Low-complexity decoding method of LDPC-Hadamard code based on prototype graph

Abstract

The invention discloses a low-complexity decoding method of an LDPC-Hadamard code based on a prototype graph, and belongs to the field of digital signal processing. The implementation method comprises the following steps of: performing LDPC (Low Density Parity Check) coding on information bits, and coding a constraint relationship of check nodes of the LDPC code into a Hadamard code to obtain a prototype graph of the LDPC-Hadamard code; after coded code words are sent and received through a channel, a PVN node and an HCN node are initialized by using the received information; carrying out Hadamard decoding by using a symbol-by-symbol maximum posterior probability decoding algorithm, reducing decoding complexity by using approximate operation of DFHT, and transmitting information obtained after decoding to a PVN node; summing the updated HCN node information and the last iteration information, and judging and decoding by using a summing result; and performing decoding judgment on the PVN information, and performing decoding. According to the method, LDPC coding, Hadamard coding and Max-Log approximate calculation methods are combined, the decoding complexity is reduced, and the stability and reliability of a communication system are enhanced.

Description

Technical Field

[0001] The invention discloses a low-complexity decoding method of an LDPC-Hadamard code based on a prototype graph, relates to an encoding and decoding algorithm of the LDPC-Hadamard code and a dual fast Hadamard transform (DFHT) algorithm, and belongs to the field of digital signal processing. Background Art

[0002] In the field of communications, low bit rate systems have attracted much attention due to their advantages in improving signal transmission reliability. Low bit rate systems increase redundancy by reducing the number of information bits per data unit, thereby improving the reliability of data transmission in environments with signal attenuation, high bit error rates or unstable channel conditions. This feature makes low bit rate systems particularly important in fields such as deep space communications, satellite communications, and mobile communications.

[0003] However, one of the main challenges facing low-code rate systems is the increase in decoding complexity. Due to the increased redundancy, the decoding process needs to process more data, resulting in a large consumption of computing resources. This is particularly prominent in resource-constrained environments, such as in mobile devices or remote communication systems, where high decoding complexity may lead to increased power consumption and processing delays. Based on this, this patent proposes a low-complexity decoding algorithm for LDPC-Hadamard codes based on prototype graphs. The core of the algorithm is to reduce the computational complexity of the decoding process through algorithm optimization and mathematical simplification, while maintaining a high level of error correction performance. By reducing the required computing resources and processing time, the algorithm is suitable for resource-constrained low-code rate communication systems, and can improve the overall system efficiency without sacrificing reliability. Summary of the invention

[0004] The purpose of the present invention is to provide a low-complexity decoding method of LDPC-Hadamard code based on a prototype graph, which utilizes the error correction capability of LDPC code close to the Shannon limit and the low code rate structure of Hadamard code to achieve low code rate and high coding gain. LDPC-Hadamard code can achieve low code rate and high coding gain by replacing the parity check of LDPC code with Hadamard constraint and attaching additional Hadamard variable nodes. During decoding, the LDPC-Hadamard code is decoded using the LLR-BP algorithm, and the dual fast Hadamard transform (DFHT) algorithm is used for verification during the decoding process, and the decoding operation process is approximated to achieve low-complexity decoding.

[0005] The object of the present invention is achieved through the following technical solutions.

[0006] The present invention discloses a low-complexity decoding method of an LDPC-Hadamard code based on a prototype graph, comprising the following steps:

[0007] Step 1: Encode the data with LDPC-Hadamard code, encode the information bits with LDPC code, and then further encode the constraint relationship of the check node of the LDPC code into Hadamard code to obtain the prototype graph of the LDPC-Hadamard code.

[0008] The Hadamard matrix is ​​an orthogonal matrix consisting of only two elements {+1, -1}. The n×n Hadamard matrix is ​​constructed recursively, where n=2 r , r is the order of the Hadamard matrix.

[0009]

[0010] The rows and columns of the Hadamard matrix are composed of orthogonal code groups. H represents a length of 2 r , Hadamard matrix carrying (r+1) bits of information, the codeword set is composed of ±H n The column structure is constructed using {±h j ∶j=0,1,...,2 r -1}. In Hadamard coding, the codeword consists of the original information bits, whose index is {0,1,2,4,...,2 r -1}.

