Bidirectional symbol level merging ternary belief propagation decoding method based on ternary LDPC (Low Density Parity Check) code

Abstract

The invention discloses a bidirectional symbol level merging ternary belief propagation decoding method based on a ternary LDPC code, and relates to a low-complexity iterative decoding method of a ternary LDPC code word. The problem that the decoding complexity of the ternary LDPC code under an additive white Gaussian noise channel is high is solved. The method comprises the following steps of: decoding a receiving signal corresponding to a ternary LDPC code word corresponding to a ternary symbol sequence code sent by a user, and initializing a zeroth forward probability in a forward probability sequence of an lth CN node in a decoding process; gradually updating the residual forward probabilities in the forward probability sequence corresponding to the CN node from front to back according to the sequence in the forward probability sequence; initializing the < lambda > (1-1) backward probability in the backward probability sequence of the 1th CN node, and gradually updating the residual backward probabilities in the backward probability sequence corresponding to the CN node from back to front according to the sequence in the backward probability sequence; and performing probability updating of the CN and VN nodes based on the updated probability, and calculating a decoding sequence.

Description

Technical Field

[0001] The present invention belongs to the technical field of 6G communication, and relates to a low-complexity iterative decoding method for ternary LDPC codewords. Background Art

[0002] In the current massive access scenario, with the explosive growth of the number of Internet of Things (IoT) devices, the limited spectrum resources have become the key bottleneck restricting the improvement of system performance. For a communication system, effectiveness and reliability, as two major performance indicators, directly affect the communication efficiency and quality of the system. How to improve the communication efficiency through limited spectrum resources while ensuring that the communication quality is within an acceptable range has become the research focus.

[0003] Although the traditional binary transmission system is simple to implement, its spectral efficiency is low, making it difficult to meet the spectral requirements of future massive device access. In contrast, a multi-ary transmission system using multi-ary amplitude shift keying (ASK) modulation can significantly increase the system capacity under the same bandwidth condition. Among them, the ternary amplitude shift keying (3ASK) used in the ternary transmission system introduces a 0 amplitude state. On the premise of maintaining compatibility with the modulation amplitudes (-1, 1) of the binary transmission system, only minimal modification of existing devices is required to achieve a significant 1.58-fold increase in spectral efficiency. This characteristic makes the ternary modulation scheme a potential solution to alleviate the shortage of spectrum resources and optimize the performance of existing communication infrastructure, especially suitable for large-scale IoT deployment scenarios sensitive to hardware modification costs. The ternary transmission system improves the spectral efficiency of the communication system but reduces the reliability of the communication system. Therefore, corresponding error control schemes are needed to further improve the reliability of the ternary transmission system.

[0004] As a channel coding scheme suitable for ternary transmission systems, the ternary LDPC code can correct errors in the received codewords caused by the transmission process at the cost of sacrificing a part of the transmission rate, thereby improving the reliability of the ternary transmission system by adding codeword redundancy. Different from binary LDPC codes, all elements in the ternary LDPC codeword are elements in the Galois field GF(3). Each information bit element corresponds to 1.58 bits of information. For a ternary LDPC code with a code rate of R, the system transmission rate is 1.58R, where 0 < R < 1. Currently, the decoding algorithms for ternary LDPC codes have not been fully studied, and the direct application of the general Q-ary sum-product algorithm (QSPA) for multi-ary LDPC codes has a high complexity.

[0005] Combining ternary LDPC codes with a ternary transmission system can improve the effectiveness of the communication system while ensuring its reliability. These two technologies can solve the problem of spectrum resource shortage in massive access scenarios, lay a solid foundation for future wireless communications, and provide new ideas for improving the spectrum efficiency of communication systems. Summary of the Invention

[0006] The present invention aims to solve the problem of high decoding complexity of ternary LDPC codes in an additive white Gaussian noise channel.

