matrix, P represents the formula for calculating conditional probability. This represents the first codeword bit of the initial codeword sequence. This represents the first codeword bit of the received sequence; This represents the edge information passed from the j-th variable node to the i-th verification node. This represents the channel observation value received by the j-th variable node.

[0007] Step 3 includes: Step 3.1, Update the verification node: (3), in This represents the information passed from the i-th check node to the j-th variable node during the l-th iteration. This represents the set of variable nodes connected to check node i, excluding variable node j. Represents the variable node at the (l-1)th iteration. Passed to the verification node Information; Step 3.2, Update the variable node: (4), in, This represents the information passed from the j-th variable node to the i-th check node during the l-th iteration. This represents the set of check nodes connected to variable node j, excluding check node i. Step 3.3: Update the posterior probability by updating each value of the received signal for the next decision. Step 3.4, Decoding and Decision.

[0008] In step 3.3, the updated formula is: (5), in, Represents variable nodes The log-likelihood ratio (LLR) output after the l-th iteration Represents the variable node A set of connected verification nodes, verification nodes It is a verification node belonging to this set. This represents the check node during the l-th iteration. Passed to variable node Information.

[0009] Step 3.4 includes: making a decision on each bit of the received signal based on the updated posterior probability; if the decision result is greater than 0, the result is judged as 0; otherwise, it is judged as 1; there are two conditions for ending the iteration: one is... H is the parity-check matrix, and T represents the transpose of the parity-check matrix H; secondly, it reaches the maximum number of iterations. If any condition is met, output the decision result Z; otherwise, repeat steps 3.1 to 3.3. The decision formula is: (6), in, Indicates to The hard judgment output.

[0010] In step 3, the prediction bit error rate of the target symbol is calculated using the following formula. : (7), in, Represents the columns of the basis matrix. It is a coupling factor. Let represent the average log-likelihood ratio of the j-th variable node, and exp represent the natural exponential function.

[0011] In step 5, the message multiplexing decoding includes: when the window slides to position p, receiving the information of the last iteration of the window at position p-1 (external read-only LLR) as side information, updating the check node and variable node of the current window, and initializing the information of the newly entered window through channel information.

[0012] In step 5, the window jumping mechanism refers to the window moving two or more positions to the lower right corner, which is different from the traditional sliding window that moves one position to the lower right corner each time.

[0013] Taking a backtracking step of 2 as an example, if the window slides to position 5 for decoding and performs the determination in step 3, and the determination requires a jump-style backtracking re-decoding optimization, then the window backtracks to position 5-2=3. After the message reuse technology described in step 5 is used to re-iterate the decoding process of the information in the window, the window jump mechanism is performed, and the window jumps from position 3 to position 5, which is the initial determination position.

[0014] The present invention also provides an electronic device, including a processor and a memory, the memory storing program code that, when executed by the processor, causes the processor to perform the steps of the method.

[0015] The present invention also provides a storage medium storing a computer program or instructions that, when the computer program or instructions are run on a computer, execute the steps of the method described.

[0016] Beneficial effects: The method of this invention compares the window position with a threshold when the window reaches the minimum number of iterations to determine the window position. After the window backtracks and decodes, it jumps back to the decision window to re-decode the information within the window. This avoids the transmission of erroneous information from the previous window to the subsequent window through the coupling structure of the SC-LDPC code, thus mitigating the error propagation phenomenon and improving the performance of sliding window decoding. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the sliding window decoding method for spatially coupled LDPC codes based on window skipping, as described in this invention.

[0018] Figure 2 This is a schematic diagram of the backtracking operation of the present invention under the condition of a backtracking step size of 1.

[0019] Figure 3 This is a schematic diagram of the operation of the window jumping back to the lower right corner along the diagonal under the condition of a backtracking step size of 1.

[0020] Figure 4 This is a schematic diagram of the backtracking operation of the present invention under the condition of a backtracking step size of 2.

[0021] Figure 5 This is a schematic diagram of the operation of the window jumping back to the lower right corner along the diagonal under the condition of a backtracking step size of 2.

[0022] Figure 6 This is a schematic diagram of the backtracking operation of the present invention under the condition of a backtracking step size of 3.

[0023] Figure 7 This is a schematic diagram of the operation of the window jumping back to the lower right corner along the diagonal under the condition of a backtracking step size of 3.

[0024] Figure 8 This is a comparison chart of the bit error rate under different signal-to-noise ratios and different backtracking step sizes according to the present invention.

[0025] Figure 9 This is a comparison chart of the complexity of the present invention.

