Soft output based stack decoding method, system, device, medium and terminal

Abstract

The application belongs to the technical field of communication, and discloses a stack decoding method, system, device, medium and terminal based on a soft output, which comprises the following steps: creating a structure and a stack and initializing; repeatedly judging the size of the path length in the structure at the top of the stack and the depth of a decoding tree, if the path length in the structure at the top of the stack is smaller than the depth of the decoding tree, recalculating the path metric, and sorting the stack according to the size of the path metric until the path length in the structure at the top of the stack is equal to the depth of the decoding tree, and counting the soft output probability of each decoding result; and correcting the decoding result according to a preset threshold to obtain a final decoding result. The method disclosed by the application can effectively reduce the calculation complexity under the premise of a low signal-to-noise ratio. In the case of (128, 64), compared with the traditional stack decoding, the stack decoding method of the polar adjustment convolution code based on the soft output can reduce the calculation amount by 82%.

Description

Technical Field

[0001] This invention belongs to the field of communication technology, and particularly relates to a stack decoding method, system, device, medium and terminal based on soft output. Background Technology

[0002] Erdal Arikan's polar codes represent a theoretical breakthrough. Polar codes offer advantages such as clear construction methods, low encoding and decoding complexity, and the ability to rigorously prove their close approximation to channel capacity. However, with finite code lengths, some information bits cannot be correctly decoded due to incomplete channel polarization. To address this issue, Serial Cancellation List (SCL) decoding was first proposed, reducing the bit error rate by increasing the number of candidate paths allowed to be retained after each path search layer. To further improve the error correction capability of the decoding algorithm, Cyclic Redundancy Check (CRC) is added to the information sequence, and the optimal decoding path is output by selecting the search path for SCL decoding. CRC-assisted Serial Cancellation List (CA-SCL) decoding significantly improves the performance of polar codes.

[0003] Arikan proposed a novel scheme that shifts the error correction component to the outer code for encoding. This new scheme, called Polar Adjusted Convolutional (PAC) coding, uses outer convolutional coding blocks for encoding and transmits them through polar channels. Compared to CRC-assisted polar codes, PAC coding offers better error correction capabilities. Since the outer convolutional code decoding part of PAC decoding is an irregular tree during the decoding process, it is more suitable for long-constrained sequence decoding than Viterbi decoding. Moradi et al. also proposed PAC decoding based on Fano decoding.

[0004] The main decoding method for PAC is sequential decoding of convolutional codes, which is mainly divided into two categories: stack decoding and Fano decoding. Currently, research on PAC mainly focuses on Fano decoding. There are almost no reports on research on stack decoding.

[0005] Based on the above analysis, the problems and shortcomings of the existing technology are as follows:

[0006] Existing PAC methods have limited research on stack decoding. 。 While PAC-based Fano decoding does not require storage, its decoding speed is relatively slow. Summary of the Invention

[0007] In view of the problems existing in the prior art, the present invention provides a stack decoding method, system, device, medium and terminal based on soft output.

[0008] This invention is implemented as follows: a stacked decoding method for soft-output polarization-adjusted convolutional codes (SOSD-PAC), wherein the stacked decoding method for soft-output polarization-adjusted convolutional codes includes:

[0009] Create and initialize the structure and stack; determine the path length in the structure at the top of the stack and the depth of the decoding tree; if the path length in the structure at the top of the stack is less than the depth of the decoding tree, recalculate the path metric and sort the stack according to the path metric until the path length in the structure at the top of the stack is equal to the depth of the decoding tree; calculate the soft output probability of each decoding result; correct the decoding result according to a preset threshold to obtain the final decoding result.

[0010] Furthermore, the structure is used to store the corresponding path, current node, path metric, and status bit; the root node structure of the decoding tree is stored in the stack, and decoding begins.

[0011] Furthermore, when the path length in the structure at the top of the stack is less than the depth of the decoding tree, it is determined whether the next node of the structure at the top of the stack is in index set A;

[0012] If the next node is in A, then remove the structure at the top of the stack from the stack and expand it into two subsequent nodes, calculate the path metric in the two subsequent nodes, and store the two subsequent nodes in the node;

[0013] If the next node is not in A, the path in the structure at the top of the stack is extended backward, and the path metric is recalculated based on the extended path.

[0014] Furthermore, after the two subsequent nodes are stored in the node, it is determined whether there is an overflow in the stack. If so, the structure at the bottom of the stack is removed from the stack and stored in an external container.

