A multi-ary LDPC decoding method based on node reliability subset partition criterion

Abstract

The application provides a kind of multinary LDPC decoding method based on node reliability subset division criterion, comprising: step 1: initialization of channel information value;Step 2: decoding iteration process, if the current iteration number reaches the maximum iteration number or decoding check succeeds, exit the iteration process, otherwise enter step 3;Step 3: information update is carried out to check node, and the division mechanism is triggered after the third iteration;Step 4: calculate the information value of the check node to the check node, and the message truncation is carried out to the check node outside information transmitted by the check node;Step 5: calculate the information value of the check node to the variable node inverse substitution;Step 6: the calculation and decision of variable node full information;Step 7: check the decision result, if it is satisfied, decoding is ended, otherwise enter step 8;Step 8: return to the decoding iteration process of step 2, while the information of last round iteration is transmitted to the check node to be updated, for the reasonable allocation of check node.

Description

Technical Field

[0001] This invention belongs to the field of multi-level LDPC encoding and decoding under the BeiDou Navigation Satellite System, specifically involving a multi-level LDPC decoding method based on the node reliability subset partitioning criterion. Background Technology

[0002] In the field of multi-ary LDPC code decoding, the Q-ary Sum Product Algorithm (QSPA) is widely considered to be the best-performing method among soft-decision iterative decoding techniques. However, the QSPA algorithm inherently possesses high computational complexity. Therefore, researchers have proposed a series of strategies to reduce complexity, including computational methods based on the Fast Fourier Transform (FFT) and message truncation. FFT helps reduce the computational load on the check nodes, while message truncation can narrow the search space of the check equations.

[0003] In 2007, Professor Declercq first proposed the Extended Min-Sum (EMS) algorithm, aiming to reduce the amount of information in each iteration. To reduce the computational complexity of multi-ary LDPC codes, Declercq and other researchers proposed an extended min-sum (EMS) algorithm in 2007. This algorithm reduces the computational burden on the check nodes by truncating the information vector input to them. Subsequently, researchers proposed a series of EMS-like algorithms, including M-EMS and T-EMS. The improved information passing decoding algorithm proposed by Han et al. in 2013 and the reliability iterative proportional logic decoding algorithm based on an adaptive decision mechanism proposed by Sun et al. in 2015 aim to partition nodes. In 2017, Sun Youming's team proposed a multivariate LDPC algorithm based on k-order information truncation. This algorithm defines a new subset partitioning criterion; however, further research is needed on how to determine the subset threshold and the partitioning criteria. Summary of the Invention

[0004] In view of the shortcomings of the prior art described above, the purpose of this invention is to provide a multi-level LDPC decoding method based on the node reliability subset partitioning criterion.

[0005] To achieve the above and other related objectives, this invention provides a multi-level LDPC decoding method based on a node reliability subset partitioning criterion for channel coding. This method includes the following steps:

[0006] Step 1: Calculate the probability function based on the channel received value y, the quantization interval Δ, and the number of quantization bits b. Will Sort in descending order; set the current iteration count l = 0 and the maximum iteration count l. max =30;

[0007] Step 2: Determine if the current iteration count has reached the preset maximum iteration count. max If the maximum number of iterations is reached, the decoding iteration is terminated and the decoding result is output; otherwise, the decoding iteration process is resumed.

[0008] Step 3: Update the information of the verification nodes; if decoding still fails after the third iteration, a partitioning mechanism is triggered. The set of verification nodes to be processed is partitioned based on the reliability of the variable nodes, resulting in the complete set of verification nodes. U (l) This indicates the verification node to be updated. This indicates a verification node that does not require processing at this time.

[0009] Step 4: Calculate the permutation node H based on the permutation constraints. ij To the verification node C i Transmitted information value and external information Perform truncation processing, and calculate the information value passed from the verification node to the replacement node based on this truncation method;

[0010] Step 5: The permutation node uses the extrinsic information value transmitted from the check node to calculate the extrinsic information value of the inverse permutation transmitted to the variable node.

[0011] Step 6: For variable node V j Calculate the full information LLR vector The decision result for each variable node is:

[0012] Step 7: Verify the judgment result. If the checksum is satisfied... Decoding complete, output the result; otherwise, proceed to step S8 for the next iteration.