[0011] According to the Hadamard coding rule, when r = 2, the generator matrix of the Hadamard code is:

[0012]

[0013] The prototype graph of LDPC-Hadamard code consists of a set of variable nodes PVN and a set of Hadamard check nodes HCN. There is an edge connection between the two sets of nodes PVN and HCN. Let the number of PVN be n and the number of HCN be m. Then the prototype graph is represented by a base matrix B of size m×n. m×nRepresents. Each PVN corresponds to a column of the basis matrix, and each HCN corresponds to a row of the basis matrix. The (i,j)th item of the basis matrix represents the number of edges connecting the i-th PVN and the j-th HCN in the prototype graph. Each SPC corresponding to the HCN is further encoded into a Hadamard code to obtain the prototype graph of the LDPC-Hadamard. The derived Hadamard parity bits are represented as level 1 Hadamard variable nodes (D1H-VN), and the level 1 Hadamard variable nodes are appended to the prototype graph to obtain the final prototype graph of the LDPC-Hadamard code.

[0014] Step 2: After the encoded codeword is sent and received through the channel, the PVN node and HCN node are initialized with the received information.

[0015] After completing the LDPC-Hadamard encoding according to step 1, the encoded LDPC-Hadamard codeword is sent through the AWGN channel. The received codeword is matched one-to-one with the PVN and sent to the HCN to which each PVN node is connected. That is:

[0016]

[0017] in represents the LLR value of the information transmitted by the channel to the β-th PVN (β=0,1,…N); Represents the LLR values ​​of the information sent from the βth PVN to the αth HCN (α=0,1…M; β=0,1…N).

[0018] The LDPC-Hadamard decoder consists of two parts: a repetition decoder and a Hadamard decoder. A Hadamard decoder is used for check node processing, and Hadamard decoding is performed using a symbol-by-symbol maximum a posteriori probability decoding algorithm. The repetition decoder is the same as the variable node processor used in the LDPC decoder.

[0019] Step 3: HCN node information processing, using the symbol-by-symbol maximum a posteriori probability decoding algorithm for Hadamard decoding, and using the DFHT approximation operation to reduce the decoding complexity, the decoded information is passed to the PVN node.

[0020] The HCN node uses a Hadamard decoder to perform Hadamard decoding using the symbol-by-symbol maximum a posteriori probability decoding algorithm. When the HCN node of the LDPC-Hadamard code processes information, equation (4) is used for verification:

[0021]

[0022] in A vector consisting of LLR values ​​representing the information of each D1H-VNs connected to the αth HCN (α=0,1,…M); It represents the LLR value obtained after the αth HCN verifies the information sent to the βth PVN; P(α) is the set of PVNs connected to the αth HCN.

[0023] It is a transformation involving FHT and DFHT operations. When doing DFHT processing, the original formula is as follows:

[0024]

[0025] in:

[0026]

[0027] Formula (5) requires multiple multiplications and pairing operations, which can be approximated as follows:

[0028] ln(e a +e b )≈max(a,b)(6)

[0029] The generalized form of formula (6) is:

[0030]

[0031] According to formula (6) and (7), formula (5) is simplified to the following form:

[0032]

[0033] Update information according to formula (8):

[0034]

[0035] in represents the a posteriori LLR value of the HCN information received by the βth PVN (β=0,1,…N); Represents the LLR values ​​of the information sent from the αth HCN to the βth PVN (α=0,1…M; β=0,1…N).

[0036] That is, according to the HCN node information processing of formula (1), the HCN node information used to update the PVN node information is obtained.

[0037] Step 4: PVN node information processing, using the updated HCN node information, summing it with the information of the previous iteration, and using the sum result to decide the decoding.

[0038] According to step 3, the HCN node information is updated and then returned to the PVN node.

[0039]

[0040] This information Used to determine the codeword. to continue iterating.

[0041]

[0042] H(β) is the set of HCNs connected to the βth PVN.

[0043] Step 5: Decode the PVN information. If the value is greater than 0, the code is judged as 1, otherwise it is judged as 0.

[0044] Step 6: According to HC T =0 or the maximum number of iterations determines whether to continue iterative decoding or end decoding.

[0045] If HC T = 0 or the maximum number of iterations is reached, the decoding ends. Otherwise, the iteration continues from step 3.