[0007] A bidirectional symbol-level merged ternary belief propagation decoding method based on ternary LDPC codes, comprising:

[0008] The ternary LDPC codeword v corresponding to the ternary symbol sequence of length K sent by the user is modulated and sent, and is received by the receiving end as a signal y=(y0,y1,…,y K-1 ); The code length of the ternary LDPC code is N, and the matrix elements in its R×N dimensional sparse check matrix H over GF(3) are used to indicate whether the l-th CN node is connected to the n-th VN node. The CN node is a check node, and the VN node is a variable node. 0≤l<R, 0≤n<N; the connection set of the CN nodes is represented as in Contains λ connected to the lth CN node l The index of the VN node; the connection set of the VN node is represented as in Contains ρ connected to the nth VN node n The index of the CN node;

[0009] Based on the signal received by the receiving end, let the codeword symbol corresponding to the nth VN node be The channel input prior probability is The codeword symbol Decoding is performed based on the channel input prior probability and the sparse check matrix H:

[0010] 1) Initialize BSM-TBP decoding information: set the number of iterations τ = 0, and give the maximum number of iterations I max ; Initialize VN node probability according to channel input prior probability

[0011] 2) Calculate the forward probability: The symbol corresponding to the lth CN node in the τth iteration is The forward probability sequence is The sequence contains λ l forward probabilities, which are used to calculate the λ passed to the CN node. lThe information of the VN nodes; the symbol corresponding to the initialization l-th CN node is The 0th forward probability in the forward probability sequence is The remaining forward probability is updated step by step from front to back according to the order in the forward probability sequence, which is expressed as: Among them, 0≤l<R, 1≤λ<λ l , represents the additive inverse of b in GF(3), Indicates that in the τth iteration process The symbol passed from the VN node to the lth CN node The corresponding probability; represents the addition operation on GF(3);

[0012] 3) Calculate the backward probability: The symbol corresponding to the lth CN node in the τth iteration is The backward probability sequence of The sequence contains λ l Backward probabilities are used to calculate the λ passed to the CN node. l The information of the VN nodes; the symbol corresponding to the initialization l-th CN node is The λth in the backward probability sequence l -1 backward probability is The remaining backward probability is updated step by step from back to front according to the order in the backward probability sequence, which is expressed as

[0013] 4) Update CN node probability: For all CN nodes, calculate the probability of the node transmitting to the VN node connected to it at the τth iteration

[0014] 5) Update VN node probability: For all VN nodes, calculate the probability of the node transmitting to the CN node connected to it at the τth iteration

[0015] 6) Calculate the decision sequence: Calculate the decision sequence r after the τth iterative decoding = (r0, r1, ..., r N-1 ), symbol within the sequence Where, 0≤n<N, the decision sequence is the output codeword sequence after the τth iterative decoding;

[0016] 7) Determine whether the decoding is successful by the syndrome corresponding to the decision sequence r after the τth iterative decoding. When the decoding is successful, stop the iteration and output the decision sequence r = (r0, r1, ..., r N-1 ).

[0017] Furthermore, for a ternary LDPC code with a code length of N, its R×N dimensional sparse check matrix on GF(3) is R is the length of the LDPC code check information sequence, and the matrix element h l,n ≠0 means that the lth CN node is connected to the nth VN node.

[0018] Furthermore, in the modulation process of the ternary LDPC codeword v corresponding to the ternary symbol sequence of length K sent by the user, the symbol v in the codeword sequence is n To the symbol x in the modulation sequence n The modulation conversion rule between

[0019]

[0020] Among them, 0≤n<N.

[0021] Furthermore, the codeword symbol corresponding to the nth VN node is The channel input prior probability is as follows:

[0022]

[0023] Where σ is the noise variance corresponding to the signal received by the receiver.

[0024] Furthermore, in the τth iteration described in step 4), the node transmits the probability Among them, 0≤l<R, 0≤λ<λ l , represents the forward probability corresponding to b∈GF(3), symbol The corresponding backward probability.

[0025] Furthermore, in the τth iteration described in step 5), the node transmits the probability Among them, 0≤n<N, 0≤ρ<ρ n , is the normalization factor.

[0026] Furthermore, the normalization factor Satisfy the constraints:

[0027] Furthermore, the syndrome s corresponding to the decision sequence r after the τth iterative decoding in step 7) is rH T .