[0013] Step 8: Return to the decoding iteration process of step S2, enter the next iteration, and pass the information from the previous iteration to the set of check nodes U to be updated. (l) The check nodes are used to redistribute check nodes, and the algorithm iteration count is incremented by 1. If the redistribution fails, the decoding iteration step is initiated. If the decoding fails in the second iteration, the check node partitioning mechanism is triggered in the third iteration, and the set of check nodes is redistributed according to the reliability of the variable nodes.

[0014] Optionally, the channel received value y can be initialized as follows: Among them, s i F represents the i-th bit in a binary vector. q Represent a finite field of order q; then quantize and preprocess the initialized information.

[0015]

[0016] In the formula, [·] represents the floor operation; This indicates the reliability of the quantified information.

[0017] quantified Sort in descending order:

[0018]

[0019] Optionally, the information transmission method between variable nodes, substitution nodes, and check nodes;

[0020] a. Variable node V j To the replacement node H ij Transmitted information value:

[0021]

[0022] In the formula, Initialize as a vector of all zeros. This represents the information passed from the edge to the variable node.

[0023] b. Replacement node H ij To the verification node C i The message conveyed:

[0024]

[0025] c. During the verification node update process, the first n bits of the LLR vector are truncated. m If the term is L, then the total set of LLR vectors is L. y for (ρ is the row weight of the i-th row of the verification matrix), verification node C i To the replacement node H ij The message conveyed:

[0026]

[0027] d. Permutation node H ij To variable node V j The message conveyed:

[0028]

[0029] Optionally, for the permutation node H ij To the verification node C iExternal information being transmitted Truncation processing;

[0030] For the replacement node H ij To the verification node C i Transmitted information outside the logarithmic field The threshold value T is set according to the T-cutting criterion. c The set of principal components after truncation is as follows:

[0031]

[0032] Optionally, the threshold value T c Selection;

[0033]

[0034] in, This criterion represents the top three extreme values ​​of the reliability sequence in descending order, and reasonably lowers the threshold value T. c This allows for a good distribution of the main and secondary components in the message vector, reducing complexity while ensuring decoding performance.

[0035] Optionally, the set of verification nodes to be processed can be divided according to the reliability of the variable nodes;

[0036] For a given variable node, its decoding checksum There are two possible scenarios:

[0037] (1) The sign determinations for all variable nodes are correct;

[0038] (2) There are two or more erroneous symbols among the symbols of the variable nodes involved in the decision, which make the check node and the decision result in 0.

[0039] For case (2), we define a new criterion for the reliability of variable nodes:

[0040]

[0041]

[0042] The sign decision indicates that the mechanism is triggered after the third iteration in a three-iteration process, and the information values ​​of the variable nodes have the same sign; the magnitude decision indicates that the difference between the total information in the current iteration and the total information in the two adjacent iterations is less than a preset threshold value T. s If both of the above conditions are met, then the variable node is determined to be reliable, denoted as T. j (l) If it is 0, otherwise record it as T. j (l) The value is 1.

[0043] Based on the reliability of the variable nodes, the set of verification nodes to be processed and the set of nodes not to be processed are divided. The set to be processed is as follows:

[0044]

[0045] The verification nodes are divided into a processing node subset and a non-processing node subset. Verification nodes in the processing node subset are characterized by either a non-zero checksum or a zero checksum, but with two or more adjacent variable nodes having a reliability less than a threshold value T. s .

[0046] Optionally, computation of all information and hard decision-making;

[0047] Variable node V j Calculate full information for:

[0048]

[0049] The verdict is as follows: if Decoding is successful, and the codeword sequence is output. Otherwise, return to the decoding iteration process; if unsuccessful, proceed to the decoding iteration step. If decoding is still unsuccessful in the second iteration, proceed to the third iteration and trigger the partitioning mechanism of the verification nodes, redistributing the set of verification nodes according to the reliability of the variable nodes.