[0015] Furthermore, when the path length in the structure at the top of the stack is equal to the depth of the decoding tree, the path information in the stack is statistically analyzed, and the formula for calculating the soft output probability is:

[0016]

[0017]

[0018] In the formula, This represents the decoding result of node j. This represents the probability that the decoding result of node j is 0. This represents the probability that the decoding result of node j is 1.

[0019] Furthermore, the specific process of correcting the decoding result using the preset threshold is as follows:

[0020] If the soft output probability is greater than a preset threshold t, the decoding result is determined based on the soft output probability result; otherwise, the result of the stack top path is used for judgment. The expression is:

[0021]

[0022] Another object of the present invention is to provide a stack decoding system for soft-output polar-adjusted convolutional codes, which implements the aforementioned stack decoding method for soft-output polar-adjusted convolutional codes, the stack decoding system comprising:

[0023] The initialization module is used to create and initialize structures and stacks;

[0024] The decoding module is used to decode based on the path length and the depth of the decoding tree in the structure at the top of the stack.

[0025] The correction module is used to correct the decoding result according to a preset threshold to obtain the final decoding result.

[0026] Another object of the present invention is to provide a computer device including a memory and a processor, the memory storing a computer program that, when executed by the processor, causes the processor to perform the steps of the stack decoding method for polarization-adjusted convolutional codes based on soft output.

[0027] Another object of the present invention is to provide a computer-readable storage medium storing a computer program that, when executed by a processor, causes the processor to perform the steps of the stack decoding method for polarization-adjusted convolutional codes based on soft output.

[0028] Another object of the present invention is to provide an information data processing terminal for implementing the stack decoding system based on soft-output polarization-adjusted convolutional codes.

[0029] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by this invention are as follows:

[0030] First, addressing the technical problems existing in the prior art and the difficulty in solving them, this paper closely analyzes, in conjunction with the technical solution to be protected by this invention and the results and data obtained during the research and development process, how the technical solution of this invention solves the technical problems, and the inventive technical effects brought about by solving these problems. The specific description is as follows:

[0031] This invention relates to SOSD-PAC decoding. Based on the SD algorithm, a new decoding result judgment method is defined. By limiting the stack size and retaining discarded path information, the decoding result is modified, reducing decoding complexity while sacrificing a certain bit error rate. Simulation results show that SOSD-PAC decoding is more efficient than SD decoding of PAC. By carefully selecting the stack size S and threshold t, the proposed soft-output stack decoder exhibits similar FER performance to the stack decoder. The results demonstrate that the proposed method achieves a good trade-off between decoding performance and complexity compared to PAC stack decoding. For PAC codes with a code length of 128 and a code rate of 1 / 2, the SOSD algorithm reduces computation by 82% compared to the traditional SD algorithm.

[0032] Second, considering the technical solution as a whole or from a product perspective, the technical effects and advantages of the technical solution to be protected by this invention are specifically described as follows:

[0033] This invention reduces decoding complexity while sacrificing a certain bit error rate, and is more efficient than PAC's SD decoding, achieving a good trade-off between decoding performance and complexity.

[0034] Third, as supplementary evidence of the inventive step of the claims of this invention, it is also reflected in the following important aspects:

[0035] The technical solution of this invention verifies the feasibility of stack decoding by using a stack decoding method that is rarely used in external decoding schemes. This provides technical support for optimizing stack decoding to improve PAC decoding and overcomes the common misconception that stack decoding has low application scenarios. Attached Figure Description

[0036] Figure 1 This is a flowchart of the stack decoding process provided in an embodiment of the present invention;

[0037] Figure 2 This is a schematic diagram of path elimination and statistical soft output probability in the stack provided in the embodiment of the present invention. (a) Path diagram of two new paths entering the stack, (b) Stack path diagram after eliminating bad paths, and (c) Statistical diagram of path decoding when bad paths are not eliminated.

[0038] Figure 3 This is a diagram of the PAC encoding and decoding process provided in an embodiment of the present invention;

[0039] Figure 4 This is a performance curve diagram on the BIAWGN channel provided in an embodiment of the present invention;

[0040] Figure 5This is a pseudocode diagram of the stack decoding method for polarization-adjusted convolutional codes based on soft output provided in an embodiment of the present invention;

[0041] Figure 6 This is a comparison chart of bit error rate curves for different stack sizes S and soft output t provided in the embodiments of the present invention;

[0042] Figure 7 This is a curve comparison chart of the number of paths S and the soft output probability t generated during the decoding process of different stacks in the case of 100,000 frames, provided by an embodiment of the present invention. Detailed Implementation

[0043] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0044] To enable those skilled in the art to fully understand how the present invention is specifically implemented, this section provides an explanatory description of the embodiments that expand upon the technical solutions of the claims.

