Multi-element ldpc decoding method based on dynamic threshold truncation strategy

Abstract

The application discloses a multi-element LDPC decoding method based on a dynamic threshold cutting strategy, and is used for solving the problem of high complexity of a multi-element LDPC decoding algorithm. The method provided by the application introduces a dynamic threshold cutting strategy based on the reliability distribution characteristics of an information vector. The strategy dynamically selects a cutting threshold value by using the difference between the maximum value and the second maximum value of the reliability. If the difference reaches a preset difference parameter, the larger threshold value is selected, thereby reducing the finite field elements participating in the operation. If the difference does not reach the preset difference parameter, the smaller threshold value is selected, thereby relatively conservatively increasing more components. In the iteration process, information screening is carried out according to the threshold value, so that the number of states and the number of edges participating in the operation on a trellis diagram are less. The application can obtain lower average decoding complexity without performance loss.

Description

Technical Field

[0001] This invention belongs to the field of computer technology, and more specifically, relates to a multivariate LDPC decoding method based on a dynamic threshold truncation strategy. Background Technology

[0002] Multi-binary low-density parity-check (NB-LDPC) codes exhibit excellent performance in terms of burst error resistance, error leveling, throughput, and integration with higher-order modulation techniques, and have been widely used in many fields such as high-speed broadband mobile communications.

[0003] Decoding multivariate LDPC codes directly using the q-ary sum-product algorithm (QSPA) is extremely complex, limiting its application in many communication scenarios. Since the decoding complexity primarily arises from the operations at the check node, researchers have proposed a series of decoding algorithms to simplify check node processing. Among them, Declercq et al. proposed the extended min-sum (EMS) decoding algorithm based on the binary min-sum algorithm. This algorithm filters the q-dimensional information vectors entering the check node edge, selecting only n of them. m The most reliable value reduces the decoding complexity to However, the performance of the EMS algorithm will change with n m The performance decreases due to the reduction in value, therefore an appropriate correction coefficient needs to be introduced for performance compensation. Building upon EMS, Boutillon et al. proposed a bubble check (BC) algorithm based on a two-dimensional information strategy, which reduces the computation of check nodes without affecting performance, lowering the complexity to [missing value]. Building upon this, Lin et al. proposed a dynamic bubble check (DBC) algorithm, further reducing the complexity of the check node. Applying the DBC algorithm to basic check node processing, Wang et al. proposed an EMS algorithm based on dynamic information truncation, where the information vector length decreases with the number of iterations, thus reducing decoding complexity.

[0004] Based on the characteristics of states and edges on a Trellis graph, the idea of ​​reducing the search using the BCJR algorithm is introduced, which is another important means to reduce the complexity of the EMS algorithm, and several variant algorithms based on the EMS algorithm have been derived from this. Among them, Ma et al. proposed a variant algorithm of EMS based on a fixed threshold truncation strategy, namely the T-EMS (threshold based EMS) algorithm (Ma X, Zhang K, Chen H, et al. Low complexity X-EMS algorithms for nonbinary LDPC codes[J].IEEE Transactions on Communications, 2012, 60(1):9-13.). The classic EMS algorithm is redescribed based on the Trellis graph. In the decoding iteration process, the T-EMS algorithm only retains the "live" states and "live" edges with a reliability greater than the threshold, achieving performance close to that of the classic QSPA algorithm, and its decoding complexity is reduced to a certain extent.

[0005] However, for the T-EMS algorithm, the value of its fixed threshold parameter has a significant impact on the algorithm's average complexity and performance. During the iteration process, the fixed threshold parameter value makes it difficult to account for factors such as channel conditions and the iteration process, resulting in a still relatively high average complexity. Therefore, it is necessary to further reduce the complexity of each iteration. Furthermore, simply adjusting the value of the fixed threshold is insufficient to simultaneously meet the requirements of complexity and decoding performance. Summary of the Invention

[0006] To address the aforementioned shortcomings and improvement needs of existing technologies, this invention provides a multivariate LDPC decoding method based on a dynamic threshold truncation strategy. During the iteration process, information is filtered according to a dynamic threshold, reducing the number of states and edges participating in the computation on the mesh graph. The aim is to achieve a lower average decoding complexity without sacrificing performance. This solves the technical problem of excessively high complexity in each iteration of T-EMS.

[0007] To achieve the above objectives, this invention provides a multivariate LDPC decoding method based on a dynamic threshold truncation strategy, the method comprising:

[0008] S1 initialization: Set quantization parameters Δ and b, and correction coefficient ε; set threshold T1. DT T2 DT (T1 DT >T2 DT ), set the difference parameter Let the number of iterations k = 0, and set the maximum number of iterations I. max; Calculate initial channel information

[0009] S2 iterative decoding: k≤I max When this happens, perform the following steps.

[0010] S21: Calculate the hard decision sequence for the k-th iteration, and obtain...

[0011] S22: Calculate the syndrome in like If so, exit the iteration and output the codeword v; otherwise, execute S23.