[0026] Figure 10 This is a comparison chart of the backtracking rate of the present invention. Detailed Implementation

[0027] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, and the advantages of the present invention in the above and / or other aspects will become clearer.

[0028] This invention provides a sliding window decoding method for spatially coupled LDPC codes based on skip-backtracking re-decoding, taking a sliding window decoding method with a backtracking length of 2 as an example. The method includes: In traditional sliding window decoding, the log-likelihood ratio of the target symbol at each window position during the last iteration is recorded under different signal-to-noise ratio (SNR) conditions. The average value for each window is calculated based on the results of multiple decoding processes. The average log-likelihood ratio is then substituted into the following formula to obtain the prediction bit error rate at different window positions. : (1), in, Represents the columns of the basis matrix. It is a coupling factor. Let represent the average log-likelihood ratio of the j-th variable node, and exp represent the natural exponential function.

[0029] The obtained prediction bit error rate is set as the window comparison threshold. In the sliding window decoding process based on window backtracking, when the window reaches the minimum number of iterations, the prediction bit error rate calculated by the log likelihood ratio of the target symbol in the window is compared with this threshold to determine the next window position.

[0030] like Figure 1 As shown, the specific implementation steps of the method include: Step 1, set the codeword sequence Where n represents the code length, after being modulated by Binary Phase Shift Keying (BPSK) and transmitted through an Additive White Gaussian Noise (AWGN) channel, the received sequence changes as follows: The received sequence is decoded. Based on the received spatially coupled low-density parity-check codeword sequence, the following parameters are set: spread factor M, window size W, and maximum number of iterations. Minimum number of iterations Coupling length L, coupling width and state value And M, W, , L and All are positive integers; Step 2: When the window is located at the top left corner of the parity check matrix, the edge information of the decoding window is initialized according to the received sequence. The window slides diagonally from the top left corner of the parity check matrix to the bottom right corner, initializing the information in the bottom right corner region of the newly entered window. The target symbol information bit receives the output log-likelihood ratio (LLR) of the previous window. The initialization formula is: (2), (3), in, This represents the j-th variable node in the current window. This represents the initialization information received by the j-th variable node. This is represented by the j-th variable node in a certain column of the matrix corresponding to the initial codeword sequence X. Let P represent the j-th variable node in a matrix corresponding to a certain column of the received sequence Y, and let P represent the formula for calculating the conditional probability. This represents the edge information passed from the j-th variable node to the i-th verification node. This represents the channel observation value received by the j-th variable node.

[0031] Step 3: Perform iterative decoding. Within the defined decoding window, implement the iterative decoding algorithm based on the belief propagation principle. The specific execution process follows steps 3.1 to 3.4. When the cumulative number of iterations reaches the preset minimum iteration threshold, the system initiates a decoding performance evaluation mechanism, calculating the predicted bit error rate (BER) statistic of the target symbol based on the mathematical model established by formula (6). By comparing this statistic with the preset performance threshold, a binary state identifier is generated: if the predicted BER is greater than the threshold, the state identifier is assigned a value of 1, indicating that the current decoding convergence state has not met expectations; conversely, if the predicted BER is less than or equal to the threshold requirement, the state identifier is assigned a value of 0, indicating that the decoding quality has reached an acceptable standard. The belief propagation decoding process includes: Step 3.1, Verification node update: (4), in Indicates the first During the nth iteration The verification node is passed to the first... Information about each variable node, Represents the node excluding variables External and verification nodes A set of connected variable nodes.

[0032] Step 3.2, Variable node update: (5), in, Indicates the first During the nth iteration The variable node is passed to the first Information about each verification node Indicates except for the check node External and variable nodes A set of connected verification nodes.

[0033] Step 3.3, posterior probability update: Update each value of the received signal for the next decision. Update formula: (6), in, Represents variable nodes No. The log-likelihood ratio (LLR) output after the iteration. Represents the variable node A set of connected verification nodes, verification nodes It is a verification node belonging to this set. This represents the check node during the l-th iteration. Passed to variable node Information.

[0034] The formula for predicting the bit error rate is: (7), in Indicates the predicted bit error rate. It represents the average log-likelihood ratio of the j-th variable node.

[0035] Step 4: When the state identifier is determined to be logic "0", calculate the output log-likelihood ratio of the target symbol after this iteration, and perform a decoding decision. If the decision result is greater than 0, the result is judged as 0; otherwise, it is judged as 1. There are two conditions for ending the iteration: one is... H is the parity-check matrix, and T represents the transpose of the parity-check matrix H; secondly, it reaches the maximum number of iterations. If any condition is met, output the decision result. Otherwise, repeat steps 3.1-3.3. After the decoding window completes the decoding of the current target symbol, it outputs the decoding result and slides down the diagonal to decode the next target symbol. The decision formula is: (8), in, Indicates to The hard judgment output.