[0028] Furthermore, in the process of determining whether the decoding is successful by the syndrome corresponding to the decision sequence r after the τth iterative decoding in step 7), if the syndrome s is an all-0 vector, it indicates that the decoding is successful.

[0029] Furthermore, in step 7), in the process of determining whether the decoding is successful by the syndrome corresponding to the decision sequence r after the τth iterative decoding, if s is not an all-zero vector and τ<I max -1, then increase τ by 1 and go to step 2); if s is not a vector of all zeros and τ=I max When -1, it means decoding failed.

[0030] The present invention improves the CN node probability update method and adopts a ternary belief propagation algorithm based on bidirectional symbol-level merging. By reusing the operation results, the decoding complexity of the ternary LDPC code can be reduced without sacrificing decoding performance, thereby reducing the decoding delay of the ternary transmission system. The present invention can effectively reduce the CN node probability update complexity when decoding the ternary LDPC code and ensure that its BER performance is consistent with QSPA. The simulation results are as follows: Figure 1 shown. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 The BER and BLER performance diagrams of the ternary LDPC code when the decoding algorithms are BSM-TBP and QSPA. DETAILED DESCRIPTION

[0032] Based on the traditional QSPA decoding algorithm for multi-element LDPC codes, the present invention improves the CN node probability update method for ternary LDPC code decoding, adopts a ternary belief propagation algorithm based on bidirectional symbol-level merging, and reduces the decoding complexity of ternary LDPC codes without losing decoding performance by multiplexing the calculation results, thereby reducing the decoding delay of the ternary transmission system. Specific implementation method one:

[0034] This embodiment is a bidirectional symbol-level combined ternary belief propagation decoding method based on ternary LDPC codes. First, the basic concept of the present invention is explained.

[0035] The concept of ternary LDPC code:

[0036] A ternary LDPC code is a sparse linear block code defined over a Galois Field (GF(3)). A ternary LDPC code of length N is given by the null space of an R×N sparse parity check matrix H over GF(3). When the sparse parity check matrix is full rank, R is the length of the parity check information sequence.

[0037] A ternary LDPC code with a code length of N and an information sequence length of K, i.e., a (N,K) ternary LDPC code, has an information sequence length K and a code length N that can be related by the rank(H) of the sparse check matrix H, i.e., K = N-rank(H). When the check matrix H is full rank, K = NR. Let v be a 1×N codeword vector, and H be an R×N sparse check matrix corresponding to the codeword. The check node constraints of the ternary LDPC code ensure that the codeword syndrome is an all-zero vector, i.e.,

[0038] s=v⊙H T =0

[0039] Here, the operator ⊙ represents the multiplication operation on GF(3).

[0040] Each codeword in the ternary LDPC codebook satisfies the check constraint, and the above constraint can be used to correct a certain amount of errors that occur during the transmission process.

[0041] The concept of ternary transmission system:

[0042] In the ternary transmission system, the user transmits information no longer as a binary information bit sequence, but as a ternary information symbol sequence over GF(3). Each symbol has about 1.58 bits of information. The user sends a ternary symbol sequence at t = (t0, t1, …, t K-1 ), where the symbol t k ∈GF(3), 0≤k<K. Define the ternary LDPC code generator matrix as G, and encode the K-length ternary symbol sequence t to obtain the corresponding ternary LDPC code codeword v=t⊙G, where v is actually a codeword sequence; then perform 3ASK modulation on the symbols in the codeword to obtain the modulated symbol sequence x. For the symbol v in the codeword sequence n To the symbol x in the modulation sequence n The modulation conversion rules between

[0043]

[0044] Among them, 0≤n<N;

[0045] The modulation sequence x is transmitted through the AWGN channel, and the receiving end receives the signal y=(y0,y1,...,y K-1 ) is y=x+z, where z represents additive white Gaussian noise. From this, the codeword symbol corresponding to each VN node can be calculated The channel input prior probability for

[0046]

[0047] in, σ is the noise variance.

