Spatial coupling low-density parity check code decoding method based on backtracking

Abstract

The invention provides a backtracking-based spatial coupling low-density parity check code decoding method. The backtracking-based spatial coupling low-density parity check code decoding method comprises the following steps: acquiring a code word sequence of a spatial coupling low-density parity check code to be decoded according to set parameters; performing side information initialization on the decoding window, executing belief propagation decoding in the decoding window, and performing judgment when the number of iterations reaches the set minimum number of iterations; and determining the decoding position and the window size of a decoding window in the next step according to a judgment result until all target symbols in the code word sequence are decoded. According to the invention, the error propagation phenomenon in the space coupling LDPC code sliding window decoding process can be effectively improved, and the sliding window decoding performance is improved.

Description

Technical Field

[0001] The present invention belongs to the field of communication technologies, and in particular relates to a decoding method for a spatially-coupled low-density parity-check code based on backtracking. Background Art

[0002] Low density parity check (LDPC) codes are linear block codes described by sparse parity-check matrices. The parity-check matrices of LDPC codes are sparse, with most elements in the parity-check matrix being 0 and a small number of elements being 1, and the elements 1 have sparsity. Spatially-coupled low density parity check (SC-LDPC) codes were first proposed by Jimenez Felstrom and Zigangirov in the paper "Time-varying periodic convolutional codes with low-density parity-check matrix" published in the 45th volume, issue 6, pages 2181 - 2191 of "IEEE Transactions on Information Theory" in 1999. SC-LDPC codes have the advantages of low bit error rate, low decoding delay, and low decoding complexity, and their application fields include 5G communication, satellite communication, etc.

[0003] The sliding window decoding (SWD) algorithm for spatially-coupled low density parity check (SC-LDPC) codes can reduce the decoding delay and decoding complexity, but there is an error propagation phenomenon. Errors in the previous window will propagate to subsequent windows through the window overlapping area, check node coupling, and iterative residual errors, affecting the overall decoding performance. Summary of the Invention

[0004] Object of the Invention: The technical problem to be solved by the present invention is to provide a decoding method for a spatially-coupled low density parity check (SC-LDPC) code based on backtracking in view of the deficiencies of the prior art, including the following steps: Step 1, coupling L regular low density parity check (LDPC) code protographs with a degree distribution of ( l , r) to obtain a spatially-coupled low density parity check (SC-LDPC) code, where L is the coupling length, l is the degree of variable nodes, and r is the degree of check nodes; the degree distribution is The original protograph of the regular low-density parity-check (LDPC) code contains check nodes and b variable nodes, where , , a represents the rows of the base matrix of the low-density parity-check (LDPC) code, b represents the columns of the base matrix, represents and 's greatest common divisor; the encoded binary codeword is modulated and mapped into a symbol sequence, and then noise is added through the channel. The receiving end obtains the spatially-coupled low-density parity-check (SC-LDPC) codeword sequence as the input to the decoder; the following parameters are set: expansion factor M0, window size W, maximum number of iterations I max , minimum number of iterations I min , coupling length L, and status value flag, and M0, W, I max , I min , L, and flag are all positive integers; Step 2, when the decoding window is located at the upper left corner of the parity-check matrix, initialize the side information for the decoding window based on the received sequence; Step 3, when the decoding window starts to slide, initialize the information in the lower right corner area newly entered into the window. The information bit of the target symbol receives the output log-likelihood ratio (LLR) of the previous window; Step 4, iterative decoding: perform belief propagation decoding within the decoding window. When the number of iterations of the current decoding window reaches the minimum number of iterations I min , make a determination, calculate the predicted bit error rate of the target symbol at this time, compare it with the threshold. If the predicted bit error rate is greater than the threshold, the status value is 1, otherwise it is 0; Step 5, if the status value is 0, calculate the output log-likelihood ratio (LLR) of the target symbol after the end of this iteration, perform decoding decision. When the decoding window completes the decoding of the current target symbol, output the decoding result of the target symbol, and the decoding window slides diagonally downwards to perform the decoding of the next target symbol; Step 6, if the status value is 1, exit the decoding of the current window position p; expand the decoding window according to the backtracking step size and slide it diagonally upwards for decoding. After completion of decoding, gradually shrink the decoding window and slide it diagonally downwards for decoding until the decoding window returns to position p. After completion of decoding, change the status value 1 to 0; Step S7, repeat Step 4 to Step 6 until the decoding window slides out of the parity-check matrix.

