CN103929210B - Hard decision decoding method based on genetic algorithm and neural network - Google Patents

Abstract

The present invention relates to the field of signal processing in communication, in particular to a hard-decision decoding method based on a hybrid intelligent algorithm of a genetic algorithm and a neural network, that is, a genetic neural network decoding (Genetic Neural-network Decoding, GND) method. This method makes full use of the self-optimization ability of the genetic algorithm and the pattern classification function of the neural network to optimize the hard-decision quantization output of the receiving matched filter to compensate for the reliability loss caused by the channel transmission error and hard-decision quantization. , so as to restore a codeword with a higher likelihood to the transmission sequence as the input of the hard decision decoder to obtain a better decoding result. From theoretical analysis and computer simulation, it can be seen that the error correction performance of the GND decoding method is close to that of traditional soft-decision decoding, and because the decoding process does not need to use statistical soft information of the channel, its complexity is significantly higher than that of traditional soft-decision decoding. reduce.

Description

A Hard Decision Decoding Method Based on Genetic Algorithm and Neural Network

technical field

The invention relates to the field of signal processing in communication, in particular to a hard-decision decoding method, which is realized based on a genetic algorithm (Genetic Algorithm, GA) and a neural network (Neural Network, NN).

Background technique

At present, error-correcting code technology has become an indispensable means and method to realize timely and reliable communication. However, the soft-decision decoding technology of error-correcting codes has always had problems such as small application range and high computational complexity, which are difficult to be solved well within a reasonable and limited time under the existing technical conditions. In addition, the general decoding algorithm is serial processing, which is only suitable for low and medium speed digital communication systems. At present, digital communication and information storage systems are developing towards high speed, high bandwidth, and high reliability, which puts forward new requirements for error-correcting codes, and the problem of decoding has become a major bottleneck in the development of error-correcting codes.

Berlekamp et al. have proved that the decoding problem of general error-correcting codes is a kind of NP (Non-deterministic Polynomial) complex problem, which can be equivalently treated as a combinatorial optimization problem. Intelligent algorithm (Intelligent Algorithm, IA), as an information processing technology that obtains and solves complex combinatorial optimization problems by imitating the inherent adaptive optimization mechanism of the natural world, is introduced into the error-correcting code technology. It has important theoretical significance and practical value to solve the difficulties faced by error correction code decoding technology by using the adaptive optimization of intelligent algorithm and fast parallel processing mechanism.

According to the relevant literature, there are many studies on the application of GA decoding algorithm and neural network algorithm in error-correcting codes for hard-decision decoding, but generally speaking, the comprehensive performance of the decoding is not good, or the complexity is high. , or poor error correction performance. This is because for complex optimization problems, an intelligent algorithm with a single mechanism is difficult to achieve global optimization, and the efficiency is low. By mixing different intelligent algorithms to maximize strengths and avoid weaknesses, it can effectively solve NP-hard problems in the fields of science and technology and engineering. As far as the genetic algorithm is concerned, its global search ability is good, but when it is used alone, it is difficult to achieve a good compromise between the convergence speed and the convergence performance, while another popular algorithm in the intelligent algorithm - the neural network algorithm has a poor convergence speed. Fast, but harsh on parameter selection. Therefore, if the two are organically combined and applied to the decoding algorithm, the disadvantages can be exploited and better solution results can be obtained.

Contents of the invention

In order to reduce the complexity of traditional soft-decision decoding and increase the decoding speed at the same time, the present invention provides a hard-decision decoding method based on genetic algorithm and neural network to make up for the loss caused by channel transmission errors and hard-decision quantization. The resulting loss of reliability, so as to restore a codeword that is more likely to the transmission sequence as the input of the hard decision decoder to obtain a better decoding result and improve its error correction.

The present invention is a hybrid intelligent decoding method, which can be called a genetic neural network decoding (Genetic Neural-network Decoding, GND) method, and the method comprises the following steps:

(1) Training neural network:

(1.1) Receive the real number symbol sequence r (r ₁ , r ₂ , r ₃ ,…) and obtain the hard decision sequence R after being quantized by the demodulator matched filter;

(1.2) The hard decision sequence R obtained after quantization by the demodulator matched filter is respectively combined with randomly generated d _h /2 n-dimensional binary sequences T to generate d _h /2 candidate sequences A after modulo 2 addition;