[0048] Decoding the received signal using the universal QSPA decoding algorithm for multi-ary LDPC codes requires an exhaustive summation approach to update the check node information. This computational complexity increases exponentially with the check node degree, placing a heavy burden on decoding ternary LDPC codes with large row weights. In fact, during the check node update process provided by the QSPA decoding algorithm, some computational results can be reused. To reduce the decoding complexity of ternary LDPC codes, we implemented state merging in the TSPA check node decoding phase. This reduced the decoding complexity without compromising decoding performance. Based on the channel input prior probability, decoding can be achieved using the Bidirectional Symbol-Level Merged Ternary Belief Propagation (BSM-TBP) algorithm.

[0049] The present embodiment provides a bidirectional symbol-level merged ternary belief propagation decoding method based on ternary LDPC codes, comprising the following steps:

[0050] For a ternary LDPC code, its R×N sparse check matrix H over GF(3) is given as follows:

[0051]

[0052] Among them, the matrix element h l,n ≠0 means that the lth check node (CN) is connected to the nth variable node (VN), 0≤l<R, 0≤n<N.

[0053] Define the degree of the lth CN node as λ l , represents the number of VN nodes connected to the CN node, that is, the number of non-zero elements in the lth row of the test matrix H. Similarly, the degree of the nth VN node is ρ n , represents the number of CN nodes connected to the VN node, that is, the number of non-zero elements in the nth column of the test matrix H. Define the symbol transmitted from the nth VN node to the lth CN node The corresponding probability is The probability that the lth CN node transmits to the nth VN node is σ l,n The connection set of CN nodes is represented as in Contains λ connected to the lth CN node l The connection set of VN nodes is represented as in Contains ρ connected to the nth VN node n The index of the CN node.

[0054] For the ternary transmission system, the codeword symbol corresponding to the nth VN node is defined as The channel input prior probability is Then get

[0055]

[0056] Among them, the code word symbol

[0057] The BSM-TBP decoding method is based on the channel input prior probability and the sparse check matrix H. The detailed steps are as follows:

[0058] 1) Initialize BSM-TBP decoding information: set the number of iterations τ = 0, and give the maximum number of iterations I max Initialize VN node probability according to channel input prior probability in 0≤l<R,0≤n<N. At this point, the iteration has not started, and the VN node probability is only determined by the channel input prior probability.

[0059] 2) Calculate the forward probability: define the symbol corresponding to the lth CN node in the τth iteration as The forward probability sequence is The sequence contains λ l forward probabilities, which are used to calculate the λ passed to the CN node. l The forward update is defined as the process of calculating the forward probability sequence of all symbols corresponding to R CN nodes. The symbol corresponding to the lth CN node is initialized as The 0th forward probability in the forward probability sequence is The remaining forward probability is updated step by step from front to back according to the order in the forward probability sequence, which is expressed as:

[0060]

[0061] Among them, 0≤l<R, 1≤λ<λ l , represents the additive inverse of b in GF(3), Indicates that in the τth iteration process The symbol passed from the VN node to the lth CN node The corresponding probability, operator represents the addition operation over GF(3).

[0062] 3) Calculate the backward probability: define the symbol corresponding to the lth CN node in the τth iteration as The backward probability sequence of The sequence contains λ l Backward probabilities are used to calculate the λ passed to the CN node.l The backward update is defined as the process of calculating the backward probability sequence of all symbols corresponding to R CN nodes. The symbol corresponding to the lth CN node is initialized as The λth in the backward probability sequence l -1 backward probability is The remaining backward probability is updated step by step from back to front according to the order in the backward probability sequence, which is expressed as:

[0063]

[0064] Among them, 0≤l<R, 0≤λ<λ l -1, represents the additive inverse of b in GF(3), Indicates that in the τth iteration process The symbol passed from the VN node to the lth CN node The corresponding probability.

[0065] 4) Update CN node probability: For all CN nodes, calculate the probability of the node transmitting to the VN node connected to it at the τth iteration. The calculation method is as follows:

[0066]

[0067] Among them, 0≤l<R, 0≤λ<λ l , represents the forward probability corresponding to b∈GF(3), symbol The corresponding backward probability.