[0005] In Step 1, the expansion factor M0 means replacing 1 and 0 in the parity-check matrix with an identity circulant shift matrix of size M0×M0 and an all-zero matrix of size M0×M0 respectively. The coupling length L means that the spatially-coupled low-density parity-check (SC-LDPC) code is constructed by replicating L single protographs.

[0006] Step 2 includes: Set the codeword sequence , where n is the code length, represents the first codeword bit of the initial codeword sequence. After being modulated by binary phase shift keying, it is transmitted over an additive white Gaussian noise channel, represents the received codeword sequence of the spatially coupled low-density parity-check (SC-LDPC) code, , represents the first codeword bit of the received codeword sequence; When the decoding window is located at the upper left corner of the parity-check matrix, the initialization of the side information for the decoding window based on the received sequence is expressed as , where represents the j-th variable node in the current window, represents the received information for initializing the j-th variable node, represents the j-th variable node corresponding to the initial codeword sequence X in the parity-check matrix, represents the j-th variable node corresponding to the received codeword sequence Y in the parity-check matrix, and P represents the function for calculating the conditional probability.

[0007] In Step 3, after the decoding window starts to slide, the initialization of the information in the newly entered lower right corner area of the window is expressed as ; represents the side information passed from the j-th variable node to the i-th parity-check node.

[0008] Step 4 includes: Step 4-1, initialize the channel information. Initialize the variable nodes according to the characteristics of the given channel. The information initialization formula: (1), (2); Step 4-2, update the parity-check nodes: (3), where represents the information passed from the i-th parity-check node to the j-th variable node at the l-th iteration, represents the set of variable nodes connected to the parity-check node except for the variable node , and tanh is the hyperbolic tangent function, and arctanh is the inverse function of tanh; represents the information passed from the variable node to the parity-check node at the (l-1)-th iteration; Step 4-3, update the variable nodes: (4), Among them, ; represents the set of check nodes other than the check node connected to the variable node Step 4-4: Update the posterior probability; Step 4-5: Decoding decision.

[0009] Step 4-4 includes: Updating each value of the received signal for the next decision. The update formula is: (5), Among them, represents the log-likelihood ratio LLR output after the l-th iteration of the variable node , represents the set of check nodes connected to the variable node The check node is the check node belonging to this set, represents the information transmitted from the check node

[0010] to the variable node Step 4-5 includes: Making a decision on each bit of the received signal according to 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 is the parity-check matrix, and the superscript represents the transpose of the matrix; The other is reaching the maximum number of iterations I max ; When either of the conditions for ending the iteration is satisfied, the decision result is output. Otherwise, repeat Steps 4-2 to 4-4. The formula is: (6), Among them represents the hard decision output of .

[0011] In Step 4, calculating the predicted bit error rate of the target symbol includes: Calculating the predicted bit error rate through the log-likelihood ratio of the target symbol: (7), Among them, is the coupling factor, represents the predicted bit error rate, and exp represents the natural exponential function.

[0012] The present invention also provides an electronic device, including a processor and a memory. The memory stores program codes, and when the program codes are executed by the processor, the processor is caused to execute the steps of the method described above.

[0013] The present invention also provides a storage medium storing a computer program or instructions. When the computer program or instructions run on a computer, the steps of the method described above are executed.