[0036] Step 5: When the status identifier is determined to be logic "1" and the backtracking step size parameter is set to 2, the system will initiate a backtracking decoding mechanism based on the reuse of historical information. For example... Figure 4 As shown, the decoding window will slide backward along the diagonal trajectory from the current position p=5 to the historical position p=3. During this process, the system receives the external read-only log-likelihood ratio information generated by the window at position p=2 during the last iteration and injects it as prior edge information into the current decoding process. This edge information will be used to update the information transmission initialization values ​​of the check nodes and variable nodes within the window p=3, thereby constructing an enhanced message multiplexing decoding environment. After the backtracking decoding process is completed, the system dynamically resets the state identifier to logic "0", and then quickly resets the decoding focus to the original decision position p=5 through the window jump mechanism, as shown. Figure 5 As shown, continue executing the standard sliding window decoding process.

[0037] Step 6: After the current decision window is decoded, the window slides along the diagonal of the parity check matrix to the lower right corner to the next window position, and repeats steps 3-5 until the decoding window slides out of the matrix.

[0038] The simulation results show that: Figure 8 Bit Error Rate (BER) is At that time, the spatially coupled LDPC code sliding window decoding (SWD) algorithm requires a signal-to-noise ratio (SNR) of approximately 3.95 dB. The spatially coupled LDPC code sliding window decoding (SSWD) algorithm based on skipping backtracking requires an SNR of approximately 3.55 dB for a backtracking length of 1, approximately 3.72 dB for a backtracking length of 2, and approximately 3.85 dB for a backtracking length of 3. This shows that the spatially coupled LDPC code sliding window decoding method based on skipping backtracking improves performance by 0.4 dB, 0.23 dB, and 0.1 dB compared to the traditional window decoding SWD algorithm at backtracking step lengths of 1, 2, and 3, respectively.

[0039] Figure 9 The complexity of SSWD at different signal-to-noise ratios with backtrack lengths of 1, 2, and 3 is shown, demonstrating that performance improvement is achieved at the expense of some complexity. Figure 10 The diagram shows the backtracking rate for different backtracking step sizes under different signal-to-noise ratios (SNR). The backtracking rate represents the ratio of the number of backtracking windows to the total number of decoding windows, and is inversely proportional to the SNR. The lower the SNR and the worse the channel environment, the higher the backtracking rate, and vice versa.

[0040] Based on the above analysis, this invention achieves better decoding performance by mitigating error propagation, at the expense of some complexity.

[0041] This invention provides a sliding window decoding method for spatially coupled LDPC codes based on skip-backtracking re-decoding. Many methods and approaches exist for implementing this technical solution; the above description is merely a preferred embodiment of the invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications should also be considered within the scope of protection of this invention. All components not explicitly stated in this embodiment can be implemented using existing technologies.