[0012] S23: Intermediate node H ij Receive information from the variable section Calculate permutation information And pass it to the verification node C. i ;

[0013] S24: Verification Node C i For intermediate node H ij The reliability vector R of each q-dimensional integer information passed in z (z)(z∈F q )(Right now First, based on the difference between the maximum and second-largest values ​​of their respective reliability components and the preset difference parameter... Dynamically determine the threshold value T DT Secondly, based on the threshold value T DT For information vector R z (z)(z∈F q By partitioning and filtering the elements of the finite field, we obtain two sets S. DT and Then based on set S DT For information vector R z (z) Perform truncation to obtain truncated information. (Right now Based on this, the verification node C is calculated using a recursive method. i The external information and corresponding truncation information are obtained and corrected to obtain the verification node C. i External information

[0014] S25: Intermediate Node H ij Receiver Inspection Node C i The message passed on Calculate its permutation information And pass it to the adjacent variable node;

[0015] S26: Update variable node information The iteration count increments by one unit; if the maximum number of iterations I is reached... max If the condition is met, the iteration exits and the decoding result is output; otherwise, the iteration continues and S21 is executed.

[0016] In one embodiment of the present invention, during initialization: let the received real number sequence be y = (y0, y1, ..., y2). n-1 ),in Define the channel and pass it to the variable node V j Reliability of real information vectors (0≤j≤n-1) z∈F q Among them, z (i) Let the i-th bit of the field element z be quantized; then quantization is performed when... At that time, Quantification when At that time, Quantification when At that time, Quantification Where Δ is the quantization interval and b is the number of quantization bits, the corresponding integer information vector reliability is obtained.

[0017] In one embodiment of the invention, in step S21 of iterative decoding: during the k-th iteration, variable node V... j (0≤j≤n-1) Perform a hard decision and obtain in For variable node V j A reliability vector of information (0≤j≤n-1);

[0018] In one embodiment of the present invention, in step S22 of iterative decoding: the finite field F q (q=2 t An (n,k) multivariate LDPC code on a given surface can be represented by an m x n parity check matrix H = (h... ij ) m×n (h ij ∈F q To represent. Define the subscript set N. i ={j:0≤j≤n-1,h i,j ≠0} is the set of non-zero elements in the i-th row of matrix H; define the subscript set M. j ={i:0≤i≤m-1,h i,j ≠0} is the set of non-zero elements in the j-th column of matrix H. The k-th iteration yields the decision sequence. Then, a concurrent verification is performed, which requires that the constraints be met. To verify whether the current codeword is correct, the syndrome is calculated. in, Represents the i-th verification node C i (0≤i≤m-1) adjoint information,

[0019] In one embodiment of the present invention, in step S23 of iterative decoding: intermediate node H ij Receive from neighboring variable node V j The message conveyed in Then it is permuted to obtain permutation information. And pass it to the verification node C. i ;

[0020] In one embodiment of the present invention, in step S24 of iterative decoding: during the k-th iteration, the verification node C... i Receive intermediate node H ij The reliability vector R of the transmitted q-dimensional integer information z (z)(z∈F q )(Right now Let R 1 Z (z) and R 2 Z (z) represents the information vector R. Z The maximum and second-highest reliability in (z) The threshold value T is a parameter to be determined, and is dynamically selected based on the magnitude of the reliability difference. DT The value;

[0021] If its maximum reliability With the second highest reliability The difference between them is greater than or equal to the preset difference parameter. Then the threshold T DT Take a larger threshold; that is, when At that time, the threshold is dynamically selected to be a larger threshold T1. DT (T DT =T1 DT This allows fewer components to participate in the calculation; if its maximum reliability is achieved... With the second highest reliability The difference between them is less than the preset difference parameter. Threshold T DT Take the smaller threshold; that is, when At that time, the threshold value T DT Take a smaller threshold The relatively conservative approach increased the amount of ingredients.

[0022] For information vector R z (z)(z∈F q )(Right now Based on the distribution characteristics of its reliability, its finite field elements can be partitioned and filtered to obtain two sets S. DT and And satisfy S DT Defined as S DT ={z∈F q |R Z (z) Exceeds a certain preset parameter T DT}, where parameter T DT The dynamic threshold value T is based on the reliability difference characteristic. DT Different values ​​are selected based on the state and the edge, i.e., the state threshold value T. s DT and the side threshold value T b DT ;

[0023] For information vector R z (z), combined with set S DT For information vector R z (z) is truncated if the finite field element z∈S DT Calculate its corresponding truncation information. Otherwise, its corresponding truncation information in Let set S DT The minimum information reliability corresponding to the elements of the finite field.

[0024] In one embodiment of the present invention, in step S24 of iterative decoding: for check node C i (0≤i≤m), let its degree be d. c The edge it is connected to is Y. ij (j∈N i Let α t =(a t (0),a t (1),…,a t (q-1)) represents the forward recursive vector, β t =(β) t (0),β t (1),…,β t (q-1) represents the backward recursive vector, which is updated by recursively updating the verification node C according to the following method. i External information Perform calculations;

[0025] First, preprocessing is performed, and node C is verified according to the truncation strategy. i For intermediate node H ij The message passed on Preprocessing is performed to calculate the corresponding truncation information. And define its "live" edges;

[0026] Then, perform forward recursive calculations to obtain... in Initialize to 0≤t <d c -1; Calculate the corresponding truncation information according to the truncation strategy. And define its "live" state;

[0027] Then, a backward recursive calculation is performed to obtain... in Initialize to d c For values ​​≥t>1, calculate the corresponding truncation information according to the truncation strategy. And define its "live" state;

[0028] Finally, external information is calculated to obtain... Where 0≤t≤d c -1; Calculate the corresponding truncation information according to the truncation strategy. And define its "live" edges;

[0029] Correct external information, if external information The corrected external information is Otherwise, the corrected external information is Where ε is the correction coefficient.