[0014] The present invention has the following beneficial effects: Under the condition that the window size is 4, the TB-SWD algorithms with a backtracking step size of 1, 2, and 3 bring signal-to-noise ratio gains of 0.6 dB, 0.45 dB, and 0.25 dB respectively compared with the SWD algorithm; under the condition that the window size is 8, the TB-SWD algorithms with a backtracking step size of 1 and 2 bring signal-to-noise ratio gains of 0.15 dB and 0.1 dB respectively compared with the SWD algorithm. The complexity of the TB-SWD algorithm is higher than that of the SWD algorithm in the low signal-to-noise ratio region. As the signal-to-noise ratio increases, the complexity of the TB-SWD algorithm gradually decreases and the gap with the complexity of the SWD algorithm gradually narrows. Description of the Drawings

[0015] Figure 1 is a schematic flow diagram of the method for backtracking-based sliding window decoding of spatially coupled LDPC codes according to the present invention.

[0016] Figure 2 is the protograph of a low-density parity-check (LDPC) code.

[0017] Figure 3 is the edge expansion of the protograph of the low-density parity-check (LDPC) code.

[0018] Figure 4 is the protograph of a spatially coupled low-density parity-check (SC-LDPC) code with a coupling length of L.

[0019] Figure 5 is a schematic diagram of the sliding window decoding (SWD) algorithm.

[0020] Figure 6 is a schematic diagram of the backtracking operation according to the present invention under the condition of a backtracking step size of 1.

[0021] Figure 7 is a schematic diagram of sliding down along the diagonal for decoding after backtracking according to the present invention under the condition of a backtracking step size of 1.

[0022] Figure 8 is a schematic diagram of the backtracking operation according to the present invention under the condition of a backtracking step size of 2.

[0023] Figure 9It is a schematic diagram of the decoding after backtracking under the condition of the backtracking step size 2 of the present invention and then sliding downward along the diagonal line.

[0024] Figure 10 It is a schematic diagram of continuing to slide downward along the diagonal line for decoding under the condition of the backtracking step size 2 of the present invention.

[0025] Figure 11 It is a schematic diagram of the backtracking operation under the condition of the backtracking step size 3 of the present invention.

[0026] Figure 12 It is a schematic diagram of the decoding after backtracking and then sliding downward along the diagonal line under the condition of the backtracking step size 3 of the present invention.

[0027] Figure 13 It is a schematic diagram of continuing to slide downward along the diagonal line for decoding under the condition of the backtracking step size 3 of the present invention.

[0028] Figure 14 It is a schematic diagram of the decoding when continuing to slide downward along the diagonal line to the position before performing the backtracking operation under the condition of the backtracking step size 3 of the present invention.

[0029] Figure 15 It is a comparison graph of the bit error rate performance between the present invention and the sliding window decoding SWD algorithm under different signal-to-noise ratio conditions under different backtracking step size conditions.

[0030] Figure 16 It is a comparison graph of the complexity between the present invention and the sliding window decoding SWD algorithm under different signal-to-noise ratio conditions under different backtracking step size conditions.

[0031] Figure 17 It is a backtracking rate graph of the present invention under different backtracking step size conditions. Detailed implementation manners

[0032] The following further specifically describes the present invention in conjunction with the accompanying drawings and specific implementation manners, and the above and / or other advantages of the present invention will become clearer.

