A joint decoding method based on BPL decoding and OSD decoding

Abstract

The application discloses a joint decoding method based on BPL decoding and OSD decoding, comprising the following steps: step 10, initializing decoding parameters; step 20, initializing each factor graph to obtain L initialized factor graphs; step 30, performing BPL decoding based on the L initialized factor graphs to obtain a first decoding result; step 40, calculating a target received sequence according to the first decoding result and an original LLR received sequence output by a channel; step 50, calculating a generating matrix for OSD decoding according to a CRC generating matrix and an original generating matrix of a polar code; and step 60, performing OSD decoding according to the target received sequence and the generating matrix for OSD decoding to obtain a second decoding result. By using the result after BPL decoding as an input sequence of OSD decoding, the OSD decoder can obtain a more reliable received sequence, and the OSD decoding error performance is effectively improved.

Description

Technical Field

[0001] This invention belongs to the field of channel coding technology, specifically relating to a joint decoding method based on BPL decoding and OSD decoding. Background Technology

[0002] Polar codes, as the first coding scheme that can be rigorously proven to meet the capacity limit, not only have excellent error rate performance but also low encoding and decoding complexity, and were therefore selected as the coding scheme for the control channel in the eMBB scenario of the 5G standard.

[0003] Currently, polar code decoding algorithms are mainly divided into two categories: serial decoding algorithms and parallel decoding algorithms. Serial decoding algorithms mainly include SC decoding and its enhanced version, SCL decoding. Parallel decoding algorithms mainly include Belief Propagation (BP) decoding and Belief Propagation List (BPL) decoding. BPL decoding, benefiting from its parallel decoding structure, has high parallelism and can achieve high throughput and low latency. In addition, Ordered Statistical Decoding (OSD) is also a soft-decision decoding algorithm. Its decoding performance is close to that of Machine Learning (ML), and it can perform parallel decoding. When the code length is short (N≤64), OSD decoding performance is close to ML decoding. When the code length is long, OSD decoding has higher complexity and is generally only suitable for short code decoding.

[0004] Backpropagation (BP) decoding can be performed in parallel, but its error rate performance at high signal-to-noise ratios is poor, and it suffers from error layering. BPL decoding can improve the error rate performance of BP decoding to some extent, but its performance is still inferior to SCL decoding. The performance of OSD decoding is related to its order; higher-order OSD decoding achieves better error rate performance, but its complexity is higher, making it unsuitable for long code lengths, while lower-order OSD decoding performs poorly. Summary of the Invention

[0005] To address the aforementioned problems in the existing technology, this invention provides a joint decoding method based on BPL decoding and OSD decoding. The technical problem to be solved by this invention is achieved through the following technical solution: A joint decoding method based on BPL decoding and OSD decoding includes the following steps: Step 10: Initialize the decoding parameters; Step 20: Initialize each factor graph to obtain... Initialized factor graph; Indicates the number of lists in the BPL decoding; Step 30, based on the above The initial factor graph is BPL decoded to obtain the first decoding result; Step 40: Calculate the target received sequence based on the first decoding result and the original LLR received sequence output by the channel; Step 50: Calculate the generator matrix for OSD decoding based on the CRC generator matrix and the original generator matrix of the polar code; Step 60: Perform OSD decoding based on the target received sequence and the generator matrix used for OSD decoding to obtain the second decoding result.

[0006] In one embodiment of the present invention, the decoding parameters include: the code length of the polar code. The length of the CRC, the CRC generator polynomial, and the number of lists in the BPL decoding. Maximum number of iterations The order of OSD decoding .

[0007] In one embodiment of the present invention, step 20 includes: Step 21: For any factor graph, initialize the value of the soft information passed to the left of the rightmost node of the factor graph; Step 22: For any factor graph, initialize the value of the soft information passed to the right of the node corresponding to the leftmost frozen position of the factor graph; Step 23: Initialize the values ​​of the soft information passed to the left and the soft information passed to the right for any other node in the factor graph to 0; Step 24, initialization complete. Initialization factor graph.

[0008] In one embodiment of the present invention, the value of the soft information passed to the left by the rightmost node of the initialized factor graph in step 21 is: ; In this context, any node in the factor graph is... , i Indicates the column number where the node is located. , j Indicates the row number where the node is located. Indicates the first j bits, This represents the transition probability.

[0009] In one embodiment of the present invention, the value of the soft information passed to the right of the node corresponding to the leftmost frozen position of the initialized factor graph in step 22 is: ; in, A set of information bit indices. This represents the set of frozen bit indices.

[0010] In one embodiment of the present invention, the calculation formula for the target received sequence is: ; in, This indicates the number of lists in the BPL decoding list. Indicates the order of OSD decoding. This indicates the first decoding result. This represents the original LLR receive sequence output by the channel.