[0030] In one embodiment of the present invention, in step S25 of iterative decoding: intermediate node H ij For verification node C i Passed to variable node V j The information is replaced to obtain the replaced information.

[0031] In one embodiment of the present invention, in step S26 of iterative decoding: during the k-th iteration, the variable node V... j (0≤j≤n-1) Receive from channel Ch j and its adjacent intermediate node H ij The received information allows us to obtain updated information about the variable nodes. in, Initialized to 0, the first term is the initial channel information, which remains unchanged during the iteration process; the second term is the sum of external information from adjacent check nodes, which jointly pushes the reliability of the variable node to shift in the correct direction.

[0032] After the information is updated, the iteration count increments by one unit. If the maximum number of iterations I is reached... max If the condition is met, the iteration exits and the codeword v is output; otherwise, the iteration continues.

[0033] In summary, compared with existing technologies, the technical solution conceived in this invention has the following beneficial effects: This invention dynamically selects a truncation threshold during the iteration process based on the difference between the maximum and second-largest reliability values ​​of the information vector. If the difference reaches a pre-set difference parameter, a larger threshold is selected, which helps reduce the number of finite field elements participating in the computation; conversely, a smaller threshold is selected, retaining a relatively larger number of finite field elements, which helps maintain performance. Overall, this reduces the number of states and edges participating in the computation on the mesh graph, achieving a lower average decoding complexity without sacrificing performance.

[0034] In summary, this invention achieves decoding performance very close to that of classic multivariate sum-product algorithms and T-EMS, demonstrating excellent decoding performance. Simultaneously, in terms of complexity, this invention is less complex than the T-EMS algorithm and significantly less complex than the QSPA algorithm. This invention provides an effective trade-off between decoding performance and decoding complexity. Attached Figure Description

[0035] Figure 1 This is a flowchart illustrating a multi-element LDPC decoding method based on a dynamic threshold truncation strategy in an embodiment of the present invention.

[0036] Figure 2 This is the Normal diagram of the LDPC code in this embodiment of the invention;

[0037] Figure 3 This is the F constructed based on finite fields in the embodiments of the present invention. 16 (225,173) Schematic diagram comparing the decoding performance of quasi-cyclic multivariate LDPC codes;

[0038] Figure 4 This is the F constructed based on finite fields in the embodiments of the present invention. 16 (225,173) A diagram comparing the complexity ratios of quasi-cyclic multivariate LDPC codes;

[0039] Figure 5 This is an F constructed based on the PEG method in the embodiments of the present invention. 64 (142,71) Schematic diagram comparing the decoding performance of multi-element PEG-LDPC codes;

[0040] Figure 6 This is an F constructed based on the PEG method in the embodiments of the present invention.64 (142,71) A schematic diagram comparing the complexity ratios of multivariate PEG-LDPC codes. Detailed Implementation

[0041] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0042] This invention proposes a multivariate LDPC decoding method (DT-EMS) based on a dynamic threshold truncation strategy. Its aim is to achieve lower average decoding complexity while maintaining decoding performance, thereby solving the problem of excessive complexity in the original T-EMS decoding scheme. Figure 1 As shown in the flowchart, a dynamic threshold truncation strategy based on the reliability distribution characteristics of the information vector is introduced. In the current iteration, the maximum and second-largest reliability components of the information vector are obtained, and it is determined whether the difference between the current maximum and second-largest reliability exceeds a preset parameter. If the difference reaches the preset difference parameter, a larger threshold parameter is selected, allowing fewer components to participate in the calculation; if not, a smaller threshold parameter is selected, conservatively increasing the number of components participating in the calculation. This allows for dynamic selection of the threshold based on the reliability difference characteristics, realizing a dynamic threshold truncation strategy. Simulation and numerical results show that the DT-EMS decoding method can achieve a lower average decoding complexity without loss of decoding performance.

[0043] This invention provides a multivariate LDPC decoding method based on a dynamic threshold truncation strategy, comprising:

[0044] S1 initialization: Set quantization parameters Δ and b, and correction coefficient ε; set threshold T1. DT T2 DT (T1 DT >T2 DT Set the difference parameter. Let the number of iterations k = 0, and set the maximum number of iterations I. max ; Calculate initial channel information

[0045] In the initialization of step S1:

[0046] Let the received sequence of real numbers be y = (y0, y1, ..., y2). n-1 ),in Define the channel and pass it to the variable node V jReliability of real information vectors (0≤j≤n-1) z∈F q Among them, z (i) Let the i-th bit of the field element z be quantized; then quantization is performed when... At that time, Quantification when At that time, Quantification when At that time, Quantification Where Δ is the quantization interval and b is the number of quantization bits, the corresponding integer information vector reliability is obtained.