[0033] An embodiment of the present invention provides a decoding method for a spatially coupled low-density parity-check code based on backtracking, including: setting a 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 becomes . Decoding the received sequence, and its specific steps (taking the backtracking step size 1 as an example) are described as follows: Preprocessing: Under different signal-to-noise ratio (SNR) conditions, record multiple complete decoding processes, record the log-likelihood ratio of the target symbol at each window position at the last iteration, calculate the average value of the multiple decoding results, and substitute the log-likelihood ratio into the following formula to calculate the predicted bit error rate of the window at each position: (1), Set the above predicted bit error rate as the threshold. During the window decoding process based on backtracking, when the minimum number of iterations is reached, use the log-likelihood ratio of the window target symbol to compare with this threshold for determination. As Figure 1 shown, the specific steps of the method include: Step 1, receive the space-coupled low-density parity-check (SC-LDPC) codeword sequence. The construction process of the original protograph of the space-coupled low-density parity-check (SC-LDPC) code is as Figure 2 、 Figure 3 and Figure 4 shown. Figure 2 is the original protograph of the low-density parity-check (LDPC) code, C represents the check node, V represents the variable node, t is the position index, and B is the base matrix of the low-density parity-check (LDPC) code; Figure 3 is the edge expansion of the original protograph of the low-density parity-check (LDPC) code at position t, is the component base matrix of the low-density parity-check (LDPC) code; as Figure 4 shown, use the edge expansion method to space-couple the original protographs of L low-density parity-check (LDPC) codes to obtain the original protograph of the space-coupled low-density parity-check (SC-LDPC) code, and L is the coupling length. Set the corresponding parameters: such as the expansion factor M0, window size W, maximum number of iterations I max 、minimum number of iterations I min 、coupling length L and status value flag, and M0, W, I max 、I min 、L and flag are all positive integers.

[0034] Step 2, window initialization. When the window is located at the upper left corner of the parity-check matrix, initialize the side information of the decoding window based on the received sequence. The calculation of the initialization information is shown in formula (1), where represents the j-th variable node of the current window, represents the initialization information of the j-th variable node, represents the j-th variable node corresponding to the initial codeword sequence X in the parity-check matrix, represents the j-th variable node corresponding to the received sequence Y in the parity-check matrix, and P represents the calculation conditional probability formula. The initialization information calculation formula is: (2), Step 3, as Figure 5 shown, p represents the window position. After the window starts to slide, initialize the information in the lower-right corner area of the newly entered window as shown in formula (2). The information bit of the target symbol receives the output log-likelihood ratio LLR of the previous window. represents the edge information passed from the j-th variable node to the i-th check node: (3); Step 4, iterative decoding. Perform belief propagation decoding within the window. When the number of iterations of the current decoding window reaches the minimum number of iterations, calculate the predicted bit error rate of the target symbol at this time, and compare it with the threshold. If the predicted bit error rate is greater than the threshold, the status value is 1, otherwise it is 0; Step 5, if the status value is 0, then perform decoding decision. Calculate the output log-likelihood ratio of the target symbol after the end of this iteration through formula (4). represents the log-likelihood ratio output by the j-th variable node after l iterations. represents the set of check nodes connected to the variable node V j connected. represents the set of check nodes in the l-th iteration in the check node set and the variable node V j edge information. represents the hard decision output of as shown in formula (6). When the log-likelihood ratio is greater than or equal to 0, judge 0. When the log-likelihood ratio is less than 0, judge 1: (4), (5), When reaching the maximum number of iterations or meeting the parity check, stop the iteration within the current window and output the decision result; the window slides diagonally downward row and column, and then return to Step 3 to decode the next target symbol.

[0035] Step 6, if the status value is 1, then exit the decoding of the current window; under the condition of backtracking step 1, as Figure 6 shown, increase the decoding window size by 1 and slide it upward along the diagonal row and column and then decode. After completion of decoding, as Figure 7 shown, restore the original window size and slide it downward row and column and decode. After completion of decoding, change the status value 1 to 0; under the condition of backtracking step 2,Figure 8 As shown, increase the decoding window size by 2 and slide it diagonally upward rows and columns and then decode. After completion of decoding, continue decoding with the window size and window position as shown in Figure 9 , Figure 10 etc. After completion of decoding, change the status value 1 to 0; under the condition of a backtracking step size of 3, as shown in Figure 11 increase the decoding window size by 3 and slide it diagonally upward rows and columns and then decode. After completion of decoding, continue decoding with the window size and window position as shown in Figure 12 , Figure 13 and Figure 14 etc. After completion of decoding, change the status value 1 to 0.

[0036] Step 7: Repeat Steps 4 to 6 until the decoding window slides out of the matrix.