(1.3) Training neural network: As a classifier, the neural network consists of a three-layer network, namely the input layer, the hidden layer and the output layer. The input layer consists of n-k neurons, the output layer has 1 neuron, and the hidden layer Including (2/3)(n-k+t+1) neurons, where k is the number of information bits of the code, and t is the maximum number of error corrections of the code; the training process is: the syndrome sequence is used as input In the training mode, the weight w of the corresponding error pattern is used as the target output, so that a corrector can be input to obtain the weight w of the corresponding error pattern (w=1,2,3...,n), and the correction Sub-S is obtained from the code word B represented by the genetic algorithm individual and the check matrix H of the code, that is,

S=B·H' formula (1);

(2) Use the genetic algorithm to optimize to obtain a codeword that is more likely to the transmission sequence:

(2.1) Population initialization: generate 2t n-bit binary vectors as the initial population

(2.1.1) The first individual member P1 of the population: Set the hard decision sequence R(r ₁ ,r ₂ ,...,r _n ) output by the matched filter as the first individual member P1 of the population:

${\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>& {\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>& {\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right.\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; no</span>}$

Among them, Q(q ₁ ,q ₂ ,...,q _n ) is the received real number sequence quantized without hard decision of matched filter;

(2.1.2) The other 2t-1 individual members Pi of the population: it is obtained by adding the randomly generated uniform binary correction sequence T(t ₁ ,t ₂ ,...,t _2t-1 ) and the hard decision sequence R, which is:

P _i = mod(R+T,2), 2≤i≤2 ^t , T=rand[0,1];

(2.2) Individual fitness evaluation:

Evaluate the fitness of genetic algorithm individuals according to the following formula

Among them, λ(P,Q) is a correlation function, which is used to calculate the Euclidean distance between the genetic body Pi and the received real number sequence Q, the more similar the individual is to the received real sequence, the larger the value of λ,

$\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}$

Weight (Error class (Indiv.)) is the output result of the neural network. To get the penalty, it is necessary to calculate the corrector sequence S of the genetic individual to be evaluated, and then input S into the neural network;

(2.3) Natural selection: Based on the roulette selection method or other selection methods, excellent individuals are selected from the initial population to participate in inheritance. The probability that the i-th individual is selected is:

$\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}{\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>}$

(2.4) Pairing crossover: The selected individuals will be paired randomly, and a new individual will be generated by crossing some of its own elements (code elements) with the other party;

(2.5) Genetic variation: the new individual generated in the random selection process (2.4) is mutated, and the processing method is to flip a certain element (code unit) of the individual, that is, from 0→1 or 1→0;

(2.6) Termination of inheritance: inheritance will be terminated when the number of genetic generations reaches the preset value. At this time, the individual with the highest fitness in the population will be output. If the number of generations is not reached, jump to step (2.3) to continue the genetic process.

(3) The best sequence output by the genetic algorithm is input into the hard-decision error correction decoder for decoding, and the final decoding result is obtained.

As can be seen from the above method, the present invention adds the neural network into the individual fitness evaluation mechanism of the genetic algorithm as a supplement to the optimization performance of the genetic algorithm. In the fitness evaluation mechanism, the neural network acts as a pattern classifier. The Hamming distance between the codeword represented by the algorithm individual and the closest available codeword is used to classify the genetic individuals, and the genetic individuals with the same Hamming distance as the nearest codeword are classified into one class. This operation utilizes the one-to-one correspondence between codeword syndromes and coset heads in the decoding standard matrix, and maps input syndrome sequences of genetic individuals to the weights of corresponding coset heads (coset heads) through the neural network. Set the first weight) to achieve. The results obtained by the neural network will be added to the evaluation mechanism of the genetic algorithm as a compensation factor to further strengthen the optimization performance of the genetic algorithm.

Therefore, the present invention makes full use of the self-optimization ability of the genetic algorithm and the pattern classification function of the neural network to optimize the hard-decision quantization output of the receiving matched filter, so as to compensate for the reliability caused by channel transmission errors and hard-decision quantization. In order to recover a codeword that is more likely to the transmission sequence as the input of the hard-decision decoder to obtain a better decoding result. It can be seen from theoretical analysis and computer simulation that its error correction performance is close to that of traditional soft-decision decoding; and its decoding process does not need to use statistical soft information of the channel, and its complexity is greatly reduced compared with traditional soft-decision decoding.

Description of drawings

Fig. 1 is the GND algorithm flowchart of the present invention;

Fig. 2 is a schematic diagram of the neural network classifier of the present invention;

Fig. 3 is a schematic diagram of the performance simulation results of the GND decoding algorithm of the present invention;

Fig. 4 is the GND algorithm corresponding to Table 2 and the complexity of Chase2, GPD algorithm

Graphical comparative analysis chart.

detailed description

In order to make the object, technical solution and advantages of the present invention more clear, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments.