[0047] S2 iterative decoding: k≤I max When this happens, perform the following steps:

[0048] S21: Calculate the hard decision sequence for the k-th iteration, and obtain...

[0049] In step S21 of the iterative decoding:

[0050] In the kth iteration, the variable node V j (0≤j≤n-1) Perform a hard decision and obtain in For variable node V j The information reliability vector is (0≤j≤n-1).

[0051] S22: Calculate the syndrome in like Then exit the iteration and output the codeword v; otherwise, execute S23.

[0052] In step S22 of the iterative decoding:

[0053] Finite field F q (q=2 t An (n,k) multivariate LDPC code on a given surface can be represented by an m x n parity check matrix H = (h... ij ) m×n (h ij ∈F q To represent, define the subscript set N. i ={j:0≤j≤n-1,h i,j ≠0} is the set of non-zero elements in the i-th row of matrix H; define the subscript set M. j ={i:0≤i≤m-1,h i,j ≠0} is the set of non-zero elements in the j-th column of matrix H;

[0054] The decision sequence is obtained in the k-th iteration. Then, a concurrent verification is performed, which requires that the constraints be met. To prove whether the current codeword is correct, the syndrome is calculated. in Represents the i-th verification node C i (0≤i≤m-1) adjoint information,

[0055] S23: Intermediate node H ij Receive information from the variable section Calculate permutation information And pass it to the verification node C. i ;

[0056] In step S23 of the iterative decoding:

[0057] intermediate node H ij Receive from neighboring variable node V j The message conveyed in Then it is permuted to obtain permutation information. And pass it to the verification node C. i .

[0058] S24: Verification Node C i For intermediate node H ij The reliability vector R of each q-dimensional integer information passed in z (z)(z∈F q )(Right now First, based on the difference between the maximum and second-largest values ​​of their respective reliability components and the preset difference parameter... Dynamically determine the threshold value T DT Secondly, based on the threshold value T DT For information vector R z (z)(z∈F q By partitioning and filtering the elements of the finite field, we obtain two sets S. DT and Then based on set S DT For information vector R z (z) Perform truncation to obtain truncated information. (Right now Based on this, the verification node C is calculated using a recursive method. i The external information and corresponding truncation information are obtained and corrected to obtain the verification node C. i External information

[0059] In step S24 of the iterative decoding:

[0060] In the k-th iteration, the verification node C i Receive intermediate node H ij The reliability vector R of the transmitted q-dimensional integer information z (z)(z∈F q )(Right now Let R 1 Z (z) and R 2 Z (z) represents the information vector R. Z The maximum and second-highest reliability in (z) The threshold value T is a parameter to be determined, and is dynamically selected based on the magnitude of the reliability difference. DT The value;

[0061] If its maximum reliability With the second highest reliability The difference between them is greater than or equal to the preset difference parameter. Then the threshold T DT Take a larger threshold; that is, when At that time, the threshold is dynamically selected to be a larger threshold T1. DT (T DT =T1 DT This allows fewer components to participate in the calculation; if its maximum reliability is achieved... With the second highest reliability The difference between them is less than the preset difference parameter. Threshold T DT Take the smaller threshold; that is, when At that time, the threshold value T DT Take the smaller threshold T2 DT (T DT =T2 DT (), relatively conservatively increased the amount of ingredients;

[0062] For information vector R z (z)(z∈F q )(Right now Based on the distribution characteristics of its reliability, its finite field elements can be partitioned and filtered to obtain two sets S. DT and And satisfy S DT Defined as S DT ={z∈F q |R Z (z) Exceeds a certain preset parameter T DT}, where parameter T DTThe dynamic threshold value T is based on the reliability difference characteristic. DT Different values ​​are selected based on the state and the edge, i.e., the state threshold value T. s DT and the side threshold value T b DT ;

[0063] For information vector R z (z), combined with set S DT For information vector R z (z) is truncated if the finite field element z∈S DT Calculate its corresponding truncation information. Otherwise, its corresponding truncation information in Let set S DT The minimum information reliability corresponding to the elements of the finite field.

[0064] In step S24 of the iterative decoding:

[0065] For verification node C i (0≤i≤m), let its degree be d. c The edge it is connected to is Y. ij (j∈N i Let α t =(a t (0),a t (1),…,a t (q-1)) represents the forward recursive vector, β t =(β) t (0),β t (1),…,β t (q-1) represents the backward recursive vector, which is updated by recursively updating the verification node C according to the following method. i External information Perform calculations;

[0066] First, preprocessing is performed, and node C is verified according to the truncation strategy. i For intermediate node H ij The message passed on Preprocessing is performed to calculate the corresponding truncation information. And define its "live" edges;

[0067] Then, perform forward recursive calculations to obtain... in Initialize to 0≤t <d c -1; Calculate the corresponding truncation information according to the truncation strategy. And define its "live" state;

[0068] Then, a backward recursive calculation is performed to obtain... in Initialize to d c For values ​​≥t>1, calculate the corresponding truncation information according to the truncation strategy. And define its "live" state;

[0069] Finally, external information is calculated to obtain... Where 0≤t≤d c -1; Calculate the corresponding truncation information according to the truncation strategy. And define its "live" edges;

[0070] Correct external information, if external information The corrected external information is Otherwise, the corrected external information is Where ε is the correction coefficient.