[0050] This invention presents a multi-level LDPC decoding method based on a node reliability subset partitioning criterion. It proposes a novel subset truncation criterion and subset partitioning method, applicable to scenarios where node reliability is determined using checksum results. This criterion provides a joint decision-making method based on the reliability of variable nodes, combining sign and magnitude judgments. Furthermore, it offers a novel T-shaped truncation method for the external information transmitted from the permutation node to the check node and defines a method for calculating the T-shaped truncation threshold. Compared to other EMS algorithms, this algorithm achieves superior decoding performance with lower complexity. Attached Figure Description

[0051] To further illustrate the contents described in this invention, the specific embodiments of the invention will be described in more detail below with reference to the accompanying drawings. It should be understood that these drawings are merely typical examples and should not be construed as limiting the scope of the invention.

[0052] Figure 1 This is a flowchart illustrating the decoding method of the present invention.

[0053] Figure 2 This is a flowchart of the algorithm provided in the implementation of the present invention.

[0054] Figure 3 This is a structural diagram of the decoding module.

[0055] Figure 4 It is a graph showing the information transfer between nodes. Detailed Implementation

[0056] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, unless otherwise specified, the following embodiments and features described therein can be combined with each other.

[0057] It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Therefore, the drawings only show the components related to the present invention and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0058] To more clearly describe the technical solution, the specific embodiments of the present invention are as follows:

[0059] For a finite field GF(q), q=2 l On the multi-dimensional LDPC code C q [n,k], after processing the codeword using binary phase shift keying modulation (BPSK), according to the corresponding mapping rule (x = 1 - 2v), the codeword v can be transformed into: Where 0 ≤ j ≤ N-1, 0 ≤ i ≤ l-1. The symbol sequence received after the bipolar codeword is subjected to additive white Gaussian noise channel interference is:

[0060] For a given parity check matrix H, it can be used as follows: Figure 4 The diagram showing the inter-node information transfer illustrates the decoding process of LDPC codes. Figure 4 In this code, edges represent variables, while vertices represent certain constraints. There are three types of nodes in the multivariate LDPC code information transmission process: variable nodes (V nodes) represent each column of the parity check matrix, parity nodes (C nodes) represent each row of the parity check matrix, and permutation nodes represent non-zero elements in the parity check matrix.

[0061] like Figure 1As shown, this invention provides a multi-level LDPC decoding method based on a node reliability subset partitioning criterion, comprising:

[0062] Step 1: Calculate the initialization information based on the channel received value y, the quantization step size Δ, and the number of quantization bits b. Will Sort in descending order; set the current iteration count l = 0 and the maximum iteration count l. max =30;

[0063] Step 2: Determine if the current iteration count has reached the preset maximum iteration count. max If the maximum number of iterations is reached, the decoding iteration is terminated and the decoding result is output; otherwise, the decoding iteration process is resumed.

[0064] Step 3: Update the information of the verification nodes; if decoding still fails after the third iteration, a partitioning mechanism is triggered. The set of verification nodes to be processed is partitioned based on the reliability of the variable nodes, resulting in the complete set of verification nodes. U (l) This indicates the verification node to be updated. This indicates a verification node that does not require processing at this time.

[0065] Step 4: Calculate the permutation node H based on the permutation constraints. ij To the verification node C i Transmitted information value and external information Perform truncation processing, and calculate the information value passed from the verification node to the replacement node based on this truncation method;

[0066] Step 5: The permutation node uses the extrinsic information value transmitted from the check node to calculate the extrinsic information value of the inverse permutation transmitted to the variable node.

[0067] Step 6: For variable node V j Calculate the full information LLR vector The decision result for each variable node is:

[0068] Step 7: Verify the judgment result. If the checksum is satisfied... Decoding complete, output the result; otherwise, proceed to step S8 for the next iteration.

[0069] Step 8: Return to the decoding iteration process of step S2, enter the next iteration, and pass the information from the previous iteration to the set of check nodes U to be updated. (l) The check nodes in the algorithm are used to redistribute check nodes, and the algorithm iteration count is incremented by 1.

[0070] according to Figure 3 Decoding module structure diagram and Figure 4 As can be seen from the information transmission diagram between nodes, the proposed improved EMS algorithm process is described in detail, mainly including channel message initialization processing; information transmission between verification nodes, replacement nodes, and variable nodes; truncation of information transmitted from replacement nodes to verification nodes; and subset partitioning of verification nodes based on the reliability of variable nodes.

