A QC-LDPC coding transmission method based on Q matrix

Abstract

The present invention discloses a QC-LDPC coding transmission scheme based on a Q matrix. The scheme is based on a hard decision decoding-bit flipping (Bit-Flipping, BF) decoding algorithm, and introduces a correlation matrix of a reversible quasi-cyclic Q matrix during encoding to make an error vector associated with the matrix Q. This connection is used during decoding to make the values ​​of the flipped reference vector also correlated. This decoding method is called a Q decoding algorithm. In addition, under the transmission scheme proposed by the present invention, in addition to using a hard decision Q decoding algorithm during decoding, some channel soft information can also be introduced to define an RQ decoding algorithm to further improve the decoding performance. Simulation results show that when the scheme adopts the Q decoding algorithm, a lower bit error rate can be obtained than that of BF decoding; when the RQ decoding algorithm is adopted, a lower bit error rate can be obtained than that of weighted bit flipping (Weighted Bit-Flipping, WBF) decoding. In addition, the number of decoding iterations under the scheme of the present invention is reduced, and the decoding performance is significantly improved.

Description

Technical Field

[0001] The present invention belongs to the field of communication technology, and in particular relates to a QC-LDPC coding transmission method based on a Q matrix, which can be used in communication system scenarios of QC-LDPC channel coding. Background Art

[0002] With the continuous development of wireless communications, improving the bit error performance of communication systems and ensuring reliable information transmission are crucial. Low-density parity-check (LDPC) codes, as a channel coding scheme with excellent error correction performance, are widely used in communication systems. Quasi-cyclic low-density parity-check (QC-LDPC) codes have become a research hotspot for LDPC codes due to their low implementation complexity. Decoding algorithms for QC-LDPC codes are mainly divided into hard-decision and soft-decision decoding algorithms. Hard-decision decoding algorithms have low complexity but relatively poor error performance; soft-decision decoding algorithms offer good error performance but relatively high computational complexity. Therefore, designing a coding scheme for QC-LDPC codes that strikes a balance between performance and complexity is of great significance. For example, the classic hard-decision decoding algorithm for LDPC codes, bit-flipping (BF), has low complexity and is easy to implement in hardware, but its error performance lags significantly behind soft-decision decoding. In the field of coding cryptography, to improve the decryption efficiency of QC-LDPC codes, M. Baldi proposed a Q-decoder for QC-LDPC codes in his 2018 paper, "LED Akem: A post-quantum key encapsulation mechanism based on QC-LDPC codes" (Post-Quantum Cryptography Anonymous Cham: Springer International Publishing, 2018, 3-24). Inspired by this, the present invention designs a Q-matrix-based QC-LDPC code encoding and transmission scheme based on the Q-decoder. Summary of the Invention

[0003] To address the shortcomings of hard-decision decoding algorithms, this paper proposes a QC-LDPC coding and transmission scheme based on the Q matrix. The goal is to improve the decoding performance of hard-decision algorithms while ensuring low decoding complexity. In the proposed QC-LDPC coding and transmission scheme, during encoding, the original message sequence must be multiplied not only by the generator matrix G of the corresponding check matrix, but also by a variant of the reversible quasi-cyclic matrix Q. Because the Q matrix is ​​also used during decoding, we call this decoding algorithm the "Q decoding algorithm." Based on Q decoding and incorporating partial channel reliability information, we define another "Reliability-based Q (RQ) decoding algorithm" with even better error performance.

[0004] In order to make the technical solution of the present invention easier to understand, the quasi-cyclic reversible matrix .Q. used in the present invention is explained:

[0005] Assume that A is a c-order circulant matrix, which means that when the first row of elements of A is known, the elements of all subsequent rows are cyclic shifts of the first row elements, that is:

[0006]

[0007] The Q matrix used in the following text is a randomly generated N×N quasi-circulant matrix, where N=n0×p (n0 is generally a small integer, such as n0=2 or n0=3, and p is generally an integer of several hundred or even several thousand);

[0008]

[0009] Where each submatrix Q i,j (0≤i≤n0-1,0≤j≤n0-1) is a p-order circulant matrix. In addition, define an integer vector Used to determine the submatrix Q i,j The row / column weights are:

[0010]

[0011] This means that the row / column weights of the Q matrix are

[0012] The technical solutions of the present invention are as follows:

[0013] Assume that there is a (N, K) QC-LDPC code, the size of the check matrix H is (NK) × N, and the size of the generator matrix G is K × N. Figure 1 ) The specific implementation steps of the present invention are described, where the Q decoding algorithm is used:

[0014] S1. The coding matrix includes the generator matrix G and the quasi-cyclic reversible matrix Q defined above. For the information sequence m=[m1,m2,…,m k ], according to the following encoding process, we get the codeword sequence c=[c1,c2,…,c N ]:

[0015]

[0016] S2, adopt BPSK modulation mode to the obtained codeword sequence, according to x i =2c i -1 to get the modulated sequence x=[x1,x2,…,x N ];

[0017] S3, for mean 0, variance is σ 2 AWGN channel, the sequence x is converted into the sequence y=x+n=[y1,y2,…,y N ], where n is the noise vector;

[0018] S4, the inverse process of the corresponding modulation, and the sequence r = [r1, r2, ..., r N ];

[0019] S5. Decoding, specifically including:

[0020] S51, obtain a hard decision receiving sequence z=[z1,z2,…,z N ];

[0021] S52. Calculate the following two vectors:

[0022] z'=zQ T =(c+e)Q T =[mG(Q T ) -1 +e]Q T =mG+eQ T

[0023] s'=(z')H T =mGH T +(eQ T )H T =(eQ T )H T

[0024] Define an extended error vector as e'=eQ T , at this time s' is the syndrome corresponding to the extended error vector e'.

[0025] S53. Input syndrome s', check matrix H, and quasi-cyclic reversible matrix Q, and execute Q decoding algorithm. The steps of the Q decoding algorithm are as follows:

[0026] 1) Initialization: initial syndrome s (0) =(s') T , error vector estimation (where 0 N is an all-zero vector of length N), the current number of iterations is t=1, and the maximum number of iterations is t max =T;

[0027] 2) Compute on the real number field: where ∑ (t) Indicates the number of error checking equations that each variable node participates in, The larger the value, the greater the extended error vector corresponding to the position, e'=eQ T The more likely the value is 1. This shows that (t) The vector e' can be estimated;

[0028] 3) Calculate bit flipping based on real number field:

[0029] 4) Find the vector R (t) The position i corresponding to the maximum value in is defined as follows:

[0030]

[0031] 5) Update the error vector estimate in Represents a binary vector of length N, where ξ (t) The index position is 1, and the remaining positions are all 0;

[0032] 6) Update the syndrome s (t) : where q v Representative Q T The v-th row of the matrix.

[0033] 7) Determine whether to stop: If the syndrome s (t) If the vector is all zero or the number of iterations is t=T, the decoding stops and the error vector estimate is output. Otherwise, the number of iterations is t←t+1, and the process returns to step 2) to proceed to the next iteration.

[0034] S6. Estimating the error vector Perform modulo-two addition with the hard decision received sequence z to obtain the codeword estimation sequence

[0035] In order to further improve the error performance of QC-LDPC code transmission based on Q matrix, the Q decoding algorithm is improved. Based on the hard decision and combined with the soft information of the channel, the "RQ decoding algorithm" is defined. The basic idea of ​​the RQ decoding algorithm is to obtain the flip bit position set ξ according to the Q decoding algorithm. (t) On the basis of , another part of bit positions with lower reliability (obtained from the absolute value of the received sequence) is selected to define a candidate flip bit position set ζ, and the intersection of the two is selected as the final bit flip position.

[0036] The following are the specific implementation steps of the QC-LDPC coded transmission scheme using the RQ decoding algorithm, including encoding, modulation, channeling, demodulation, calculation of the syndrome s', and finally the error vector estimation The codeword estimation sequence is obtained by adding the hard decision received sequence z to the codeword estimation sequence These steps are the same as those for the encoding scheme using the Q decoding algorithm. The following describes the operation process of the different parts.

[0037] S53. Input: received sequence y, syndrome s', check matrix H, quasi-cyclic reversible matrix Q, determine the ratio η (0≤η≤1) of the candidate flipped bit position set size, and execute the RQ decoding algorithm. The steps of the Q decoding algorithm are as follows:

[0038] 1) Initialization: initial syndrome s (0) =(s') T , error vector estimation (where 0 N is an all-zero vector of length N), the current number of iterations is t=1, and the maximum number of iterations is t max =T;

[0039] 2) Take the absolute value sequence of the received sequence y, defined as: τ=[τ1,τ2,…,τ N ]=[y1|,|y2|,…|y N |]; according to τ i The values ​​are arranged in ascending order, and the subscripts are obtained to form a vector: φ=[φ1,φ2,…,φ N ],in

[0040] 3) Select the first η·N elements in the position vector φ to form the candidate bit flip position set ζ;

[0041] 4) Execute the Q decoding algorithm to obtain the bit flip set ξ (t) , i.e., executing steps 53.1-53.5) of the Q decoding algorithm;

[0042] 5) Calculate the final set of flipped bit positions:

[0043] 6) Update error vector estimate in Represents a binary vector of length N, where Γ (t) The index position is 1, and the remaining positions are all 0;

[0044] 7) Update the syndrome s (t) : where q v Representative Q T The v-th row of the matrix.