[0071] S25: Intermediate Node H ij Receiver Inspection Node C i The message passed on Calculate its permutation information And pass it to the adjacent variable node;

[0072] In step S25 of the iterative decoding: intermediate node H ij For verification node C i Passed to variable node V j The information is replaced to obtain the replaced information.

[0073] S26: Update variable node information

[0074] In step S26 of the iterative decoding: during the k-th iteration, the variable node V... j (0≤j≤n-1) Receive from channel Ch j and its adjacent intermediate node H ij The received information allows us to obtain updated information about the variable nodes. in, Initialized to 0, the first term is the initial channel information, which remains unchanged during the iteration process; the second term is the sum of external information from adjacent check nodes, which jointly pushes the reliability of the variable node to shift in the correct direction.

[0075] After the information is updated, the iteration count increments by one unit. If the maximum number of iterations I is reached... max If the condition is met, the iteration exits and the codeword v is output; otherwise, the iteration continues.

[0076] The Normal graph and the calculation of initial channel information involved in this invention will be described in further detail below.

[0077] Finite field F q (q=2 t An (n,k) multivariate LDPC code on a given surface can be represented by an m x n parity check matrix H = (h... ij ) m×n (h ij ∈F q To represent this, we define the subscript set N. i ={j:0≤j≤n-1,h i,j Let {≠0} represent the set of non-zero elements in the i-th row of matrix H; define the subscript set M. j ={i:0≤i≤m-1,h i,j ≠0} is used to represent the set of non-zero elements in the j-th column of matrix H.

[0078] The parity-check matrix H of a multivariate LDPC code can also be used as follows: Figure 2 The Normal graph shown below is described, and its main characteristics are as follows:

[0079] 1) In a normal graph, edges represent random variables. The edges between channels and variable nodes are denoted by Ch. j (0≤j≤n-1) represents the edge between the variable node and the intermediate node, denoted by X. ij The edge between the intermediate node and the check node is represented by Y. ij express;

[0080] 2) Normal graphs have three types of nodes: among which, Representative variable node V j (0≤j≤n-1), each node corresponds to each column in the H matrix; This represents the verification node C. i (0≤i≤m-1), each node corresponds to each row in the H matrix; when h ij When ≠0, introduce an intermediate node H. ij ;

[0081] 3) Nodes represent certain constraints. Among them, variable nodes satisfy constraint X. ij =V j (i∈M j The verification node meets the constraints. Intermediate nodes satisfy the constraints or

[0082] Suppose the received real number sequence is y = (y0, y1, ..., y2) n-1 ),in The channel transmits to variable node V j The reliability of the real-valued information vector is defined as follows:

[0083]

[0084] where z (i) is the i-th bit of the field element z. After quantization, the corresponding integer information vector reliability can be obtained The quantization method is as follows:

[0085]

[0086] where Δ is the quantization interval and b is the number of quantization bits.

[0087] Secondly, describe the truncation strategy based on dynamic thresholds.

[0088] During the iterative decoding of the extended min-sum (EMS) algorithm, for the q-dimensional information vectors on the edges entering the check nodes, only a fixed n m (n m (n < q) of the most reliable values are selected, thus effectively reducing the computational amount of the check nodes. Based on this, Ma et al. re-described it based on the Trellis diagram and combined with the idea of the BCJR algorithm for reducing search, and proposed an extended min-sum (T-EMS) decoding algorithm based on a fixed threshold truncation strategy. During the decoding iteration process, the T-EMS algorithm only retains the "live" states and "live" edges with reliabilities greater than this threshold, and obtains performance close to the classical QSPA algorithm, but its average complexity is much lower. However, the fixed threshold value limits the flexibility of the algorithm and still has a relatively high complexity, thus restricting its application in many scenarios.

[0089] For the T-EMS algorithm, any variable node is selected, and its iterative output in different data frame input cases is analyzed. The relationship between the difference between the maximum reliability and the second maximum reliability of its information vector and the hard decision of the symbol can be observed, showing the following rule: when the difference is relatively large, the iterative decision result of the symbol of the variable node generally alternates between the finite field elements corresponding to a few of the largest reliabilities in the initial reliability of the information vector. The larger the difference, the smaller the range of this change, that is, it changes between the finite field elements corresponding to fewer of the largest reliabilities. On the contrary, when the difference is relatively small, during the hard decision decoding of the variable node, it will change between the finite field elements corresponding to more of the largest reliabilities.

[0090] Based on the above analysis, it can be seen that when the difference is relatively large, the information is mainly concentrated on a few components, so fewer components can be selected when filtering. Conversely, when the difference is relatively small, the information is distributed across more components, so more components should be retained when filtering. Therefore, when filtering information vector components, the distribution characteristics of the reliability of each information vector should be considered to dynamically select an appropriate number of components to participate in information calculation in order to obtain better results. To this end, the above idea is combined with a truncation strategy based on a fixed threshold, and a dynamic threshold truncation strategy based on the iterative characteristics of information vector reliability is proposed.