The present invention is a hard-decision decoding method based on genetic algorithm and neural network. Taking block code (n, k) as an example, its implementation process is shown in Figure 1, including:

1. Train the neural network:

1) Receive the real number symbol sequence r(r ₁ ,r ₂ ,r ₃ ,…) and obtain the hard decision sequence R after being quantized by the demodulator matched filter;

2) The hard decision sequence R obtained by the demodulator matched filter quantization is respectively combined with randomly generated d _h /2 n-dimensional binary sequences T to generate d _h /2 candidate sequences A after modulo 2 addition;

3) Training neural network: The neural network required for GND decoding is shown in Figure 2. As a classifier, it consists of a three-layer network, namely an input layer, a hidden layer and an output layer. The input layer consists of n-k neurons, the output layer has 1 neuron, and the hidden layer includes (2/3)(n-k+t+1) neurons, where k is the number of information bits of the code, t is the maximum error correction number of the code. This operation is realized according to the following steps: take the correction sub-sequence as the input training pattern, and take the weight w of the corresponding error pattern as the target output, so that a syndrome can be input to obtain the weight w of the corresponding error pattern (w =1,2,3...,n), the syndrome S can be obtained according to the code word B represented by the genetic algorithm individual and the check matrix H of the code, namely

S=B·H' formula (1)

According to the minimum distance decoding criterion and the standard matrix theory, the greater the Hamming distance between the codeword and the nearest available codeword, the greater the weight of the corresponding co-lead set in the standard matrix, that is, the error that it may contain The larger the number of bits, the larger the output value of the neural network that takes its corresponding syndrome as input.

2. Use the genetic algorithm to optimize to obtain a codeword that is more likely to the transmission sequence:

1) Population initialization: generate 2 ^t n-bit binary vectors as the initial population

a. The first individual member P ₁ of the population: Set the hard decision sequence R(r ₁ ,r ₂ ,...,r _n ) output by the matched filter as the first individual of the population:

$P_1=R(r_1,r_2,...,r_{\mathrm{no}}),r_i=\left\{\begin{array}{cc}1,& q_i>0\\ 0,& q_i\&le;0\end{array}\right.0<i<\mathrm{no}$ Formula (2)

Wherein, Q(q ₁ ,q ₂ ,...,q _n ) is the received real number sequence quantized without hard decision of the matched filter.

b. The other 2 ^t -1 individual members P _i of the population: it is obtained by adding the randomly generated uniform binary correction sequence T(t ₁ ,t ₂ ,...,t _2t-1 ) and the hard decision sequence R, namely :

P _i ＝mod(R+T,2), 2≤i≤2t, T＝rand[0,1] formula (3)

2) Individual fitness evaluation:

Evaluate the fitness of genetic algorithm individuals according to formula 4.11

Formula (4)

a. λ(P,Q) is a correlation function, which is used to calculate the Euclidean distance between the genetic body Pi and the received real number sequence Q. The more similar the individual is to the received real sequence, the larger the value of λ.

$\mathrm{\&lambda;}(P,Q)=\underset{i=1}{\overset{\mathrm{no}}{\mathrm{\&Sigma;}}}{p}_i\&CenterDot;q_i$ Formula (5)

b.Weight (Error class (Indiv.)) is the output result of the neural network, which, as a compensation factor, represents the weight of the most likely error pattern of the codeword corresponding to the genetic individual. When the number of error bits contained in the genetic individual is greater The smaller the value of Weight(Error class(Indiv.)), the smaller the value of the final fitness will be. To get the penalty, it is necessary to use formula (1) to calculate the corrector sequence S of the genetic individual to be evaluated, and then input S into the neural network.

3) Natural selection: Based on the roulette selection method or other selection methods, excellent individuals are selected from the initial population to participate in inheritance. The probability of an individual being selected to participate in inheritance is determined by its fitness. The higher the fitness, the higher the probability of being selected. Big. Generally, the probability that the i-th individual is selected is:

$p\left(P_i\right)=\frac{a\left(P_i\right)}{\underset{j=0}{\overset{N-1}{\mathrm{\&Sigma;}}}a\left(P_j\right)}$ Formula (6)

4) Paired crossover: The selected individuals will be paired randomly, and new individuals will be generated by crossing some of their own elements (code units) with each other. There are many ways to pair crossover, the most common ones are single-point crossover and multi-point crossover. In the study, a single-point crossover was selected, and the crossover probability was set to 0.9;

5) Genetic variation: Randomly select new individuals generated in process 4), and perform mutation processing on them, specifically as follows: Flip a certain element (code element) of the individual, that is, from 0→1 or 1→0, The mutation probability in this study is set to 0.025;

6) Termination of inheritance: inheritance will be terminated when the number of genetic generations reaches the preset value. At this time, the individual with the highest fitness in the population will be output. If the number of generations is not reached, skip to step 3) to continue the genetic process. The number of generations is set to 20.