[0068] 5) Update VN node probability: For all VN nodes, calculate the probability of the node transmitting to the CN node connected to it at the τth iteration. The calculation method is as follows:

[0069]

[0070] Among them, 0≤n<N, 0≤ρ<ρ n , is the normalization factor, satisfying the following constraints:

[0071]

[0072] 6) Calculate the decision sequence: Calculate the decision sequence r after the τth iterative decoding = (r0, r1, ..., r N-1 ), the calculation method of symbols in the sequence is as follows:

[0073]

[0074] Wherein, 0≤n<N, the decision sequence is the output codeword sequence after the τth iterative decoding.

[0075] 7) Iteration termination judgment: Calculate the syndrome s=rH through the decision sequence r after the τth iterative decoding T , when the syndrome s is a vector of all 0s, it is recorded as a successful decoding, the iteration stops, and the process goes to step 8); when s is not a vector of all 0s and τ=I max -1, it is recorded as a decoding failure, the iteration stops, and goes to step 8); when s is not a full 0 vector and τ<I max -1, τ increases by 1 and goes to step 2);

[0076] 8) Output decoding result: Output decision sequence r=(r0,r1,...,r N-1 ).

[0077] For the decoding of ternary LDPC codes in ternary transmission systems, when QSPA is used for decoding, the CN node probability update needs to exhaustively enumerate a large number of possible symbol combinations, and the system decoding complexity is relatively high. This makes the ternary transmission system unable to be applied to some scenarios with low delay requirements. Based on the ternary LDPC code decoding algorithm, the present invention improves the CN node probability update method, and adopts a ternary belief propagation algorithm based on bidirectional symbol-level merging. By reusing the calculation results, the decoding complexity of the ternary LDPC code can be reduced without losing the decoding performance, thereby reducing the decoding delay of the ternary transmission system. The BSM-TBP algorithm proposed in the present invention can effectively reduce the CN node probability update complexity when decoding the ternary LDPC code, and ensure that its BER performance is consistent with QSPA. The simulation results are as follows. Figure 1 shown.

[0078] The above examples are merely illustrative of the calculation model and process of the present invention and are not intended to limit the embodiments of the present invention. Persons skilled in the art will readily appreciate that other variations or modifications based on the above description are possible. This list of embodiments is not exhaustive; however, any obvious variations or modifications derived from the technical solution of the present invention remain within the scope of protection of the present invention.

Claims

1. A bidirectional symbol-level merged ternary belief propagation decoding method based on ternary LDPC codes, characterized in that: include: The ternary LDPC codeword v corresponding to the ternary symbol sequence of length K sent by the user is modulated and sent, and is received by the receiving end as a signal y=(y0,y1,...,y K-1 ); The code length of the ternary LDPC code is N, and the matrix elements in its R×N dimensional sparse check matrix H over GF(3) are used to indicate whether the l-th CN node is connected to the n-th VN node. The CN node is a check node, and the VN node is a variable node. 0≤l<R, 0≤n<N; The connection set of CN nodes is represented as in Contains λ connected to the lth CN node l The index of the VN node; the connection set of the VN node is represented as in Contains ρ connected to the nth VN node n The index of the CN node; Based on the signal received by the receiving end, let the codeword symbol corresponding to the nth VN node be The channel input prior probability is The codeword symbol Decoding is performed based on the channel input prior probability and the sparse check matrix H: 1) Initialize BSM-TBP decoding information: set the number of iterations τ = 0, and give the maximum number of iterations I max ; Initialize VN node probability according to channel input prior probability 2) Calculate the forward probability: The symbol corresponding to the lth CN node in the τth iteration is The forward probability sequence of The sequence contains λ l forward probabilities, which are used to calculate the λ passed to the CN node. l The information of the VN nodes; the symbol corresponding to the initialization l-th CN node is The 0th forward probability in the forward probability sequence is The remaining forward probability is updated step by step from front to back according to the order in the forward probability sequence, which is expressed as: Among them, 0≤l<R, 1≤λ<λ l , represents the additive inverse of b in GF(3), Indicates that in the τth iteration process The symbol passed from the VN node to the lth CN node The corresponding probability; represents the addition operation on GF(3); 3) Calculate the backward probability: The symbol corresponding to the lth CN node in the τth iteration is The backward probability sequence of The sequence contains λ l Backward probabilities are used to calculate the λ passed to the CN node. l The information of the VN nodes; the symbol corresponding to the initialization l-th CN node is The λth in the backward probability sequence l -1 backward probability is The remaining backward probability is updated step by step from back to front according to the order in the backward probability sequence, which is expressed as 4) Update CN node probability: For all CN nodes, calculate the probability of the node transmitting to the VN node connected to it at the τth iteration 5) Update VN node probability: For all VN nodes, calculate the probability of the node transmitting to the CN node connected to it at the τth iteration 6) Calculate the decision sequence: Calculate the decision sequence r after the τth iterative decoding = (r0, r1, ..., r N-1 ), symbol within the sequence Where, 0≤n<N, the decision sequence is the output codeword sequence after the τth iterative decoding; 7) Determine whether the decoding is successful by the syndrome corresponding to the decision sequence r after the τth iterative decoding. If the decoding is successful, stop the iteration and output the decision sequence r = (r0, r1, ..., r N-1 ).

