CN111342935A - High-performance soft-decision decoding method based on QC-LDPC code - Google Patents
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Abstract
The invention discloses a high-performance soft-decision decoding method for QC-LDPC codes, which mainly solves the problems of poor decoding performance and difficult realization of the existing algorithm and has the implementation scheme that MATLAB simulation is carried out on the relation between a signal-to-noise ratio and multiplicative factors according to the characteristics of the value of the multiplicative factor and the signal-to-noise ratio to obtain the corresponding relation between the signal-to-noise ratio and the multiplicative factor, least square curve fitting is carried out on the corresponding relation to obtain a relation α(s) between the multiplicative factor and the signal-to-noise ratio, the multiplicative factor α(s) and a minimum sum decoding algorithm are utilized to update check node messages in the decoding iteration process, then variable node messages are updated, the decoding messages are judged by combining the check node update messages and the variable node update messages, decoding is stopped after the maximum iteration times are reached, and decoding results are output.
Description
Technical Field
The invention belongs to the technical field of communication, and further relates to a soft-decision decoding method which can be used in a communication system scene of QC-LDPC channel coding.
Background
QC-LDPC code as a linear error correcting code gets more and more attention because of its strong error correcting capability and low decoding complexity, and has strong realizability. At present, the performance loss of the QC-LDPC hard-decision decoding algorithm is large, the reliability requirement of a communication system on information transmission cannot be met, and few researches are carried out, so that the researches on the QC-LDPC decoding algorithm are mainly based on soft-decision decoding. On the other hand, the soft-decision decoding algorithm for hardware implementation cannot achieve higher decoding performance due to reduced complexity and simplified computation, and therefore, the algorithm performance of the decoding algorithm must be improved under the condition of ensuring low decoding complexity.
MPC Fossoorier in its published paper "Reduced complex iterative decoding of low-density parity codes based on belief propagation" (IEEE transaction on Communications,1999,47:673-680) proposes a method for simplifying belief propagation algorithm to a minimum sum algorithm, which reduces the decoding complexity of the belief propagation algorithm that must calculate the probability product because only real addition is used for decoding, and does not need to know the characteristics of the related channel, and can be effectively implemented in hardware. Compared with a belief propagation algorithm, the method has the advantage that the decoding performance loss is large.
In the published paper "Reduced-complex decoding of LDPC codes" (IEEE Transactions on Communications,2005,53: 1288-. And (3) selecting a proper correction factor to enable the decoding performance of the check node update to be close to the belief propagation algorithm, and obtaining an offset term minimum sum algorithm and a normalization term minimum sum algorithm. The method has improved performance relative to the min-sum decoding algorithm, but has still a large loss of decoding performance compared to the belief propagation algorithm.
Jeongseok Ha proposes a method of a two-bit weighted bit flipping algorithm in a published paper of 'A two-bit weighted bit-flipping decoding algorithm for LDPC codes' (IEEE Communications Letters, 2018, 22: 874-. However, the complexity is high and the decoding performance has a large gap compared with the soft decision decoding algorithm, so the method is not suitable for a communication system scenario with high reliability requirement.
Irina E.Bochorva in its published paper "BP-LED decoding algorithm for LDPCcodes over AWGN channels" (IEEE Transactions on Information Theory, 2019, 65: 1677-.
Disclosure of Invention
The present invention aims to provide a high-performance soft-decision decoding method based on QC-LDPC codes to improve the decoding performance without significantly increasing the computational complexity.
The technical idea of the invention is that MATLAB simulation is carried out on the influence of the value of multiplicative factor α on the performance of the decoding algorithm under the condition of different signal-to-noise ratios, the corresponding relation α(s) of the signal-to-noise ratio s and the optimal multiplicative factor α is obtained through least square curve fitting, α(s) are introduced into a check node updating module of the minimum sum decoding algorithm, and the decoding performance is further improved.