[0011] In one embodiment of the present invention, the formula for calculating the generator matrix used for OSD decoding is as follows: ; in, Represents the CRC generation matrix. , Represents the identity matrix, matrix The Rows through the identity matrix The first in The rows are generated using CRC encoding. The original generator matrix of polar codes The rows corresponding to the information bits in the middle are composed.

[0012] The beneficial effects of this invention are: This invention uses the processed result of BPL decoding as the input sequence for OSD decoding, which enables the OSD decoder to obtain a more reliable received sequence and effectively improves the error performance of low-order OSD decoding. Therefore, when the code length is long, using low-order OSD decoding can achieve better decoding performance, thus improving the performance of OSD decoding.

[0013] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0014] Figure 1 A flowchart illustrating a joint decoding method based on BPL decoding and OSD decoding provided in an embodiment of the present invention; Figure 2 A schematic diagram of a factor graph provided for an embodiment of the present invention; Figure 3 A schematic diagram of a basic butterfly-shaped arithmetic unit provided in an embodiment of the present invention; Figure 4A schematic diagram of the decoding process of a joint decoding method based on BPL decoding and OSD decoding provided for an embodiment of the present invention; Figure 5 This is a performance comparison chart of the simulation results of the existing technology and the method of the present invention in Simulation 1; Figure 6 This is a performance comparison chart of the simulation results of existing technologies and the method of this invention in Simulation 2. Detailed Implementation

[0015] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0016] like Figure 1 As shown, a joint decoding method based on BPL decoding and OSD decoding includes the following steps: Step 10, initialize decoding parameters; decoding parameters include: the code length of the polar code. The length of the CRC, the CRC generator polynomial, and the number of lists in the BPL decoding. Maximum number of iterations The order of OSD decoding .

[0017] Step 20, for Each factor graph of the factor graphs is initialized to obtain... An initialization factor diagram. The factor diagram is the permutation factor diagram used during BPL decoding of polar codes, for a code length of... The polar code has the following number of nodes: ,in .by Taking a factor graph as an example, the factor graph is as follows: Figure 2 As shown. Each basic butterfly operation unit in the factor graph contains a variable node and a check node, used to complete the calculation and transmission of soft information, such as... Figure 3 As shown. Among them. and Representing nodes respectively Soft information passed to the left and soft information passed to the right, i Indicates the column number where the node is located. , j Indicates the row number where the node is located. Specifically, step 20 includes steps 21-24: Step 21: For any factor graph, initialize the leftward soft information value of the rightmost node of the factor graph to the value corresponding to the original LLR (Log Likelihood Ratio) received sequence of the channel output. The initialized leftward soft information value of the rightmost node of the factor graph is: ; in, Indicates the first j bits, This represents the transition probability.

[0018] Step 22: For any factor graph, initialize the soft information passed to the right of the node corresponding to the leftmost frozen position in the factor graph. The initialized soft information passed to the right of the node corresponding to the leftmost frozen position in the factor graph is as follows: ; in, A set of information bit indices. This represents the set of frozen bit indices.

[0019] Step 23: Initialize the values ​​of the soft information passed to the left and the soft information passed to the right for any other node in the factor graph to 0; Step 24, initialization complete. Initialization factor graph.

[0020] Step 30, based on The initial factor graph is BPL decoded to obtain the first decoding result; Step 40: Calculate the target received sequence based on the first decoding result and the original LLR received sequence output by the channel. Specifically, the formula for calculating the target received sequence is: ; in, This indicates the first decoding result. This represents the original LLR receive sequence output by the channel. The calculation formula is: .

[0021] In this step, The BP decoding results are integrated into an optimal result, which serves as the input sequence (target received sequence) for OSD decoding. To obtain this optimal input sequence, reliable soft information in the BPL decoding results is filtered out as much as possible, while unreliable soft information is removed. This is achieved by averaging the bit-by-bit values ​​of the BPL decoding results and the received sequence LLR. The target received sequence serves as the input sequence for OSD decoding, enabling the OSD decoder to obtain a more reliable received sequence.

[0022] Step 50: Calculate the generator matrix for OSD decoding based on the CRC (Cyclic Redundancy Check) generator matrix and the original generator matrix of the polar code; the generator matrix for OSD decoding can be obtained based on the polar code codeword generation relationship of the concatenated CRC. The calculation formula is: ; in, Represents the CRC generation matrix. , Represents the identity matrix, matrix The Rows through the identity matrix The first in The rows are generated using CRC encoding. The original generator matrix of polar codes The rows corresponding to the information bits in the middle are composed.

[0023] For example, if the codeword length is 3 and the CRC length is 2, the generator polynomial is: Then the CRC generation matrix is: .