[0046] Beneficial effects:

[0047] 1. A low-complexity decoding method of LDPC-Hadamard code based on a prototype graph disclosed in the present invention utilizes the high error correction performance of LDPC code, the grid structure of Hadamard code, and the DFHT algorithm with simplified input to significantly reduce the complexity of the decoding algorithm.

[0048] 2. The present invention discloses a low-complexity decoding method for LDPC-Hadamard codes based on a prototype graph, which adopts a DFHT algorithm with simplified input to reduce the items in the amount of calculation that grow exponentially with the coding parameters to constant terms, and adopts Max-Log approximation to transform multiplication and exponential operations into simple addition and maximum value operations, thereby reducing the complexity of decoding and enhancing the stability and reliability of the communication system.

[0049] 3. The present invention discloses a low-complexity decoding method of LDPC-Hadamard code based on a prototype graph. On the basis of achieving beneficial effects 1 and 2, the low code rate and high coding gain are achieved by utilizing the error correction capability of LDPC code close to the Shannon limit and the low code rate structure of Hadamard code. LDPC-Hadamard code is formed by replacing the parity check of LDPC code with Hadamard constraint and attaching additional Hadamard variable nodes. During decoding, an LLR-BP algorithm similar to that used in LDPC code decoding is used to change the parity check of LDPC code to the check of Hadamard code. During verification, a dual fast Hadamard transform (DFHT) algorithm is used, and the operation process therein is approximated to achieve low-complexity decoding. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] In order to more clearly illustrate the technical solution of the present invention, the following is a brief introduction to the drawings required for use in the present invention. The drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can also be obtained based on these drawings without creative work.

[0051] Figure 1 A prototype diagram of LDPC-Hadamard code.

[0052] Figure 2 It is a decoding structure used for PVN information processing.

[0053] Figure 3 It is a decoding structure used for HCN information processing.

[0054] Figure 4 The present invention is a flowchart of a low-complexity decoding method of LDPC-Hadamard codes based on a prototype graph. DETAILED DESCRIPTION

[0055] Embodiment 1:

[0056] like Figure 1 The present embodiment discloses a low-complexity decoding method for LDPC-Hadamard codes based on a prototype graph. The specific implementation process is as follows Figure 4 As shown, the steps are as follows:

[0057] Step 1: Encode the data with LDPC-Hadamard code, encode the information bits with LDPC code, and then further encode the constraint relationship of the check node of the LDPC code into Hadamard code to obtain the prototype graph of the LDPC-Hadamard code.

[0058] The Hadamard matrix is ​​an orthogonal matrix consisting of only two elements {+1, -1}. The n×n Hadamard matrix is ​​constructed recursively, where n=2 r , r is the order of the Hadamard matrix.

[0059]

[0060] The rows and columns of the Hadamard matrix are composed of orthogonal code groups. H represents a length of 2 r , Hadamard matrix carrying (r+1) bits of information, the codeword set is composed of ±H n The column structure is constructed using {±h j ∶j=0,1,...,2 r -1}. In Hadamard coding, the codeword consists of the original information bits, whose index is {0,1,2,4,...,2 r -1}.

[0061] According to the Hadamard coding rule, when r = 2, the generator matrix of the Hadamard code is:

[0062]

[0063] The prototype graph of LDPC-Hadamard code consists of a set of variable nodes PVN and a set of Hadamard check nodes HCN. There is an edge connection between the two sets of nodes PVN and HCN. Let the number of PVN be n and the number of HCN be m. Then the prototype graph is represented by a base matrix B of size m×n. m×n Represents. Each PVN corresponds to a column of the basis matrix, and each HCN corresponds to a row of the basis matrix. The (i,j)th item of the basis matrix represents the number of edges connecting the i-th PVN and the j-th HCN in the prototype graph. Each SPC corresponding to the HCN is further encoded into a Hadamard code to obtain the prototype graph of the LDPC-Hadamard. The derived Hadamard parity bits are represented as level 1 Hadamard variable nodes (D1H-VN), and the level 1 Hadamard variable nodes are appended to the prototype graph to obtain the final prototype graph of the LDPC-Hadamard code.

[0064] Step 2: After the encoded codeword is sent and received through the channel, the PVN node and HCN node are initialized with the received information.