The method comprises the following implementation steps:
(1) initializing decoding information:
setting the decoding information transmitted to check node j by variable node i as qijThe log-likelihood ratio information input to the decoder is L (P)i) Obtain the initial message that i passed to j: l is(0)(qij)＝L(Pi)；
(2) Obtaining the relation between multiplicative factor and signal-to-noise ratio by least square curve fitting:
(2a) according to the characteristic that the value of the multiplicative factor is related to the signal-to-noise ratio, simulating the relationship between the signal-to-noise ratio and the multiplicative factor, and obtaining the corresponding relationships (0.5, 0.625), (0.75, 0.675), (1, 0.725), (1.25, 0.75), (1.5, 0.775), (1.75, 0.8), (2, 0.825), (2.25, 0.85) and (2.5, 0.85) between the signal-to-noise ratio and the multiplicative factor α(s);
(2b) performing least square curve fitting on the corresponding relation in the step (2a) to obtain a relation between a multiplicative factor and the signal-to-noise ratio, wherein α(s) is 0.1s +0.6(s is less than or equal to 2.5), and if s is more than 2.5, α(s) is 0.85;
(3) carrying out an iterative process on the decoding, and outputting a final decoding result:
(3a) setting the maximum iteration number as N;
(3b) the check node message is updated by a multiplicative factor α(s), wherein the decoding information transmitted to the variable node i by the check node j is set as rjiAnd updating the check node information by combining the multiplicative factor α(s) and the minimum sum decoding algorithm to obtain the updating information L transmitted to the variable node i by the check node j during the decoding iteration of the first time(l)(rji) Comprises the following steps:
wherein i' represents the remaining variable nodes, V, adjacent to the check node j and excluding the ith variable nodej\ i represents the set of remaining variable nodes adjacent to check node j with the ith variable node removed, qi'jRepresenting decoding information transmitted by the variable node i' to the check node j, sgn (·) represents a symbolic function, and min (·) represents a minimum function;
(3c) updating the variable node message, namely obtaining the updating information L transmitted by the variable node i to the check node j when the decoding iteration is performed for the first time(l)(qij) Comprises the following steps:
wherein j' represents the remaining check nodes adjacent to the variable node i with the jth check node removed, Ci\ j represents a set of remaining check nodes adjacent to variable node i with the jth check node removed, rj'iRepresenting the decoding information transmitted by the check node j' to the variable node i;
(3d) setting the posterior probability information of variable node i as qiObtaining check node update information L according to the decoding iteration of the first time(l)(rji) And variable node update information L(l)(qij) Calculating decision information L of decoding for the first time(l)(qi)：
Wherein, CiRepresenting a set of check nodes adjacent to variable node i;
(3e) for the decision message L obtained by the decoding of the first time(l)(qi) And (4) judging: if L is(l)(qi) If the decoding judgment result is more than 0, the first time decoding judgment result is 0; if L is(l)(qi) If the decoding judgment result is less than or equal to 0, the first decoding judgment result is 1;
(3f) judging whether the maximum iteration number is reached: after the decoding iteration of the first time is finished, if the iteration time l reaches the preset maximum iteration time N, stopping the iteration and outputting a final decoding result; otherwise, returning to (3b) and continuing the iteration.
Compared with the prior art, the invention has the following advantages:
firstly, the invention fully considers the difference of the optimal multiplicative factors under different signal-to-noise ratios, utilizes the value of the multiplicative factor α under different SNR conditions to carry out MATLAB simulation on the influence of the performance of the decoding algorithm, obtains the signal-to-noise ratio s and the optimal multiplicative factor α(s), obtains the corresponding relation between the signal-to-noise ratio s and the optimal multiplicative factor α(s) through least square curve fitting, and overcomes the loss of the fixed multiplicative factor on the decoding performance.
Secondly, the invention brings α(s) into the check node updating module for decoding, thereby overcoming the problem of poor decoding performance in the prior art, improving the performance of the decoding algorithm and strengthening the practicability.
Drawings
FIG. 1 is a block diagram of an emulation platform system for use in the present invention;
FIG. 2 is a graph of the results of the present invention simulating multiplicative factor versus signal-to-noise ratio (0.5dB-1.5 dB);
FIG. 3 is a graph of the results of the present invention simulating multiplicative factor versus signal-to-noise ratio (1.75dB-2.5 dB);
FIG. 4 is a flow chart of an implementation of the present invention;
fig. 5 is a diagram showing the results of decoding by the method of the present invention and three existing soft-decision decoding methods.
Detailed Description
Embodiments and effects of the present invention will be described in further detail below with reference to the accompanying drawings.