2. The method of claim 1, wherein the bidirectional symbol-level merged ternary belief propagation decoding method based on ternary LDPC codes is characterized in that: For a ternary LDPC code with a code length of N, its R×N dimensional sparse check matrix on GF(3) is R is the length of the LDPC code check information sequence, and the matrix element h l,n ≠0 means that the lth CN node is connected to the nth VN node.

3. The method of claim 1, wherein the bidirectional symbol-level merged ternary belief propagation decoding method based on ternary LDPC codes is characterized in that: In the modulation process of the ternary LDPC codeword v corresponding to the ternary symbol sequence of length K sent by the user, the symbol v in the codeword sequence is n To the symbol x in the modulation sequence n The modulation conversion rule between Among them, 0≤n<N.

4. The method of claim 3 for bidirectional symbol-level combined ternary belief propagation decoding based on ternary LDPC codes, characterized in that: The codeword symbol corresponding to the nth VN node is The channel input prior probability is as follows: Where σ is the noise variance corresponding to the signal received by the receiver.

5. The method of claim 1, wherein the bidirectional symbol-level merged ternary belief propagation decoding method based on ternary LDPC codes is characterized in that: In the τth iteration of step 4), the node transmits the probability Among them, 0≤l<R, 0≤λ<λ l , represents the forward probability corresponding to b∈GF(3), symbol The corresponding backward probability.

6. The method of claim 5, wherein the bidirectional symbol-level merged ternary belief propagation decoding method based on ternary LDPC codes is characterized in that: In the τth iteration of step 5), the node transmits the probability Among them, 0≤n<N, 0≤ρ<ρ n , is the normalization factor.

7. The method of claim 6, wherein the bidirectional symbol-level merged ternary belief propagation decoding method based on ternary LDPC codes is characterized in that: Normalization factor Satisfy the constraints:

8. The bidirectional symbol-level merged ternary belief propagation decoding method based on ternary LDPC codes according to any one of claims 1 to 7, characterized in that: The syndrome s corresponding to the decision sequence r after the τth iterative decoding in step 7) is rH T .

9. The method of claim 8, wherein the bidirectional symbol-level combined ternary belief propagation decoding method based on ternary LDPC codes is characterized in that: In step 7), in the process of determining whether the decoding is successful by the syndrome corresponding to the decision sequence r after the τth iterative decoding, if the syndrome s is an all-0 vector, it means that the decoding is successful.

10. The method of claim 9, wherein the bidirectional symbol-level merged ternary belief propagation decoding method based on ternary LDPC codes is characterized in that: Step 7) In the process of determining whether the decoding is successful by the syndrome corresponding to the decision sequence r after the τth iterative decoding, if s is not an all-zero vector and τ<I max -1, then increase τ by 1 and go to step 2); if s is not a vector of all zeros and τ=I max When -1, it means decoding failed.

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