[0065] After completing the LDPC-Hadamard encoding according to step 1, the encoded LDPC-Hadamard codeword is sent through the AWGN channel. The received codeword is matched one-to-one with the PVN and sent to the HCN to which each PVN node is connected. That is:

[0066]

[0067] in represents the LLR value of the information transmitted by the channel to the β-th PVN (β=0,1,…N); Represents the LLR values ​​of the information sent from the βth PVN to the αth HCN (α=0,1…M; β=0,1…N).

[0068] The LDPC-Hadamard decoder consists of two parts: a repetition decoder and a Hadamard decoder. A Hadamard decoder is used for check node processing, and Hadamard decoding is performed using a symbol-by-symbol maximum a posteriori probability decoding algorithm. The repetition decoder is the same as the variable node processor used in the LDPC decoder.

[0069] Step 3: HCN node information processing, using the symbol-by-symbol maximum a posteriori probability decoding algorithm for Hadamard decoding, and using the DFHT approximation operation to reduce the decoding complexity, the decoded information is passed to the PVN node.

[0070] The HCN node uses a Hadamard decoder to perform Hadamard decoding using the symbol-by-symbol maximum a posteriori probability decoding algorithm. When the HCN node of the LDPC-Hadamard code processes information, equation (4) is used for verification:

[0071]

[0072] in A vector consisting of LLR values ​​representing the information of each D1H-VNs connected to the αth HCN (α=0,1,…M); It represents the LLR value obtained after the αth HCN verifies the information sent to the βth PVN; P(α) is the set of PVNs connected to the αth HCN.

[0073] It is a transformation involving FHT and DFHT operations. When doing DFHT processing, the original formula is as follows:

[0074]

[0075] in:

[0076]

[0077] Formula (5) requires multiple multiplications and pairing operations, which can be approximated as follows:

[0078] ln(e a +e b )≈max(a,b)(6)

[0079] The generalized form of formula (6) is:

[0080]

[0081] According to formula (6) and (7), formula (5) is simplified to the following form:

[0082]

[0083] Update information according to formula (8):

[0084]

[0085] in represents the a posteriori LLR value of the HCN information received by the βth PVN (β=0,1,…N); Represents the LLR values ​​of the information sent from the αth HCN to the βth PVN (α=0,1…M; β=0,1…N).

[0086] That is, according to the HCN node information processing of formula (1), the HCN node information used to update the PVN node information is obtained.

[0087] Step 4: PVN node information processing, using the updated HCN node information, summing it with the information of the previous iteration, and using the sum result to decide the decoding.

[0088] According to step 3, the HCN node information is updated and then returned to the PVN node.

[0089]

[0090] This information Used to determine the codeword. to continue iterating.

[0091]

[0092] H(β) is the set of HCNs connected to the βth PVN.

[0093] Step 5: Decode the PVN information. If the value is greater than 0, the code is judged as 1, otherwise it is judged as 0.

[0094] Step 6: According to HCT =0 or the maximum number of iterations determines whether to continue iterative decoding or end decoding.

[0095] If HC T = 0 or the maximum number of iterations is reached, the decoding ends. Otherwise, the iteration continues from step 3.

[0096] The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A low-complexity decoding method for LDPC-Hadamard codes based on a prototype graph, characterized in that: The following steps are included: Step 1: Encode the data using LDPC-Hadamard code, encode the information bits using LDPC code, and then further encode the constraint relationship of the check nodes of the LDPC code into Hadamard code to obtain the prototype graph of the LDPC-Hadamard code; Step 2: After the encoded codeword is sent and received through the channel, the PVN node and HCN node are initialized with the received information; Step 3: HCN node information processing, using the symbol-by-symbol maximum a posteriori probability decoding algorithm to perform Hadamard decoding, and using the DFHT approximation operation to reduce the decoding complexity, and the decoded information is passed to the PVN node; Step 4: PVN node information processing, using the updated HCN node information and the information of the previous iteration to sum, and using the sum result to determine the decoding; Step 5: Decode the PVN information. If the value is greater than 0, the code is judged as 1, otherwise it is judged as 0; Step 6: According to HC T =0 or the maximum number of iterations determines whether to continue iterative decoding or end decoding.