Referring to fig. 1, the QC-LDPC system adopted in the present invention is mainly composed of a pseudo-random PN sequence generation module, a QC-LDPC encoder module, a QPSK digital modulation module, an AWGN gaussian channel module, a QPSK digital demodulation module, a QC-LDPC decoder module, and an error rate statistics module, wherein:
the pseudo-random PN sequence generation module generates a bit data source through a random function and transmits the data source to the QC-LDPC encoder module;
the QC-LDPC encoder module is used for encoding the bit data generated by the PN sequence generation module through a QC-LDPC encoder, and transmitting the bit data obtained after encoding to the QPSK digital modulation module;
the QPSK digital modulation module is used for carrying out quadrature phase shift keying modulation on the coded bit data, mapping the bit data into symbol data and transmitting the symbol data to the AWGN Gaussian channel module;
the AWGN Gaussian channel module adds additive white Gaussian noise to the symbol data obtained by digital modulation and transmits the additive white Gaussian noise to the QPSK digital demodulation module through a white Gaussian noise channel;
the QPSK digital demodulation module is used for demapping the symbol data after the Gaussian channel to obtain log-likelihood ratio information and transmitting the log-likelihood ratio information to the QC-LDPC decoder module;
the QC-LDPC decoder module carries out soft decision decoding on the log-likelihood ratio information, the decoding method adopts the LS-NMS algorithm of the invention to obtain decoded bit data, and the bit data is transmitted to the bit error rate statistical module;
and the bit error rate statistical module is used for comparing the received decoded bit data with bit data generated by the PN sequence, calculating the total number of bits with errors after decoding, and obtaining the system bit error rate.
Referring to fig. 4, the implementation steps of the present invention are as follows:
Setting the decoding information transmitted to check node j by variable node i as qijThe log-likelihood ratio information input to the decoder is L (P)i) Obtain the initial message that i passed to j: l is(0)(qij)＝L(Pi)。
And 2, obtaining the relation between the multiplicative factor and the signal-to-noise ratio through least square curve fitting.
2.1) simulating the relation between the signal-to-noise ratio and the multiplicative factor according to the characteristic that the value of the multiplicative factor is related to the signal-to-noise ratio:
2.1.1) combining the simulation system diagram of fig. 1, respectively simulating multiplicative factors with signal-to-noise ratios s of 0.5dB, 0.75dB, 1dB, 1.25dB and 1.5dB under MATLAB 2018B software, and as a result, as shown in fig. 2, the horizontal axis in fig. 2 represents multiplicative factors, the vertical axis represents error bit rate BER, the multiplicative factor corresponding to the minimum number of error bits is the optimal multiplicative factor α(s), and the values of the optimal multiplicative factor α(s) are respectively 0.625, 0.675, 0.725, 0.75 and 0.775, namely, the corresponding relations of the signal-to-noise ratios s and the multiplicative factor α(s) are (0.5, 0.625), (0.75, 0.675), (1, 0.725), (1.25, 0.75), (1.5, 0.775);
2.1.2) combining the simulation system diagram of fig. 1, respectively simulating multiplicative factors with signal-to-noise ratios s of 1.75dB, 2dB, 2.25dB and 2.5dB under MATLAB 2018B software, and as a result, as shown in fig. 3, the horizontal axis in fig. 3 represents multiplicative factors, the vertical axis represents error bit rate BER, the multiplicative factor corresponding to the minimum number of error bits is the optimal multiplicative factor α(s), and the obtained optimal multiplicative factor α(s) has values of 0.8, 0.825, 0.85 and 0.85, namely, the corresponding relations between the signal-to-noise ratios s and the multiplicative factor α(s) are (1.75, 0.8), (2, 0.825), (2.25, 0.85) and (2.5, 0.85);
2.2) performing least square curve fitting on the corresponding relation between the signal-to-noise ratio s in 2.1) and the multiplicative factor α(s) to obtain a relation between the multiplicative factor and the signal-to-noise ratio, wherein α(s) is 0.1s +0.6(s is less than or equal to 2.5), and if s is greater than 2.5, α(s) is 0.85.
And 3, carrying out an iterative process on the decoding, and outputting a final decoding result.