[0045] Stack decoding is a type of sequential decoding. Stack decoding stores paths into a stack in descending order of path metrics. During each decoding process, the top path of the stack is removed and split into two new paths. These two new paths are then inserted into the stack, and their metrics are calculated. Next, the stack is reordered according to the path metrics. Finally, the above operations are repeated until the top path in the stack reaches the end of the decoding tree, completing the decoding process. The decoding process is as follows: Figure 1 As shown.

[0046] As can be seen from the stack decoding process above, the best path at the top of the stack is expanded during each decoding process. When the stack capacity is limited, the worst path at the bottom of the stack is discarded. Soft output records the discarded paths, and this invention aims to explore some valuable information from these discarded paths.

[0047] Figure 2 This is a program for calculating the soft output probability, as demonstrated in an embodiment of the present invention. Figure 2 In (a), two new paths are added to the stack, their metrics are calculated, and the paths in the stack are reordered. Paths marked with dashed lines represent bad paths to be removed from the stack. For example... Figure 2 As shown in (b), this figure represents the stack after bad paths have been eliminated. Figure 2 (c) is the statistics of the path branches stored in the stack, which is the same as the statistics of (a).

[0048] When introducing a soft-output probability calculation procedure, it is necessary to determine the amount of valid information present at the current node i, for example, in Figure 2 In (c), i=2 has 4 valid pieces of information. Then, the valid information is converted into probabilities using formulas (1) and (2), and the decoding result of the current node is determined based on the probabilities.

[0049]

[0050]

[0051] This invention provides a brief overview of PAC codes. Regardless of whether the error correction part is placed in the outer code, PAC codes still require polarization before polarization encoding. The block length n of PAC codes is similar to that of polarization codes, also a power of 2, such as... Figure 3 As shown, the PAC encoding process is divided into three parts.

[0052] The first part is rate profiling. In this part, the embodiments of the present invention need to determine the index set A, which is crucial for the good performance of PAC decoding. Arikan proposed using RM rate analysis, that is, using Hamming weights to determine the binary spread of the channel and extracting the top k largest values ​​to form the index set A. Next, the source word d of length k is inserted into the data carrier vector v of length n using formula (3).

[0053]

[0054] The second step is to perform convolutional code precoding. Similar to traditional convolutional coding, convolution is performed using impulse responses, where c = (c0, c1, ..., c...). n ),c0≠0,c n ≠0. Using the vector v obtained in the previous step, the output vector u is obtained through formula (4).

[0055]

[0056] Unlike convolutional codes, PAC codes are not generated as an irregular tree during the encoding process. Splitting operations are only performed when the current tree node contains information bits.

[0057] Finally, in the polarization encoding stage of the PAC code, the encoding method is consistent with that of the polar code encoding. and It becomes an N*N matrix. The output vector x is obtained by formula (5), where the polarization generation matrix is... and B N It is a bit inverse permutation matrix.

[0058]

[0059] PAC stack decoding is similar to stack algorithms, the main difference being the style of the decoding tree. PAC decoding generates an irregular tree, so the following corrections are needed during the decoding splitting stage: First, extract the top of the stack path and remove it from the stack. Then, determine whether the next node is in index set A. If it is in A, split it into two new paths; otherwise, split it into two new paths. c In the middle, the path is not split, but expanded along the nodes.

[0060] It is important to note that the calculation method for the PAC decoding path metric differs from that for the convolutional code path metric. First, the current path needs to be substituted into the polar code, and then the log-likelihood ratio (LLR)z is calculated according to formula (6). j .

[0061]

[0062] Then z j The stack decoder passed to the PAC calculates the metric of the current path according to formula (7).

[0063]

[0064] PAC's stack decoding can preserve the path of each segment and select the best path possible, thus approaching Shannon capacity. However, at low signal-to-noise ratios, memory limits the stack size, leading to stack overflow and increasing the bit error rate.

[0065] Figure 4 The frame error rate (FER) is shown for Polar code SC decoding, PAC Fano decoding, and PAC stack decoding, where the signal is BPSK modulated and transmitted through a white Gaussian noise (AWGN) channel. It can be observed that when the stack is large enough, the FER of PAC stack decoding is comparable to that of PAC Fano decoding.