[0045] 8) Determine whether to stop: If the syndrome s (t) If the vector is all zero or the number of iterations is t=T, the decoding stops and the error vector estimate is output. Otherwise, the number of iterations is t←t+1, and the process returns to step 4) to proceed to the next iteration.

[0046] S6. Estimating the error vector Perform modulo-two addition with the hard decision received sequence z to obtain the codeword estimation sequence

[0047] The beneficial effects of the present invention are mainly reflected in two points:

[0048] 1. Compared with the traditional BF decoding algorithm, the error performance of the present invention is improved, the number of iterations is reduced, and the advantage of low complexity of hard decision decoding is maintained. In the BF decoding algorithm, whether to flip the bit is determined by the number of times a variable node does not satisfy the check equation. Since all variable nodes are calculated independently, the values ​​of the flip reference vector in the BF algorithm are independent and unrelated. On the contrary, in the Q-matrix-based QC-LDPC coding transmission scheme, due to the connection between the error vector and the reversible quasi-cyclic matrix Q, the values ​​of the flip reference vector during Q decoding are also correlated, which is more reliable than BF's analysis of the error probability of each variable node separately.

[0049] 2. In the Q-matrix-based QC-LDPC coding transmission scheme proposed in this invention, by introducing soft channel information on the basis of the hard-decision Q decoding algorithm, minimal complexity is added. When the RQ decoding algorithm is adopted, higher performance gain can be achieved. The algorithm performance is better than the weighted bit-flipping (WBF) decoding algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 Flowchart for realizing the encoding and decoding scheme of the present invention;

[0051] Figure 2 is the bit error rate performance curve of (1262,631) QC-LDPC code under different encoding and decoding methods;

[0052] Figure 3 The bar chart shows the average number of iterations for the (1262,631) QC-LDPC code under different encoding and decoding methods.

[0053] Figure 4 Figure 2 is the bit error rate performance curve of the (1248,624) QC-LDPC code constructed according to the 802.16e standard under different coding methods. DETAILED DESCRIPTION

[0054] The technical solution of the present invention is described in detail below with reference to the accompanying drawings and simulation examples:

[0055] Here is a method for constructing the H matrix of the QC-LDPC code used in the simulation. Assume that an integer p (usually tens or larger) is used to define the code length N = n0p of a certain (N,K) QC-LPDC code, the original information sequence length K = k0p, and the check bit length r = p, where n0 is a small integer (for example, n0 = 2, 3). According to the relationship between the check bit and the code length, it can be known that the code rate of the QC-LDPC code constructed using this method is (n0-1) / n0, and the size of the H matrix is ​​p×n0p. Definition There are n0 sparse circulant matrices of size p×p, and H i Each row / column of (i=0,1,…,n0-1) contains the same number of 1s, that is, each H i (i=0,1,…,n0-1) all have the same row / column weight, thus constructing the check matrix of (N,K)QC-LPDC code

[0056] First, we take p = 631, n0 = 2, that is, the code length N = 1262, the code rate R = 1 / 2, the row weight of the check matrix H is 3, and the row / column weight of the reversible quasi-cyclic matrix Q is w(Q) = [21; 12]. In the QC-LDPC coding transmission scheme based on the Q matrix, when the RQ decoding method is used, the ratio η is set to 1 / 10. Under the AWGN channel, BPSK modulation is adopted. The existing BF decoding algorithm, WBF decoding algorithm, and the transmission scheme proposed by the present invention respectively adopt the Q decoding algorithm and the RQ decoding algorithm. A total of four coding schemes are used to encode and decode the QC-LDPC code. The maximum number of iterations of the four algorithms is set to 100. The bit error rate result curves are shown as follows: Figure 2 As shown in the figure, the average number of iterations per frame for each algorithm is as follows: Figure 3To verify the effectiveness of the present invention, the QC-LDPC code in the 802.16e standard is used for further simulation. The same simulation conditions as above, the (1248,624) QC-LDPC code with code length N = 1248 and code rate R = 1 / 2 under the 802.16e standard has the following bit error rate results curves under different encoding and decoding methods: Figure 4 In the above drawings, Figure 2 、 Figure 4 The horizontal axis represents the signal-to-noise ratio, which is in decibels (dB), and the vertical axis represents the bit error rate (BER); Figure 3 The horizontal axis represents the signal-to-noise ratio in decibels (dB), and the vertical axis represents the average number of iterations.