3.1) setting the maximum iteration number as N;
3.2) updating the check node message by utilizing the multiplicative factor α(s) and a minimum sum decoding algorithm:
3.2.1) during the first decoding iteration, the decoding information transmitted to the variable node i by the check node j is set as rji(b) B is 0 or 1, and when b is 0, the calculation is carried out
When b is 1, calculating
3.2.2) decoding the information r in the logarithmic domainji(b) Taking logarithm of the ratio to obtain the log-likelihood ratio information L (r) transmitted by the check node j to the variable node iji)：
3.2.3) setting the decoding information transmitted to the check node j by the variable node i to be qij(b) B has a value of 0 or 1, according to rji(b) And q isij(b) The relationship of (1):
and combining a hyperbolic tangent function formula, and simultaneously taking hyperbolic tangent functions at two sides of the equation to obtain:
wherein i' represents the remaining variable nodes, V, adjacent to the check node j and excluding the ith variable nodej\ i represents the set of remaining variable nodes adjacent to check node j with the ith variable node removed, qi'j(1) Denotes that q is equal to 1 when b takes on the valueij(b) Value of (a), L (q)i'j) Representing the update information transmitted by the variable node i' to the check node j;
3.2.4) simplifying the formula in 3.2.3) to obtain the information L (r) transmitted to the variable node i by the check node jji)：
3.2.5) combining the hyperbolic tangent function and the inverse hyperbolic tangent function formula, further simplifying the formula in 3.2.4) to obtain information L (r) transmitted to the variable node i by the check node jji)：
Wherein sgn (-) represents a sign function, and min (-) represents a minimum function;
3.2.6) combining the multiplicative factors α(s) and 3.2.5) to obtain the update information L transmitted by the check node j to the variable node i in the first iteration(l)(rji) Comprises the following steps:
3.3) updating the variable node message:
3.3.1) let the decoding information transmitted from the variable node i to the check node j be qij(b) And b takes a value of 0 or 1, the initial information is:
3.3.2) in the first decoding iteration, when b takes 0, calculating
When b is 1, calculating
Wherein j' represents the remaining check nodes adjacent to the variable node i with the jth check node removed, Ci\ j represents a set of remaining check nodes adjacent to variable node i with the jth check node removed, rj'iRepresenting the decoded information passed by check node j' to variable node i, coefficient αijIs a correction factor for normalization, such that
If true;
3.3.3) decoding information q in the logarithmic domainij(b) Taking logarithm of the ratio to obtain the log-likelihood ratio information L (q) transmitted by the variable node i to the check node jij)：
3.3.4) combining with a logarithmic function formula, simplifying the formula in 3.3.3) to obtain a variable node i and transmitting the variable node i to a correctionUpdate information L of node j(l)(qij)：
3.4) calculating the decoded decision message:
3.4.1) after the updating process is finished, calculating a judgment message, and setting the posterior probability information of the variable node i as qi(b) B is 0 or 1, and when b is 0, the calculation is carried out
When b is 1, calculating
Wherein, CiRepresenting the set of check nodes adjacent to variable node i, coefficient αiIs a correction factor for normalization, such that
If true;
3.4.2) in the logarithmic domain, for decoding information qi(b) Taking logarithm of the ratio to obtain the posterior probability information L (q) received by the variable node ii)：
3.4.3) combining with a logarithmic function formula, simplifying the formula in 3.4.2) to obtain a decision message L of the decoding for the first time(l)(qi)：
3.5) decision message L obtained by decoding the first time(l)(qi) And (4) judging: if L is(l)(qi) If the decoding judgment result is more than 0, the first time decoding judgment result is 0; if L is(l)(qi) If the decoding judgment result is less than or equal to 0, the first decoding judgment result is 1;
3.6) judging whether the maximum iteration number is reached: after the decoding iteration of the first time is finished, if the iteration time l reaches the preset maximum iteration time N, stopping the iteration and outputting a final decoding result; otherwise, return to 3.2) and continue iteration.
The effect of the present invention will be further explained with the simulation experiment.
1. Simulation conditions are as follows:
the simulation experiment of the invention is carried out under MATLAB 2018B software, the maximum iteration number of decoding is 25, and the maximum simulation frame number is 1 × 105And (4) frames, adopting QC-LDPC code with code rate of 1/2 and code length of 1944.
2. Simulation content and result analysis:
under the above conditions, the method of the present invention and the existing MS algorithm, OMS algorithm and NMS algorithm are used to decode QC-LDPC code respectively, and the result is shown in FIG. 5.
The horizontal axis in fig. 5 represents the signal-to-noise ratio EbNo in dB and the vertical axis represents the error bit rate BER.
As can be seen from fig. 5, the error rate curve using the method of the present invention is lower than the error rate curve using the existing soft-decision decoding method, which indicates that the performance of the decoder can be effectively improved using the method of the present invention.