[0091] Based on the dynamic threshold truncation strategy of information vector reliability iteration characteristics, the corresponding finite field elements are partitioned and filtered to obtain two sets S. DT and And satisfy The set S corresponding to this strategy DT The definition is as follows:

[0092] S DT ={z∈F q |R Z (z) Exceeds a certain preset parameter T DT} (3)

[0093] Wherein, parameter T DT The selection method is as follows:

[0094]

[0095] Among them, R 1 Z (z) and R 2 Z (z) represents the information vector R. Z The maximum and second-highest reliability in (z) It is a difference parameter to be determined.

[0096] T1 DT and T2 DT The preset threshold parameter (T1) DT >T2 DT The value can be determined through simulation. When the difference exceeds the preset parameter value, the selected threshold value is T1. DT If its value is large, then the set S DT The number of filtered components should be smaller; conversely, when the difference is less than the preset parameter, the selected threshold value is T2. DT If its value is small, then set S DT The number of filtered components should be greater. In practice, the threshold value will vary depending on the state and edge, i.e., the state threshold value. ( and and side threshold ( and ).

[0097] Based on this, and using set S DT For R Z (z) Perform truncation to obtain truncated information. Its definition is as follows:

[0098]

[0099] in, Let set S DT The minimum information reliability corresponding to the elements of the finite field.

[0100] Finally, based on the Normal graph, the steps of information transmission and processing between nodes in the multivariate LDPC decoding method based on the dynamic threshold truncation strategy are described.

[0101] 1. Variable node information processing

[0102] Variable node V j (0≤j≤n-1) Receive from channel Ch j and its adjacent intermediate node H ij The received information is updated in the following manner during the k-th iteration.

[0103]

[0104] in, Initialize to 0.

[0105] After the information update is complete, variable node V j A hard decision shall be made in the following manner:

[0106]

[0107] Variable node V j The updated information is then passed to the adjacent intermediate node H. ij The calculation method is as follows:

[0108]

[0109] 2. Intermediate node H ij Calculate permutation information

[0110] intermediate node H ij Receive from neighboring variable node V j The message conveyed Then, the information is replaced and passed to the verification node C. i The permutation information is calculated as follows:

[0111]

[0112] 3. Verification node information processing

[0113] For verification node C i (0≤i≤m), let its degree be d. c The edge it is connected to is Y. ij (j∈N i Let α t =(a t (0),a t (1),…,a t (q-1)) represents the forward recursive vector, β t =(β) t (0),β t (1),…,β t (q-1) represents the backward recursive vector. During the update, the verification node C is processed according to the following recursive algorithm. i External information Perform the calculation.

[0114] 1) First, perform preprocessing.

[0115] Verification node C i Receive the adjacent intermediate node H ij The message passed on Based on the truncation strategies defined in equations (3) and (5), the corresponding truncation information is calculated. Define the live edges;

[0116] 2) Forward recursive calculation

[0117]

[0118] in Initialize to 0≤t <d c -1. Calculate the corresponding truncation information according to the truncation strategies defined in equations (3) and (5). Define the state of being alive;

[0119] 3) Backward recursive calculation

[0120]

[0121] in Initialize to d c≥t>1. Calculate the corresponding truncation information according to the truncation strategies defined in equations (3) and (5). Define the state of being alive.

[0122] 4) Calculation of external information

[0123]

[0124] Where 0≤t≤d c -1. Calculate the corresponding truncation information according to the truncation strategies defined in equations (3) and (5). Define the live edges.

[0125] 5) Revise external information

[0126]

[0127] Here, ε is a correction coefficient, which can be optimized using density evolution methods.

[0128] 4. Intermediate node H ij Calculate permutation information

[0129] intermediate node H ij Receive from neighboring verification node C i The message conveyed Then, information is replaced and passed to variable node V. j The permutation information is calculated as follows:

[0130]

[0131] Information transmission between nodes, such as Figure 2 As shown in ①-⑤.

[0132] The multivariate LDPC decoding method based on the dynamic threshold truncation strategy described above is referred to as the DT-EMS method. The specific implementation steps are described below.

[0133]

[0134]

[0135] Then, we analyze the complexity and decoding performance.

[0136] In the decoding method proposed in this invention, only a subset of states / edges satisfying the conditions participate in the relevant operations on the Trellis graph, and the number of these states / edges changes dynamically during the iteration process. Therefore, the complexity of the algorithm also varies. Based on this, similar to the T-EMS decoding method, a complexity ratio is used to analyze the algorithm's complexity. Similarly, states / edges satisfying the constraints are called "live" states and "live" edges.

[0137] make This represents the average number of live states / edges per frame for a given algorithm. The complexity ratio ρ represents the average number of states / edges per frame in the QSPA algorithm, and is specifically defined as follows:

[0138]

[0139] For comparison, the performance of the DT-EMS decoding method proposed in this invention is simulated using two different construction methods for multi-element LDPC codes. The comparison algorithms include the T-EMS algorithm and the QSPA algorithm. The simulation channel is an additive white Gaussian noise (AWGN) channel, using a simple binary phase shift keying (BPSK) modulation scheme. All correction coefficients involved are represented by ε, the quantization parameters are set to Δ = 1 / 64, b = 8, and the maximum number of iterations is set to 50.