[0057] from Figure 2 It can be found that the QC-LDPC code of (1262,631) reaches a bit error rate of 10 -3 When using the Q decoding algorithm, the performance gain is 1.56dB compared to BF, and the performance gain is 0.3dB compared to WBF. In the RQ decoding algorithm, the bit error rate is further reduced by introducing some soft information to assist Q decoding. Figure 2 When the bit error rate reaches 10 -4 When using the QC-LDPC coding transmission scheme based on the Q matrix, RQ decoding can achieve a performance gain of 0.46dB compared to Q decoding. Figure 3 This shows that under the same signal-to-noise ratio, the WBF decoding algorithm has the most iterations and the RQ decoding algorithm has the least iterations. Figure 4 Results and Figure 2 There are basically the same trends.

[0058] In summary, from the comparison of the above groups of simulation result graphs, it can be seen that the bit error rate of the Q decoding algorithm is lower than that of the BF decoding algorithm, and the bit error rate of the RQ decoding algorithm is lower than that of the WBF decoding algorithm. In addition, the average number of iterations of the Q and RQ decoding algorithms is lower than that of the BF and WBF decoding algorithms, indicating that the QC-LDPC coding transmission scheme based on the Q matrix proposed in the present invention can effectively improve the decoding performance. Especially under high signal-to-noise ratio conditions, the error performance advantages of Q decoding and RQ decoding are more obvious. RQ decoding adds soft information to assist decoding on the basis of Q decoding. Although it increases a small amount of decoding complexity, it significantly improves the error performance.

Claims

1. A QC-LDPC coding transmission method based on Q matrix, defining the size of the check matrix H of (N, K) QC-LDPC code as (NK)×N, the size of the generator matrix G as K×N, wherein the code length N=n0×p, n0 and p are integers, and p>>n0, K is the length of the information sequence, and defining a randomly generated reversible quasi-cyclic matrix Q of size N×N, which has the following form: Where each submatrix Q i,j is a p-order circulant matrix, 0≤i≤n0-1,0≤j≤n0-1, defining an integer vector Used to determine the submatrix Q i,j The row / column weights are: The row / column weights of the Q matrix are It is characterized in that The method comprises the following steps: S1, the coding matrix includes the generator matrix G and the quasi-cyclic reversible matrix Q. For the information sequence m = [m1, m2, ..., m k ], according to the following encoding process, we get the codeword sequence c = [c1, c2, ..., c N ]: S2, the obtained codeword sequence is modulated by BPSK, according to x i =2c i -1 to get the modulated sequence x = [x1, x2, ..., x N ]; S3, for mean 0, variance is σ 2 AWGN channel, after the sequence x passes through the channel, the sequence y=x+n=[y1,y2,…,y N ], where n is the noise vector; S4, corresponding to the inverse process of modulation, we get the sequence r = [r1, r2, ..., r N ]; S5, decoding, specifically including: S51, obtain a hard decision receiving sequence z=[z1,z2,…,z N ]; S52. Calculate the following two vectors: z'=zQ T =(c+e)Q T =[mG(Q T ) -1 +e]Q T =mG+eQ T s'=(z')H T =mGH T +(eQ T )H T =(eQ T )H T Define an extended error vector as e' = eQ T , at this time, s' is the syndrome corresponding to the extended error vector e'; S53, input received sequence y, syndrome s', check matrix H, quasi-cyclic reversible matrix Q, determine the ratio η of the candidate flip bit position set size, 0≤η≤1, use RQ decoding algorithm to obtain error vector estimation The steps of the RQ decoding algorithm are: 1) Initialization: initial syndrome s (0) =(s') T , error vector estimation Where 0 N is a zero vector of length N, the current iteration number t = 1, and the maximum iteration number t max =T; 2) Take the absolute value sequence of the received sequence y, defined as: τ = [τ1, τ2, …, τ N ]=[|y1|,|y2|,…|y N |]; according to τ i The values ​​are arranged in ascending order, and the subscripts are obtained to form a vector: φ=[φ1,φ2,…,φ N ],in 3) Select the first η·N elements in the position vector φ to form the candidate bit flip position set ζ; 4) Execute the Q decoding algorithm to obtain the bit flip set ξ (t) ; 5) Calculate the final flip bit position set: 6) Update the error vector estimate in Represents a binary vector of length N, where Γ (t) The index position is 1, and the remaining positions are all 0; 7) Update the syndrome s (t) : where q v Representative Q T The vth row of the matrix; 8) Determine whether to stop: If the correction factor s (t) If the vector is all zero or the number of iterations is t = T, the decoding stops and the error vector estimate is output. Otherwise, the number of iterations is t←t+1, and the process returns to step 4) to proceed to the next iteration; S6. Estimating the error vector Perform modulo-two addition with the hard decision received sequence z to obtain the codeword estimation sequence

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