Claims (2)
1. The high-performance soft-decision decoding method based on the QC-LDPC code is characterized by comprising the following steps of:
(1) initializing decoding information:
setting the decoding information transmitted to check node j by variable node i as qijThe log-likelihood ratio information input to the decoder is L (P)i) Obtain the initial message that i passed to j:L(0)(qij)＝L(Pi)；
(2) obtaining the relation between multiplicative factor and signal-to-noise ratio by least square curve fitting:
(2a) according to the characteristic that the value of the multiplicative factor is related to the signal-to-noise ratio, simulating the relationship between the signal-to-noise ratio and the multiplicative factor, and obtaining the corresponding relationships (0.5, 0.625), (0.75, 0.675), (1, 0.725), (1.25, 0.75), (1.5, 0.775), (1.75, 0.8), (2, 0.825), (2.25, 0.85) and (2.5, 0.85) between the signal-to-noise ratio and the multiplicative factor α(s);
(2b) performing least square curve fitting on the corresponding relation in the step (2a) to obtain a relation between a multiplicative factor and the signal-to-noise ratio, wherein α(s) is 0.1s +0.6(s is less than or equal to 2.5), and if s is more than 2.5, α(s) is 0.85;
(3) carrying out an iterative process on the decoding, and outputting a final decoding result:
(3a) setting the maximum iteration number as N;
(3b) the check node message is updated by a multiplicative factor α(s), wherein the decoding information transmitted to the variable node i by the check node j is set as rjiAnd updating the check node information by combining the multiplicative factor α(s) and the minimum sum decoding algorithm to obtain the updating information L transmitted to the variable node i by the check node j during the decoding iteration of the first time(l)(rji) Comprises the following steps:
wherein i' represents the remaining variable nodes, V, adjacent to the check node j and excluding the ith variable nodej\ i represents the set of remaining variable nodes adjacent to check node j with the ith variable node removed, qi'jRepresenting decoding information transmitted by the variable node i' to the check node j, sgn (·) represents a symbolic function, and min (·) represents a minimum function;
(3c) updating the variable node message, namely obtaining the updating information L transmitted by the variable node i to the check node j when the decoding iteration is performed for the first time(l)(qij) Comprises the following steps:
wherein j' represents the remaining check nodes adjacent to the variable node i with the jth check node removed, Ci\ j represents a set of remaining check nodes adjacent to variable node i with the jth check node removed, rj'iRepresenting the decoding information transmitted by the check node j' to the variable node i;
(3d) setting the posterior probability information of variable node i as qiObtaining check node update information L according to the decoding iteration of the first time(l)(rji) And variable node update information L(l)(qij) Calculating decision information L of decoding for the first time(l)(qi)：
Wherein, CiRepresenting a set of check nodes adjacent to variable node i;
(3e) for the decision message L obtained by the decoding of the first time(l)(qi) And (4) judging: if L is(l)(qi) If the decoding judgment result is more than 0, the first time decoding judgment result is 0; if L is(l)(qi) If the decoding judgment result is less than or equal to 0, the first decoding judgment result is 1;
(3f) judging whether the maximum iteration number is reached: after the decoding iteration of the first time is finished, if the iteration time l reaches the preset maximum iteration time N, stopping the iteration and outputting a final decoding result; otherwise, returning to (3b) and continuing the iteration.
2. The method of claim 1, wherein (3b) the check node message is updated in combination with multiplicative factor α(s) and a min-sum decoding algorithm as follows:
(3b1) during the decoding iteration of the first time, the decoding information transmitted to the variable node i by the check node j is set as rji(b) B is 0 or 1, and when b is 0, the calculation is carried out
When b is 1, calculating
(3b2) In the logarithmic domain, the information r is decodedji(b) Taking logarithm of the ratio, and calculating to obtain log likelihood ratio information L (r) transmitted to variable node i by check node jji)：
(3b3) Setting the decoding information transmitted to check node j by variable node i as qij(b) B has a value of 0 or 1, according to rji(b) And q isij(b) The relationship of (1):
and combining a hyperbolic tangent function formula, and simultaneously taking hyperbolic tangent functions at two sides of the equation to obtain:
wherein i' represents the remaining variable nodes adjacent to the check node j and excluding the ith variable node, qi'j(1) Denotes that q is equal to 1 when b takes on the valueij(b) Value of (a), L (q)i'j) Representing the update information transmitted by the variable node i' to the check node j;
(3b4) simplifying the formula in (3b3), and calculating the information L (r) transmitted by the check node j to the variable node iji)：
(3b5) The formula in (3b4) is further simplified by combining the hyperbolic tangent function formula and the inverse hyperbolic tangent function formula, and the information L (r) transmitted to the variable node i by the check node j is calculatedji)：
(3b6) L (r) calculated in (3b5)ji) Combined with multiplicative factor α(s), calculating L obtained from the first decoding iteration(l)(rji)：
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| CN112350737A (en) * | 2020-11-23 | 2021-02-09 | 南京信息工程大学滨江学院 | Transmission method for updating grouping information based on LDPC code |
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