[0024] The original generator matrix of polar codes The information bits in the middle are composed of rows. Polar codes can be composed of quadruplets. It is confirmed that, among them, It's the code length. This represents the length of the information bits, and also the dimension of the coding subspace. For encoding bitrate, A set of information bit indices, also known as an information set. For frozen bits. Original generator matrix. Can be made by Ar Kan kernel matrix Obtained recursively through the Kronecker product.

[0025] by Taking the polar code as an example, the original generator matrix of the polar code is as follows:

[0026] but .

[0027] at this time for: .

[0028] Step 60: Perform OSD decoding based on the target received sequence and the generator matrix used for OSD decoding to obtain the second decoding result.

[0029] For example, the decoding process of the joint decoding method in this embodiment is as follows: Figure 4 As shown, the code for the joint decoding method is as follows:

[0030] In this embodiment, by using the processed result of BPL decoding as the input sequence for OSD decoding, the OSD decoder can obtain a more reliable received sequence. When the code length is long, it can effectively improve the error performance of low-order OSD decoding. Therefore, when the code length is long, low-order OSD decoding can achieve better decoding performance, thus improving the performance of OSD decoding.

[0031] To verify the effectiveness and superiority of this algorithm, simulation experiments were conducted. Simulation performance of traditional BPL decoding algorithm and OSD decoding algorithm performed separately was also presented for comparison.

[0032] Simulation 1: In the simulation: the channel is an AWGN channel, and the modulation scheme is BPSK modulation. The polar code length used is... , The CRC length is 6, and the construction method is 5G. The number of lists in BPL decoding... Maximum number of iterations The simulation results are as follows: Figure 5 As shown, by combining BPL decoding and OSD decoding, the block error rate is significantly reduced compared to decoding either one separately, and the performance is greatly improved.

[0033] Simulation 2 Considering the case of longer code lengths, BPSK modulation is used in AWGN channels, and the code length is [not specified]. , The CRC length is 10, and the 5G construction method was used in the simulation. The number of lists in the BPL decoding... Maximum number of iterations The simulation results are as follows: Figure 6 As shown, even with longer code lengths, the joint decoding method of this invention can still bring significant performance improvements.

[0034] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0035] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0036] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A joint decoding method based on BPL decoding and OSD decoding, characterized in that, Includes the following steps: Step 10: Initialize the decoding parameters; Step 20: Initialize each factor graph to obtain... Initialized factor graph; Indicates the number of lists in the BPL decoding; Step 30, based on the above The initial factor graph is BPL decoded to obtain the first decoding result; Step 40: Calculate the target received sequence based on the first decoding result and the original LLR received sequence output by the channel; Step 50: Calculate the generator matrix for OSD decoding based on the CRC generator matrix and the original generator matrix of the polar code; Step 60: Perform OSD decoding based on the target received sequence and the generator matrix used for OSD decoding to obtain the second decoding result; The decoding parameters include: the code length of the polar code. The length of the CRC, the CRC generator polynomial, and the number of lists in the BPL decoding. Maximum number of iterations The order of OSD decoding ; The formula for calculating the target received sequence is: ； in, This indicates the number of lists in the BPL decoding list. Indicates the order of OSD decoding. This indicates the first decoding result. This represents the original LLR receive sequence output by the channel.

2. The joint decoding method based on BPL decoding and OSD decoding according to claim 1, characterized in that, Step 20 includes: Step 21: For any factor graph, initialize the value of the soft information passed to the left of the rightmost node of the factor graph; Step 22: For any factor graph, initialize the value of the soft information passed to the right of the node corresponding to the leftmost frozen position of the factor graph; Step 23: Initialize the values ​​of the soft information passed to the left and the soft information passed to the right for any other node in the factor graph to 0; Step 24, initialization complete. Initialization factor graph.

3. The joint decoding method based on BPL decoding and OSD decoding according to claim 2, characterized in that, The value of the soft information passed to the left by the rightmost node of the initialized factor graph in step 21 is: ； In this context, any node in the factor graph is... , i Indicates the column number where the node is located. , j Indicates the row number where the node is located. Indicates the first j bits, This represents the transition probability.

4. The joint decoding method based on BPL decoding and OSD decoding according to claim 2, characterized in that, The soft information passed to the right by the node corresponding to the leftmost frozen position in the initialized factor graph in step 22 is: ； in, A set of information bit indices. This represents the set of frozen bit indices.

5. The joint decoding method based on BPL decoding and OSD decoding according to claim 1, characterized in that, The formula for calculating the generator matrix used for OSD decoding is as follows: ； in, Represents the CRC generation matrix. , Represents the identity matrix, matrix The Rows through the identity matrix The first in The rows are generated using CRC encoding. The original generator matrix of polar codes The rows corresponding to the information bits in the middle are composed.

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