[0140] Experiment 1: Select F 16 The (225,173) regular quasi-cyclic LDPC code is constructed based on the finite field method. For the T-EMS algorithm, its correction coefficient ε = 0.6. The DT-EMS decoding algorithm proposed in this invention has a correction coefficient ε = 0.6 and a difference parameter. Threshold parameters

[0141] Decoding performance such as Figure 3 As shown. By Figure 3 It is evident that the decoding performance of the DT-EMS algorithm proposed in this invention is very close to that of the classic QSPA algorithm and T-EMS algorithm (the difference is within 0.1dB); its decoding performance curve shows the same trend as the performance curves of the QSPA algorithm and T-EMS algorithm, at BER / FER=10. -6 No incorrect leveling phenomenon was observed at that time.

[0142] Complexity ratio such as Figure 4 As shown. By Figure 4As can be seen, the complexity of the DT-EMS algorithm proposed in this invention is significantly lower than that of the QSPA algorithm. Compared with the T-EMS algorithm based on a fixed threshold truncation strategy, the algorithm proposed in this invention achieves an even lower average decoding complexity. For example, at a signal-to-noise ratio (SNR) of 3.0 dB, the complexity ratio of the DT-EMS algorithm proposed in this invention is approximately 0.3, representing a reduction in decoding complexity of about 19% while maintaining essentially unchanged decoding performance.

[0143] Example 2: Choose F 64 The (142,71) multi-element LDPC code is constructed based on the PEG method. For the T-EMS algorithm, the correction coefficient ε = 0.9. The DT-EMS algorithm proposed in this invention has a correction coefficient ε = 0.9 and a difference parameter. Threshold parameters

[0144] Decoding performance such as Figure 5 As shown. By Figure 5 It is evident that the decoding performance of the DT-EMS algorithm proposed in this invention is very close to that of the classic QSPA algorithm and the T-EMS algorithm (the difference is within 0.1dB); their curve trends are consistent, especially at BER / FER = 10. -6 No incorrect leveling phenomenon was observed at that time.

[0145] Complexity ratio such as Figure 6 As shown. By Figure 6 It is evident that the complexity of the DT-EMS algorithm proposed in this invention is significantly lower than that of the QSPA algorithm. Compared to the T-EMS algorithm with a fixed threshold truncation strategy, the algorithm proposed in this invention achieves an even lower average decoding complexity. For example, at a signal-to-noise ratio of 1.4 dB, the complexity ratio of the algorithm proposed in this invention is 0.35, representing a reduction of approximately 10% in decoding complexity while maintaining essentially unchanged decoding performance.

[0146] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A multivariate LDPC decoding method based on a dynamic threshold truncation strategy, characterized in that, The method includes: S1 initialization: Set quantization parameters Δ and b, and correction coefficient ε; set threshold. Set the difference parameter Let the number of iterations k = 0, and set the maximum number of iterations I. max ; Calculate initial channel information S2 iterative decoding: k≤I max When this happens, perform the following steps: S21: Calculate the hard decision sequence for the k-th iteration, and obtain... S22: Calculate the syndrome in like Then exit the iteration and output the codeword v; otherwise, execute S23. S23: Intermediate node H ij Receive information from the variable section Calculate permutation information And pass it to the verification node C. i ; S24: Verification Node C i For intermediate node H ij The reliability vector R of each q-dimensional integer information passed in z (z)(z∈F q )(Right now First, based on the difference between the maximum and second-largest values ​​of their respective reliability components and the preset difference parameter... Dynamically determine the threshold value T DT Secondly, based on the threshold value T DT For information vector R z (z)(z∈F q By partitioning and filtering the elements of the finite field, we obtain two sets S. DT and Then based on set S DT For information vector R z (z) Perform truncation to obtain truncated information. (Right now Based on this, the verification node C is calculated using a recursive method. i The external information and corresponding truncation information are obtained and corrected to obtain the verification node C. i External information S25: Intermediate Node H ij Receiver Inspection Node C i The message passed on Calculate its permutation information And pass it to the adjacent variable node; S26: Update variable node information The iteration count increments by one unit; if the maximum number of iterations I is reached... max If the condition is met, the iteration exits and the decoding result is output; otherwise, the iteration continues and S21 is executed.

2. The multivariate LDPC decoding method based on a dynamic threshold truncation strategy as described in claim 1, characterized in that, In the initialization of step S1: Let the received sequence of real numbers be y = (y0, y1, ..., y2). n-1 ),in Define the channel and pass it to the variable node V j Reliability of real information vectors (0≤j≤n-1) Among them, z (i) Let the i-th bit of the field element z be quantized; then quantization is performed when... At that time, Quantification when At that time, Quantification when At that time, Quantification Where Δ is the quantization interval and b is the number of quantization bits, the corresponding integer information vector reliability is obtained.

3. The multivariate LDPC decoding method based on a dynamic threshold truncation strategy as described in claim 1 or 2, characterized in that, In step S21 of the iterative decoding: In the kth iteration, the variable node V j (0≤j≤n-1) Perform a hard decision and obtain in For variable node V j The information reliability vector is (0≤j≤n-1).