[0066] like Figure 5 As shown, the SOSD-PAC decoding method based on soft-output polarization-adjusted convolutional codes provided in this embodiment of the invention is obtained by improving the stack decoding of PAC. The specific process is as follows:

[0067] First, this invention defines a structure to store the corresponding path, current node, path metric, and state bit. Then, a stack is created and its size is limited. A structure is created based on the root node of the decoding tree, stored in the stack, and decoding begins.

[0068] If the path length in the structure at the top of the stack is less than the depth of the decoding tree, this invention needs to determine whether the next node of this structure is in index set A. If the next node is in A, the structure at the top of the stack is removed from the stack and expanded into two subsequent nodes. The path metric in these two nodes is calculated, and then these two modules are stored in the nodes. After storage, it is necessary to determine whether there is an overflow in the stack. If so, the structure at the bottom of the stack is removed from the stack and stored in an external container. If the next node of the structure is not in A, then the path in the structure at the top of the stack is extended directly backward, and the path metric is recalculated based on the extended path. After sorting the stack according to the path metric size, the above steps are repeated.

[0069] When the path length in the top structure of the stack is equal to the depth of the decoding tree, the path information in the stack is counted, and the counted information and the information in the outer container are substituted into formulas (1) and (2) to convert them into corresponding probabilities. Then, the final decoding result is obtained by judging according to formula (8).

[0070]

[0071] This invention also provides a stacked decoding system for polarization-adjusted convolutional codes based on soft output, comprising:

[0072] The initialization module is used to create and initialize structures and stacks;

[0073] The decoding module is used to decode based on the path length and the depth of the decoding tree in the structure at the top of the stack.

[0074] The correction module is used to correct the decoding result according to a preset threshold to obtain the final decoding result.

[0075] To demonstrate the inventiveness and technical value of the technical solution of this invention, this section provides specific product or related technology application examples of the technical solution claimed.

[0076] The stack decoding method of polarization-adjusted convolutional codes based on soft output provided in the application embodiment of the present invention is applied to signal transmission, which is used to realize intermediate processes such as optical communication and encrypted communication.

[0077] The stack decoding method for polarization-adjusted convolutional codes based on soft output provided in the application embodiment of the present invention is applied to a computer device, the computer device including a memory and a processor, the memory storing a computer program, and when the computer program is executed by the processor, the processor performs the steps of the stack decoding method for polarization-adjusted convolutional codes based on soft output.

[0078] The stack decoding method of polarization-adjusted convolutional codes based on soft output provided in the application embodiment of the present invention is applied to an information data processing terminal, which is used to implement the stack decoding system of polarization-adjusted convolutional codes based on soft output.

[0079] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0080] The embodiments of the present invention have achieved some positive effects during the research and development or use process, such as... Figure 4 As shown, compared with existing PAC based on Fano decoding, the bit error rate is similar, but the decoding efficiency is higher. The following content describes the experimental process with data, charts, etc.

[0081] Next, this embodiment of the invention provides a simple analysis of the complexity of SOSD-PAC decoding. The branches of the PAC decoding tree are generated by information bit nodes, and this embodiment of the invention assumes that L is the height of the decoding tree. The decoding process from the root node to the leaf node doubles the path each time it passes through an information bit node, until the end of L, resulting in a total of many paths.

[0082] On the one hand, limiting the stack size is equivalent to deleting all sub-decoding trees rooted at the current path, thus reducing the number of decisions and improving speed. Secondly, soft-output statistics are only recorded during access, and the overhead is negligible. The actual number of paths in SOSD-PAC decoding is affected by factors such as signal-to-noise ratio and code rate, making it difficult to provide a mathematical description. Through simulation, this invention obtains the actual number of accessed paths.

[0083] This invention compares the performance and complexity of PAC codes under standard stack decoding and soft-output-based stack decoding algorithms. Consider a binary input additive white Gaussian noise (BIAWGN) channel with frame size N = 128, code rate R = 0.5, and impulse response c = (1,0,1,1,0,1,1).

[0084] First, the size of the stack S needs to be considered. If S is too small, a large number of paths will be removed when the signal-to-noise ratio is low, affecting the bit error rate. If it is too large, a large number of bad paths will be retained, which not only wastes memory but also increases the complexity of decoding. Second, the impact of the soft output threshold t on the bit error rate also needs to be considered. If the threshold t is too large or too small, it cannot be effectively judged.