2. The low complexity decoding method of LDPC-Hadamard code based on prototype graph as claimed in claim 1, characterized in that: The implementation method of step one is: The Hadamard matrix is ​​an orthogonal matrix consisting of only two elements {+1, -1}. The n×n Hadamard matrix is ​​constructed recursively, where n=2 r , r is the order of the Hadamard matrix; The rows and columns of the Hadamard matrix are composed of orthogonal code groups; H represents a length of 2 r , Hadamard matrix carrying (r+1) bits of information, the codeword set is composed of ±H n The column structure is constructed using {±h j ∶j=0,1,...,2 r -1}; in Hadamard coding, the codeword includes the original information bits, whose index is {0,1,2,4,...,2 r -1}; According to the Hadamard coding rule, when r = 2, the generator matrix of the Hadamard code is: The prototype graph of LDPC-Hadamard code consists of a set of variable nodes PVN and a set of Hadamard check nodes HCN. There is an edge connection between the two sets of nodes PVN and HCN. Let the number of PVN be n and the number of HCN be m. Then the prototype graph uses a base matrix B of size m×n. m×n Representation; each PVN corresponds to a column of the basis matrix, and each HCN corresponds to a row of the basis matrix; the (i, j)th item of the basis matrix represents the number of edges connecting the i-th PVN and the j-th HCN in the prototype graph; each SPC corresponding to the HCN is further encoded into a Hadamard code to obtain the prototype graph of the LDPC-Hadamard code; the derived Hadamard parity bits are represented as a level 1 Hadamard variable node D1H-VN, and the level 1 Hadamard variable node is appended to the prototype graph to obtain the final prototype graph of the LDPC-Hadamard code.

3. The low complexity decoding method of LDPC-Hadamard code based on prototype graph as claimed in claim 1, characterized in that: The implementation method of step 2 is: After completing the LDPC-Hadamard encoding according to step 1, the encoded LDPC-Hadamard codeword is sent through the AWGN channel; the received codeword is matched with the PVN one by one and sent to the HCN to which each PVN node is connected; Right now: in represents the LLR value of the information transmitted by the channel to the β-th PVN (β=0,1,…N); represents the LLR value of the information sent from the βth PVN to the αth HCN (α=0,1…M; β=0,1…N); The LDPC-Hadamard decoder consists of two parts: a repetition decoder and a Hadamard decoder. The check node processing uses a Hadamard decoder and uses a symbol-by-symbol maximum a posteriori probability decoding algorithm for Hadamard decoding. The repetition decoder is the same as the variable node processor used in the LDPC decoder.

4. The low complexity decoding method of LDPC-Hadamard code based on prototype graph as claimed in claim 3, characterized in that: The implementation method of step three is: The HCN node uses a Hadamard decoder to perform Hadamard decoding using the symbol-by-symbol maximum a posteriori probability decoding algorithm. When the HCN node processes information of the LDPC-Hadamard code, equation (4) is used for verification: in A vector consisting of LLR values ​​representing the information of each D1H-VNs connected to the αth HCN (α=0,1,…M); represents the LLR value obtained after the αth HCN verifies the information sent to the βth PVN; P(α) is the set of PVNs connected to the αth HCN; It is a transformation involving FHT and DFHT operations; when doing DFHT processing, the original formula is as follows: in: Formula (5) requires multiple multiplications and pairing operations, which can be approximated as follows: ln(ie a +e b )≈max(a,b)(6) The generalized form of formula (6) is: According to formula (6) and (7), formula (5) is simplified to the following form: Update information according to formula (8): in represents the a posteriori LLR value of the HCN information received by the βth PVN (β=0,1,…N); represents the LLR value of the information sent from the αth HCN to the βth PVN (α=0,1…M; β=0,1…N); That is, according to formula (10), the HCN node information is processed to obtain the HCN node information used to update the PVN node information.

5. The low complexity decoding method of LDPC-Hadamard code based on prototype graph as claimed in claim 4, characterized in that: The implementation method of step 4 is: Update the HCN node information according to step 3, and then return this information to the PVN node; This information Used to determine codewords; update To continue iterating; H(β) is the set of HCNs connected to the βth PVN.

6. The low complexity decoding method of LDPC-Hadamard code based on prototype graph as claimed in claim 5, characterized in that: The implementation method of step six is: If HC T =0 or the maximum number of iterations is reached, the decoding ends; otherwise, the iteration continues from step 3.

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