[0037] The simulation uses a codeword with a code length of 1200 and a code rate of 0.48, a coupling length L of 30, a coupling width w of 2, an expansion factor M0 of 20, a window size W of 4, a maximum number of iterations I max of 50, and a minimum number of iterations I min of 10. Under an additive white Gaussian noise channel, after binary phase shift keying modulation, on the matlab simulation platform.

[0038] As Figure 15 shown, at the same signal-to-noise ratio, the TB-SWD algorithm has an improvement in bit error rate performance compared with the existing SWD algorithm. The longer the backtracking step size of the TB-SWD algorithm, the lower the bit error rate. To achieve the BER performance, the signal-to-noise ratio of the SWD algorithm needs to be greater than 4.5 dB, the signal-to-noise ratio of the TB-SWD algorithm with a backtracking step size of 1 needs about 4.4 dB, the signal-to-noise ratio of the TB-SWD algorithm with a backtracking step size of 2 needs about 4.2 dB, and the signal-to-noise ratio of the TB-SWD algorithm with a backtracking step size of 3 needs about 4.05 dB. As Figure 16 shown, as the signal-to-noise ratio increases, the channel environment improves and the complexity decreases. At a signal-to-noise ratio of 3.5 dB, the complexities of the TB-SWD algorithms with backtracking step sizes of 1, 2, and 3 increase by about 12%, 16%, and 22% respectively compared with the existing SWD algorithm.

[0039] As Figure 17 shown, the lower the signal-to-noise ratio, the greater the backtracking rate, and the higher the signal-to-noise ratio, the lower the backtracking rate. The backtracking rate is greater when the backtracking step size is smaller because the improvement in the decoding performance of subsequent windows is smaller when the backtracking step size is smaller, so the backtracking rate will be slightly greater than that of the algorithm under the condition of a longer backtracking step size.

[0040] The present invention provides a decoding method for spatially coupled low-density parity-check codes based on backtracking. There are many methods and approaches to specifically implement this technical solution. The above description is only the preferred embodiment of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention. Each component not clearly defined in this embodiment can be implemented using existing technologies.

Claims

1. A decoding method for spatially coupled low-density parity-check codes based on backtracking, characterized in that It includes the following steps: Step 1, couple L original protographs of regular low-density parity-check (LDPC) codes with degree distribution ( l , r) to obtain a spatially-coupled low-density parity-check (SC-LDPC) code, where L is the coupling length, l is the degree of variable nodes, and r is the degree of check nodes; the original protograph of the regular LDPC code with degree distribution contains check nodes and variable nodes, where , , a represents the row of the base matrix of the LDPC code, b represents the column of the base matrix, represents and 's greatest common divisor; the encoded binary codeword is modulated and mapped into a symbol sequence, and then added with noise through the channel. The receiving end obtains the SC-LDPC codeword sequence as the input of the decoder; set the following parameters: expansion factor M0, window size W, maximum number of iterations I max , minimum number of iterations I min , coupling length L, and status value flag, and M0, W, I max , I min , L, and flag are all positive integers; Step 2: When the decoding window is located at the upper left corner of the parity-check matrix, initialize the side information for the decoding window based on the received sequence. Step 3: After the decoding window starts to slide, initialize the information in the lower right corner area of the newly entered window. The information bit of the target symbol receives the output log-likelihood ratio (LLR) of the previous window. Step 4, iterative decoding: Perform belief propagation decoding within the decoding window. When the number of iterations of the current decoding window reaches the minimum number of iterations I min make a determination, calculate the predicted bit error rate of the target symbol at this time, compare it with the threshold. If the predicted bit error rate is greater than the threshold, the state value is 1, otherwise it is 0; Step 5: If the state value is 0, calculate the output log-likelihood ratio (LLR) of the target symbol after the end of this iteration, perform decoding decision. When the decoding window completes the decoding of the current target symbol, output the decoding result of the target symbol, and the decoding window slides diagonally downward to perform the decoding of the next target symbol. Step 6: If the state value is 1, exit the decoding of the current window position p; expand the decoding window according to the backtracking step size and slide it diagonally upward for decoding. After completion of decoding, gradually shrink the decoding window and slide it diagonally downward for decoding until the decoding window returns to position p. After completion of decoding, change the state value 1 to 0. Step S7: Repeat Steps 4 to 6 until the decoding window slides out of the parity-check matrix.