Claims

1. A sliding window decoding method for spatially coupled LDPC codes based on skip-backtracking re-decoding, characterized in that, Includes the following steps: Step 1, for L degree distributions The spatially coupled low-density parity-check (LDPC) code original model is coupled to obtain a spatially coupled LDPC code, where L is the coupling length, l is the degree of the variable node, and r is the degree of the parity node. Based on the received codeword sequence of the spatially coupled LDPC code, the following parameters are set: spread factor M, window size W, and maximum number of iterations. Minimum number of iterations Coupling length L, coupling width and state value flag, and M, W, , L Both `flag` and `flag` are positive integers; Step 2: Initialize the decoding window with side information according to the codeword sequence of the spatially coupled low-density parity-check code. The window slides from the upper left corner of the parity-check matrix along the diagonal to the lower right corner. Initialize the information of the newly entered lower right corner region of the window. The target symbol information bit receives the output log-likelihood ratio (LLR) of the previous window. Step 3, perform iterative decoding: within the decoding window of the spatially coupled low-density parity-check code, implement a multi-round iterative decoding strategy based on confidence propagation; if the number of iterations in the current decoding window accumulates to the preset minimum iteration threshold, start the decoding performance evaluation process: first, perform maximum a posteriori probability hard decision on the target symbol sequence, and then calculate the prediction bit error rate based on the decision result; Set a preset performance threshold and compare it with the prediction error rate in the current window to achieve a binary determination of the decoding status: when the prediction error rate in the current window is greater than the threshold, it means that the current decoding convergence status has not met expectations, and the status identifier is assigned a value of 1, indicating that a jump-back re-decoding optimization is needed, and step 5 is executed; otherwise, when the prediction error rate in the current window is less than or equal to the threshold requirement, the identifier is assigned a value of 0, indicating that the current window decoding has reached the reliability standard, and step 4 is executed; Step 4: Under the condition that the state identifier is detected as logic 0, calculate the output log-likelihood ratio of the target symbol after this iteration and make a decoding decision; after the decoding window completes the decoding of the current target symbol, it outputs the decoding result and slides down along the diagonal to decode the next target symbol. Step 5: When the state identifier is detected to be logic 1, the skip-backtracking re-decoding protocol is activated. The skip-backtracking re-decoding protocol first controls the decoding window to move backward along the diagonal trajectory, and the displacement is determined by the preset backtracking step size parameter. Within the window after backtracking positioning, message multiplexing technology is used to re-iterate the decoding process of the information within the window. After the re-iteration decoding is completed, the state identifier is reset to logic 0, indicating that the abnormal state has been effectively handled. Finally, the window skipping mechanism is used to reset to the initial judgment position and restore the standard sliding window decoding operation sequence. Step 6: After the current judgment window is decoded, the window slides along the diagonal of the parity check matrix to the lower right corner to the next window position, and repeats steps 3 to 5 until the decoding window slides out of the matrix.

2. The method according to claim 1, characterized in that, In step 2, the calculation formula for initializing the edge information is: （1）， （2）， in, This represents the j-th variable node in the current window. This represents the initialization information received by the j-th variable node. Represented as the initial codeword sequence The j-th variable node in the verification matrix Indicates the received sequence In the j-th variable node of the verification matrix, P represents the formula for calculating conditional probability. This represents the first codeword bit of the initial codeword sequence. This represents the first codeword bit of the received sequence; This represents the edge information passed from the j-th variable node to the i-th verification node. This represents the channel observation value received by the j-th variable node.

3. The method according to claim 2, characterized in that, Step 3 includes: Step 3.1, Update the verification node: （3）， in This represents the information passed from the i-th check node to the j-th variable node during the l-th iteration. This represents the set of variable nodes connected to check node i, excluding variable node j. Represents the variable node at the (l-1)th iteration. Passed to the verification node Information; Step 3.2, Update the variable node: （4）， in, This represents the information passed from the j-th variable node to the i-th check node during the l-th iteration. This represents the set of check nodes connected to variable node j, excluding check node i. Step 3.3: Update the posterior probability by updating each value of the received signal for the next decision. Step 3.4, Decoding and Decision.

4. The method according to claim 3, characterized in that, In step 3.3, the updated formula is: （5）， in, Represents variable nodes The log-likelihood ratio (LLR) output after the l-th iteration Represents the variable node A set of connected verification nodes, verification nodes It is a verification node belonging to this set. This represents the check node during the l-th iteration. Passed to variable node Information.

5. The method according to claim 4, characterized in that, Step 3.4 includes: making a decision on each bit of the received signal based on the updated posterior probability; if the decision result is greater than 0, the result is judged as 0; otherwise, it is judged as 1; there are two conditions for ending the iteration: one is... H is the parity check matrix, and T represents the transpose of the parity check matrix H; secondly, it reaches the maximum number of iterations. If any condition is met, output the decision result Z; otherwise, repeat steps 3.1 to 3.

3. The decision formula is: （6）， in, Indicates to The hard judgment output.

6. The method according to claim 5, characterized in that, In step 3, the prediction bit error rate of the target symbol is calculated using the following formula. : （7）， in, Represents the columns of the basis matrix. It is a coupling factor. Let represent the average log-likelihood ratio of the j-th variable node, and exp represent the natural exponential function.

7. The method according to claim 6, characterized in that, In step 5, the message multiplexing decoding includes: when the window slides to position p, receiving the information from the last iteration of the window at position p-1 as edge information, updating the check node and variable node of the current window, and initializing the information of the newly entered window through channel information.

8. The method according to claim 7, characterized in that, In step 5, the window jumping mechanism refers to the window moving to the lower right corner two or more positions.

9. An electronic device, characterized in that, It includes a processor and a memory, the memory storing program code that, when executed by the processor, causes the processor to perform the steps of the method as described in any one of claims 1 to 8.

10. A storage medium, characterized in that, It stores a computer program or instructions that, when run on a computer, perform the steps of the method as described in any one of claims 1 to 8.

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