[0071] in accordance with Figure 2 The flowchart shown in the embodiment of the present invention illustrates the specific steps of the present invention as follows:

[0072] 1. For a finite field GF(q=2 l The multi-level LDPC code on the ) is processed using binary phase shift keying modulation (BPSK). Based on the corresponding mapping rule (x = 1-2s), the initialized likelihood information value is:

[0073]

[0074] In the formula, s i F represents the i-th bit in a binary vector. q Let represent a finite field of order q.

[0075] The likelihood information value is simplified by quantization preprocessing. The quantization step size Δ and quantization bits b are determined by fully considering factors such as channel transmission characteristics and computational complexity during decoding, and must satisfy 2... b • The value of Δ is large enough.

[0076]

[0077] In the formula, [·] represents the floor operation; This indicates the reliability of the quantified information.

[0078] Then the quantified Sort in descending order:

[0079]

[0080] 2. Divide the set of verification nodes to be processed according to the reliability of the variable nodes;

[0081] For a given variable node, its decoding checksum There are two possible scenarios:

[0082] (1) The sign determinations for all variable nodes are correct;

[0083] (2) There are two or more erroneous symbols among the symbols of the variable nodes involved in the decision, which make the check node and the decision result in 0.

[0084] For case (2), we define a new criterion for the reliability of variable nodes:

[0085]

[0086]

[0087] The sign decision in equation (4) indicates that the mechanism is triggered after the third iteration in three consecutive iterations, and the signs of the information values ​​of the variable nodes are the same; the magnitude decision in equation (5) indicates that the difference between the total information in the current iteration and the total information in the two adjacent iterations is less than the preset threshold value T. s If both of the above conditions are met, then the variable node is determined to be reliable, denoted as T. j (l) If it is 0, otherwise record it as T. j (l) The value is 1.

[0088] The verification nodes are divided into a processing node subset and a non-processing node subset. Verification nodes in the processing node subset are characterized by either a non-zero checksum or a zero checksum where two or more of their adjacent variable nodes have a reliability less than a threshold value T. s .

[0089] Based on the reliability of the variable nodes, the set of verification nodes to be processed and the set of nodes not to be processed are divided. The set to be processed is as follows:

[0090]

[0091] 3. Information transfer between variable nodes, replacement nodes, and check nodes;

[0092] a. Variable node V j To the replacement node H ij Transmitted information value:

[0093]

[0094] In the formula, Initialize as a vector of all zeros. This represents the information passed from the edge to the variable node.

[0095] b. Replacement node H ij To the verification node C i The message conveyed:

[0096]

[0097] c. During the verification node update process, the first n bits of the LLR vector are truncated. m If the term is L, then the total set of LLR vectors is L. y for (ρ is the row weight of the i-th row of the verification matrix), verification node C i To the replacement node H ij The message conveyed:

[0098]

[0099] d. Permutation node H ij To variable node V j The message conveyed:

[0100]

[0101] 4. Handling of intercepted external information;

[0102] For the replacement node H ij To the verification node C i Information transmitted in the logarithmic field The threshold value T is set according to the T-cutting criterion. c After truncating the external information, the set of domain elements is:

[0103]

[0104] This truncation criterion applies to step c in step 3, and the verification node C is calculated based on this new truncation method. i To the replacement node H ij The information being transmitted, the threshold value T c The definition is as follows:

[0105]

[0106] in, This criterion represents the top three maximum values ​​in descending order of the reliability sequence, and it reasonably lowers the threshold value T. c This allows for a good distribution of the main and secondary components in the message vector, reducing complexity while ensuring decoding performance.

[0107] 5. Full information computation and hard decision-making;

[0108] Variable node V j Calculate full information for:

[0109]

[0110] The verdict is as follows: if Decoding is successful, and the codeword sequence is output.

[0111] If unsuccessful, the decoding iteration step is initiated. If decoding is still unsuccessful in the second iteration, the verification node partitioning mechanism is triggered in the third iteration, and the set of verification nodes is allocated according to the reliability of the variable nodes.