3. Input the best sequence output by the genetic algorithm into the hard-decision error correction decoder for decoding to obtain the final decoding result.

Analyze from complexity analysis and bit error performance below, further illustrate the advantages of the present invention:

1. Complexity analysis:

The calculation overhead of the GND algorithm mainly includes the optimization of the genetic algorithm module, the classification of the neural network, and the error correction of the hard-decision decoder. The genetic algorithm module accounts for the largest proportion. As far as the neural network is concerned, as long as the network is trained well, When it is used, there are only a few simple steps of addition, multiplication and weight accumulation, and the calculation cost is very small. This analysis evaluates the complexity of the decoding algorithm in terms of the amount of addition and multiplication calculations required throughout the decoding process. Take the linear block code BCH(n,k,d _h ,t) as an example, where d _h is the minimum Hamming distance of the block code, and t is the maximum number of error corrections of the block code.

1) Genetic Algorithm Optimization Module: Genetic Algorithm needs to carry out gen-generation inheritance. In each generation, 2(dh/2-1) individuals need to be processed, and each processing will perform (n-1) additions and n multiplications. So in the end it is necessary to execute addition operations and second multiplication operation;

2) Neural network classification module: The neural network classifier in this study has (2/3)(n-k+t+1) hidden units in total. When using a model for a trained neural network, each hidden unit needs to perform (nk-1) additions and (nk) multiplications, and the output unit performs (2/3)(n-k+t+1) -1 addition and (2/3)(n-k+t+1) multiplication. Therefore, for an input, in the entire decoding process, the number of addition operations required by the neural network module is {(2/3)(n-k+t+1)+nk-2}·gen·2 ^t and {(2/3)(n-k+t+1)+nk}·gen·2 ^t multiplication operations.

3) Hard-decision decoder module: Taking the BM decoding algorithm of BCH as an example, each hard-decision decoding needs to perform (2nt+2t2-t) addition operations and (2nt+2t2) multiplication operations.

If hard decision quantization is regarded as an addition operation, then the GND algorithm of the present invention and the Chase2, GPD algorithm complexity comparison situation are shown in Table 1:

Taking the BCH(31,16,7,3) code as an example, the comparative analysis data of the GND algorithm and the Chase2 and GPD algorithm complexity are shown in Table 2:

For comparison, Fig. 4 also shows the complexity comparison of traditional soft-decision decoding Chase2 and a GPD decoding algorithm based on genetic algorithm given in related literature.

Careful analysis of the data in Table 2 shows that among the three types of decoding, GND decoding has the smallest calculation overhead, followed by GPD decoding, and soft decision CHASE2 has the largest calculation amount. This is because in the decoding process, the CHASE2 and GPD algorithms use additional soft information to generate candidate sequences, while GND directly processes the filter output of the demodulator without borrowing soft information to generate candidate spaces. It can be seen that the GND algorithm is a decoding method with relatively low complexity and strong operability.

2. Bit error performance analysis:

During simulation simulation of the present invention, used BCH (31,16) as decoding object, and parameter setting value is as table 3,

For performance comparison, the applicant simultaneously simulated the optimal decoding algorithm of MLD and GPD decoding (see the literature "Yuan Jianguo, Wang Lin, Huang Sheng, Wang Yong. Probabilistic decoding algorithm based on genetic algorithm [J]. Beijing Post and Telecommunications University Journal. 2012,35(5):98～101”), the bit error performance of CHASE2 soft-decision decoding and BM hard-decision decoding, as shown in Figure 3. In the figure, R represents the matched filter output of the receiving modulator, BER represents the bit error rate, and SNR (dB) represents the signal-to-noise ratio.

Through the careful analysis of Figure 3, various decoding algorithms can reduce the bit error rate of the received sequence to varying degrees by adopting different processing methods for the output result R of the matched filter of the demodulator. For example, as shown in the figure, when the bit error rate is 10 ^-4 , BM hard-decision decoding can obtain about 1.5dB more gain on the basis of the output result of the matched filter, GND algorithm is about 2dB, chase2 is about 2.4GPD decoding Code is about 2.6dB, and MLD decoding can get about 3.8dB. It can be seen that GND decoding has better error correction performance and is close to traditional soft-decision decoding. Although the gain obtained by GND decoding is not as large as that obtained by chase2 and GPD algorithms, as analyzed above, since there is no need to use channel statistical probability soft information to generate search space, the complexity of GND algorithm is much lower than that of chase2 soft decoding and GPD decoding. Stronger. From the above analysis, it can be concluded that the GND algorithm has achieved a good compromise between decoding complexity and decoding error correction performance, and is a superior new decoding method.