4. The multivariate LDPC decoding method based on a dynamic threshold truncation strategy as described in claim 1 or 2, characterized in that, In step S22 of the iterative decoding: Finite field F q (q=2 t An (n,k) multivariate LDPC code on a given surface can be represented by an m x n parity check matrix H = (h... ij ) m×n (h ij ∈F q To represent, define the subscript set N. i ={j:0≤j≤n-1,h i,j ≠0} is the set of non-zero elements in the i-th row of matrix H; define the subscript set M. j ={i:0≤i≤m-1,h i,j ≠0} is the set of non-zero elements in the j-th column of matrix H; The decision sequence is obtained in the k-th iteration. Then, a concurrent verification is performed, which requires that the constraints be met. To prove whether the current codeword is correct, the syndrome is calculated. in Represents the i-th verification node C i (0≤i≤m-1) adjoint information, 5. The multivariate LDPC decoding method based on a dynamic threshold truncation strategy as described in claim 1 or 2, characterized in that, In step S23 of the iterative decoding: intermediate node H ij Receive from neighboring variable node V j The message conveyed in Then it is permuted to obtain permutation information. And pass it to the verification node C. i .

6. The multivariate LDPC decoding method based on a dynamic threshold truncation strategy as described in claim 1 or 2, characterized in that, In step S24 of the iterative decoding: In the k-th iteration, the verification node C i Receive intermediate node H ij The reliability vector R of the transmitted q-dimensional integer information z (z)(z∈F q )(Right now Let R 1 Z (z) and R 2 Z (z) represents the information vector R. Z The maximum and second-highest reliability in (z) The threshold value T is a parameter to be determined, and is dynamically selected based on the magnitude of the reliability difference. DT The value; If its maximum reliability With the second highest reliability The difference between them is greater than or equal to the preset difference parameter. Then the threshold T DT Take a larger threshold; that is, when At that time, the threshold is dynamically selected to be a larger threshold T1. DT (T DT =T1 DT This allows fewer components to participate in the calculation; If its maximum reliability With the second highest reliability The difference between them is less than the preset difference parameter. Threshold T DT Take the smaller threshold; that is, when At that time, the threshold value T DT Take the smaller threshold T2 DT (T DT =T2 DT (), relatively conservatively increased the amount of ingredients; For information vector R z (z)(z∈F q )(Right now Based on the distribution characteristics of its reliability, its finite field elements can be partitioned and filtered to obtain two sets S. DT and And satisfy S DT Defined as S DT ={z∈F q |R Z (z) Exceeds a certain preset parameter T DT }, where parameter T DT The dynamic threshold value T is based on the reliability difference characteristic. DT Different values ​​are selected based on the state and the edge, i.e., the state threshold value T. s DT and the side threshold value T b DT ; For information vector R z (z), combined with set S DT For information vector R z (z) is truncated if the finite field element z∈S DT Calculate its corresponding truncation information. Otherwise, its corresponding truncation information in Let set S DT The minimum information reliability corresponding to the elements of the finite field.

7. The multivariate LDPC decoding method based on a dynamic threshold truncation strategy as described in claim 1 or 2, characterized in that, In step S24 of the iterative decoding: For verification node C i (0≤i≤m), let its degree be d. c The edge it is connected to is Y. ij (j∈N i Let α t =(a t (0),a t (1),…,a t (q-1)) represents the forward recursive vector, β t =(β) t (0),β t (1),…,β t (q-1) represents the backward recursive vector, which is updated by recursively updating the verification node C according to the following method. i External information Perform calculations; First, preprocessing is performed, and node C is verified according to the truncation strategy. i For intermediate node H ij The message passed on Preprocessing is performed to calculate the corresponding truncation information. And define its "live" edges; Then, perform forward recursive calculations to obtain... in Initialize to Calculate the corresponding truncation information based on the truncation strategy. And define its "live" state; Then, a backward recursive calculation is performed to obtain... in Initialize to Calculate the corresponding truncation information based on the truncation strategy. And define its "live" state; Finally, external information is calculated to obtain... Where 0≤t≤d c -1; Calculate the corresponding truncation information according to the truncation strategy. And define its "live" edges; Correct external information, if external information The corrected external information is Otherwise, the corrected external information is Where ε is the correction coefficient.

8. The multivariate LDPC decoding method based on a dynamic threshold truncation strategy as described in claim 1 or 2, characterized in that, In step S25 of the iterative decoding: intermediate node H ij For verification node C i Passed to variable node V j The information is replaced to obtain the replaced information.

9. The multi-element LDPC decoding method based on a dynamic threshold truncation strategy as described in claim 1 or 2, characterized in that, In step S26 of the iterative decoding: In the k-th iteration, the variable node V j (0≤j≤n-1) Receive from channel Ch j and its adjacent intermediate node H ij The received information allows us to obtain updated information about the variable nodes. in, Initialized to 0, the first term is the initial channel information, which remains unchanged during the iteration process; the second term is the sum of external information from adjacent check nodes, which jointly pushes the reliability of the variable node to shift in the correct direction. After the information is updated, the iteration count increments by one unit. If the maximum number of iterations I is reached... max If the condition is met, the iteration exits and the codeword v is output; otherwise, the iteration continues.

Images