Claims

1. A multi-level LDPC decoding method based on node reliability subset partitioning criteria, used for channel encoding and decoding of navigation messages under the BeiDou navigation system, characterized in that... include: Step 1: Initialize Information Reliability Sort in descending order; set the current iteration count l = 0 and the maximum iteration count l. max =30; In the first iteration, all verification nodes are assigned to the set U to be processed. (l) middle; Step 2: Determine if the current iteration count has reached the preset maximum iteration count. max If the maximum number of iterations is reached, the decoding iteration is terminated and the decoding result is output; otherwise, the decoding iteration process is resumed. Step 3: Divide the set of verification nodes to be processed according to the reliability of the variable nodes. The complete set of verification nodes is as follows: U (l) This indicates the verification node to be updated. This indicates the verification nodes that do not need to be processed for the time being, after partitioning U. (l) The verification nodes in the set are updated with information; Step 4: Calculate the permutation node H based on the permutation constraints. ij To the verification node C i Transmitted information value external information Perform truncation and set corresponding threshold truncation rules. Based on this truncation method, calculate the information value passed from the verification node to the replacement node: Step 5: The permutation node uses the extrinsic information value transmitted from the check node to calculate the extrinsic information value of the inverse permutation transmitted to the variable node. Step 6: For variable node V j Calculate the full information LLR vector The decision result for each variable node is: Step 7: Verify the judgment result. If the checksum is satisfied... Decoding complete, output the result; Otherwise, proceed to step S8 for the next iteration; Step 8: Return to the decoding iteration process in Step 2 and enter the next iteration, incrementing the iteration count by 1; if the decoding is still unsuccessful in the second iteration, the check node partitioning mechanism will be triggered after the third iteration, and the set of check nodes will be redistributed according to the reliability of the variable nodes, incrementing the iteration count by 1.

2. The multi-level LDPC decoding method based on node reliability subset partitioning criterion according to claim 1, characterized in that, The information transmission methods among the variable nodes, the substitution nodes, and the verification nodes include: a. Variable node V j To the replacement node H ij Transmitted information value: In the formula, Initialize as a vector of all zeros. This represents the information passed from the edge to the variable node; b. Replacement node H ij To the verification node C i The message conveyed: c. During the verification node update process, the first n bits of the LLR vector are truncated. m If the term is L, then the total set of LLR vectors is L. y for (ρ is the row weight of the i-th row of the verification matrix), verification node C i To the replacement node H ij The message conveyed: d. Permutation node H ij To variable node V j The message conveyed:

3. The multi-level LDPC decoding method based on node reliability subset partitioning criterion according to claim 1, characterized in that, external information Perform truncation and set corresponding threshold truncation rules; For the replacement node H ij To the verification node C i Information transmitted in the logarithmic field The threshold value T is set according to the T-cutting criterion. c After truncating the external information, the set of domain elements is: Threshold value T based on T-type threshold truncation method c Selection of threshold values, definition of threshold values: in, This represents the top three maximum values ​​in the reliability sequence, arranged in descending order.

4. The multi-level LDPC decoding method based on node reliability subset partitioning criterion according to claim 1, characterized in that, The set of verification nodes to be processed is divided according to the reliability of the variable nodes; For a given variable node, its decoding checksum There are two possible scenarios: (1) The sign determinations for all variable nodes are correct; (2) There are two or more erroneous symbols among the symbols of the variable nodes involved in the decision, and these erroneous symbols make the check node and the judgment result 0; For case (2), we define a new criterion for the reliability of variable nodes: The sign decision in equation (7) indicates that the mechanism is triggered after the third iteration in three consecutive iterations, and the signs of the information values ​​of the variable nodes are the same; the magnitude decision in equation (8) indicates that the difference between the total information in the current iteration and the total information in the two adjacent iterations is less than the preset threshold value T. s If both of the above conditions are met, then the variable node is determined to be reliable, denoted as T. j (l) If it is 0, otherwise record it as T. j (l) =1; The verification nodes are divided into a processing node subset and a non-processing node subset. Verification nodes in the processing node subset are characterized by either a non-zero checksum or a zero checksum, but with two or more adjacent variable nodes having a reliability less than a threshold value T. s ; Based on the reliability of the variable nodes, the set of verification nodes to be processed and the set of nodes not to be processed are divided. The set to be processed is as follows:

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