Those skilled in the art clearly understand and understand that the examples given by the method of the present invention are only used to illustrate the present invention, and are not intended to limit the present invention. While the invention has been effectively described by way of example, those skilled in the art will recognize that there are many variations of the invention without departing from the spirit of the invention. Without departing from the spirit and essence of the present invention, those skilled in the art should make corresponding changes or deformations according to the present invention, but these corresponding changes or deformations all belong to the protection scope of the claims of the present invention.

Claims (5)

1. A hard decision decoding method based on genetic algorithm and neural network hybrid intelligent algorithm, is characterized in that, comprises the following steps: (1) Training neural network: (1.1) Receive the real number symbol sequence r (r ₁ , r ₂ , r ₃ ,…) and obtain the hard decision sequence R after being quantized by the demodulator matched filter; (1.2) The hard decision sequence R obtained after quantization by the demodulator matched filter is respectively combined with randomly generated d _h /2 n-dimensional binary sequences T to generate d _h /2 candidate sequences A after modulo 2 addition; (1.3) Training neural network: the input layer of the neural network consists of n-k neurons, the output layer has 1 neuron, and the hidden layer includes (2/3)(n-k+t+1) neurons, where k is the number of information bits of the code, and t is the maximum number of error corrections of the code; the training process is: the correction subsequence is used as the input training mode, and the weight w of the corresponding error mode is used as the target output, so that it is input into a The syndrome can obtain the weight w of the corresponding error pattern (w=1,2,3...,n), and the syndrome S can be obtained according to the code word B represented by the genetic algorithm individual and the check matrix H of the code ,Right now S=B·H' formula (1); (2) Use the genetic algorithm to optimize to obtain a codeword that is more likely to the transmission sequence: (2.1) Population initialization: generate 2t n-bit binary vectors as the initial population (2.1.1) The first individual member P ₁ of the population: set the hard decision sequence R(r ₁ ,r ₂ ,...,r _n ) output by the matched filter as the first individual member P ₁ of the population : $\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>& {\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>& {\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right.& \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; no</span>}\end{array}$ Among them, Q(q ₁ ,q ₂ ,...,q _n ) is the received real number sequence quantized without hard decision of matched filter; (2.1.2) The other 2t-1 individual members P _i of the population: add the randomly generated uniform binary correction sequence T(t ₁ ,t ₂ ,...,t _2t-1 ) and the hard decision sequence R ,which is: P _i =mod(R+T,2),2≤i≤2 ^t , T = rand[0,1]; (2.2) Individual fitness evaluation: Evaluate the fitness of genetic algorithm individuals according to the following formula Among them, λ(P,Q) is a correlation function, which is used to calculate the Euclidean distance between the genetic body P _i and the received real sequence Q, the more similar the individual is to the received real sequence, the larger the value of λ, $\mathrm{<span\; class="notranslate">\; \&lambda;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; Q</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}$ Weight (Error class (Indiv.)) is the output result of the neural network. To get the penalty, it is necessary to calculate the corrector sequence S of the genetic individual to be evaluated, and then input S into the neural network; (2.3) Natural selection: Based on the roulette selection method or other selection methods, excellent individuals are selected from the initial population to participate in inheritance. The probability that the i-th individual is selected is: $\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}{\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>}$ (2.4) Pairing crossover: The selected individuals will be paired randomly, and a new individual will be generated by crossing some of its own elements, that is, code elements, with the other party; (2.5) Genetic variation: the new individual generated in the random selection process (2.4) is subjected to mutation processing, and the processing method is to flip a certain element of the individual, that is, the code element, that is, from 0→1 or 1→0; (2.6) Termination of inheritance: inheritance will be terminated when the number of genetic generations reaches the preset value. At this time, the individual with the highest fitness in the population will be output. If the number of generations is not reached, jump to step (2.3) to continue the genetic process; (3) The best sequence output by the genetic algorithm is input into the hard-decision error correction decoder for decoding, and the final decoding result is obtained. 2. The method according to claim 1, characterized in that the paired crossover methods in the step (2.4) include single-point crossover and multi-point crossover. 3. The method according to claim 1, characterized in that the step (2.4) is preferably single-point intersection, and the intersection probability is set to 0.9. 4. The method according to claim 1, characterized in that the variation probability of the genetic variation in the step (2.5) is set to 0.025. 5. The method according to claim 1, characterized in that the number of hereditary generations terminated in said step (2.6) is set to 20.