2. The method according to claim 1, characterized in that, In Step 1, the expansion factor M0 means replacing 1 and 0 in the parity-check matrix with an identity circulant shift matrix of size M0×M0 and a all-zero matrix of size M0×M0 respectively. The coupling length L means that the spatially coupled low-density parity-check (SC-LDPC) code is constructed by replicating L single protographs.

3. The method according to claim 2, wherein Step 2 includes: Set the codeword sequence , where n is the code length, represents the first codeword bit of the initial codeword sequence. After binary phase shift keying modulation, it is transmitted over an additive white Gaussian noise channel, represents the received codeword sequence of the spatially coupled low-density parity-check (SC-LDPC) code, , represents the first codeword bit of the received codeword sequence; When the decoding window is located at the upper left corner of the parity-check matrix, the initialization of side information for the decoding window based on the received sequence is expressed as , where represents the j-th variable node in the current window, represents the received information initialized for the j-th variable node, represents the j-th variable node corresponding to the initial codeword sequence X in the parity-check matrix, represents the j-th variable node corresponding to the received codeword sequence Y in the parity-check matrix, and P represents the function for calculating the conditional probability.

4. The method according to claim 3, wherein In step 3, after the decoding window starts to slide, the information in the lower right corner area newly entering the window is initialized and represented as ; represents the edge information passed from the j-th variable node to the i-th check node.

5. The method according to claim 4, wherein Step 4 includes: Step 4-1: Initialize the channel information, initialize the variable nodes according to the characteristics of the given channel, and the information initialization formula: （1）， （2）； Step 4-2: Update the check nodes: （3）， Among them, represents the information passed from the \(i\)-th check node to the \(j\)-th variable node at the \(l\)-th iteration, represents the set of variable nodes connected to the check node except for the variable node , where tanh is the hyperbolic tangent function and arctanh is the inverse function of tanh; represents the information passed from the variable node to the check node at the \((l - 1)\)-th iteration; Step 4-3: Update the variable nodes: （4）， Among them, ; represents the set of check nodes connected to the variable node except for the check node ; Step 4-4: Update the posterior probability; Step 4-5: Decoding decision.

6. The method according to claim 5, characterized in that, Step 4-4 includes: Update each value of the received signal for the next decision, and the update formula is: （5）， Among them, represents the variable node the log-likelihood ratio LLR output after the l-th iteration, represents the set of check nodes connected to the variable node and the check node is a check node belonging to this set, represents the information passed by the check node to the variable node at the l-th iteration.

7. The method according to claim 6, wherein Step 4-5 includes: making a decision on each bit of the received signal according to 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 , is the parity-check matrix, and the superscript represents transposing the matrix; the other is reaching the maximum number of iterations I max ; when either of the conditions for ending the iteration is satisfied, the decision result is output. Otherwise, repeat steps 4-2 to 4-4. The formula is: （6）， Among them represents the hard decision output of .

8. The method according to claim 7, wherein In Step 4, the calculation of the predicted bit error rate of the current target symbol includes: calculating the predicted bit error rate through the log-likelihood ratio of the target symbol: （7）， Among them, is the coupling factor, represents the predicted bit error rate, and exp represents the natural exponential function.

9. An electronic device, characterized in that, It includes a processor and a memory. The memory stores program codes. When the program codes are executed by the processor, the processor is caused to execute the steps of the method according to any one of claims 1 to 8.

10. A storage medium, characterized in that, Stores a computer program or instruction. When the computer program or instruction runs on a computer, it executes the steps of the method according to any one of claims 1 to 8.

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