[0085] Figure 5 and Figure 6 The comparison of bit error rate and complexity with a traditional stack is shown under different stack sizes S and soft output threshold t. By limiting the stack size and retaining some information about the stack algorithm, a 90% gain can be achieved at low signal-to-noise ratios. However, as the signal-to-noise ratio increases, the gain gradually decreases when the bit error rate remains relatively consistent.

[0086] This invention proposes a SOSD-PAC decoding method. Based on this, a new decoding result judgment method is defined. By limiting the stack size and retaining discarded path information, the decoding result is modified, reducing decoding complexity while sacrificing a certain bit error rate. Simulation results show that SOSD-PAC decoding is more efficient than PAC stack decoding. By carefully selecting the stack size S and threshold t, the proposed soft-output stack decoder achieves similar FER performance to the stack decoder; compared to PAC stack decoding, the proposed method achieves a good trade-off between decoding performance and complexity.

[0087] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A stacked decoding method for polarization-adjusted convolutional codes based on soft output, characterized in that, Its input is: the received vector y is obtained through a binary input additive white Gaussian noise (BIAWGN) channel, index set A, and the output is: the decoded codeword; the method specifically includes: S1, Create a structure and a stack, the structure is used to store the corresponding path, current node, path metric and status bit, and initialize it; put the root node structure of the decoding tree into the stack, and start decoding; S2, when the path length in the stack top structure is less than the decoding tree depth, calculate the path log-likelihood ratio (LLR) in the stack item structure; remove the stack top structure from the stack and store it in a temporary container; S3, if the current node in the stack top structure ∈ A, then expand the path to 0 according to the temporary container path; otherwise, expand to 0 and 1 respectively according to the temporary container path. S4, calculate the path metric; store the structure corresponding to the path in a stack; if the stack overflows, store the structure in the container sdp at the bottom of the stack, and then remove it from the stack; the stack is sorted by path metric. S5: Obtain the corresponding probabilities through the statistical information of the paths in the stack and SDP, and then use these probabilities to obtain the decoding result; When the path length in the structure at the top of the stack is equal to the depth of the decoding tree, the path information in the stack is statistically analyzed, and the formula for calculating the soft output probability is: ； ； In the formula, This represents the decoding result of node j. This represents the probability that the decoding result of node j is 0. This represents the probability that the decoding result of node j is 1; The specific process of correcting the decoding result using the preset threshold is as follows: If the soft output probability is greater than the preset threshold t, the decoding result is determined based on the soft output probability result; otherwise, the result of the top stack path is used for judgment. The expression is: 。 2. The stacked decoding method for polarization-adjusted convolutional codes based on soft output as described in claim 1, characterized in that, When the path length in the structure at the top of the stack is less than the depth of the decoding tree, determine whether the next node of the structure at the top of the stack is in index set A; If the next node is in A, then remove the structure at the top of the stack from the stack and expand it into two subsequent nodes, calculate the path metric in the two subsequent nodes, and store the two subsequent nodes into the stack; If the next node is not in A, the path in the structure at the top of the stack is extended backward, and the path metric is recalculated based on the extended path.

3. The stacked decoding method for polarization-adjusted convolutional codes based on soft output as described in claim 2, characterized in that, After the two subsequent nodes are stored in the stack, it is determined whether there is an overflow in the stack. If there is, the structure at the bottom of the stack is removed from the stack and stored in an external container. If there is no overflow, the stack is sorted by path metric and the loop restarts.

4. A stack decoding system for soft-output polar-adjusted convolutional codes, implementing the stack decoding method for soft-output polar-adjusted convolutional codes as described in any one of claims 1-3, characterized in that, The stacked decoding system based on soft-output polarization-adjusted convolutional codes includes: The initialization module is used to create and initialize structures and stacks; The decoding module is used to decode based on the path length and the depth of the decoding tree in the structure at the top of the stack. The correction module is used to correct the decoding result according to a preset threshold to obtain the final decoding result.

5. A computer device, characterized in that, The computer device includes a memory and a processor. The memory stores a computer program that, when executed by the processor, causes the processor to perform the steps of the stack decoding method for polarization-adjusted convolutional codes based on soft output as described in any one of claims 1-3.

6. A computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the stack decoding method for polarization-adjusted convolutional codes based on soft output as described in any one of claims 1-3.

7. An information data processing terminal, characterized in that, The information data processing terminal is used to implement the stack decoding system for polarization-adjusted convolutional codes based on soft output as described in claim 4.

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