Research On Decoding Methods Based On Neural Networks For BCH/RS Codes

With the rapid development of communication technology,channel coding has made great progress in theory and engineering,which improves the reliability and accuracy of information transmission.The Bose–Chaudhuri–Hocquenghem(BCH)code and the Reed-Solomn(RS)code are high-density linear block codes in channel coding.Due to their good error correction performance,they have been widely used in satellite communication and high-density storage.Nowadays neural network is an emerging technology,which provides a new idea for solving traditional communication problems.Improving error correction performance via this technology is an interesting research direction in the future.In this thesis,the neural network decoding method is explored.Based on the belief propagation neural network of BCH code,a method of using the deep convolutional neural network to reduce the estimation error of the belief propagation network is proposed.Since RS code is a kind of M-ary BCH code,it cannot be decoded by a belief propagation neural network.In view of this,a denoising neural network and an error correction neural network cascading decoding method are proposed for RS code.The results show that the neural network decoding methods of BCH code and RS code proposed by us can achieve lower frame error rate.The main contents and work contained in this article are as follows:1.Firstly,the basic theory of the Galois field,the characteristics of the linear block code and the cyclic code are briefly summarized.Then,the encoding method of the BCH code using the generator matrix is introduced.The hard decision decoding is performed by the syndrome,the error location polynomial and the money search method.In this method,due to the M-ary nature of RS code,it is necessary to use the generator polynomial to decode.Based on the decoding of the BCH code,the Berlekamp-Massey(BM)iterative algorithm and the Forney algorithm are used to complete the hard decision decoding.2.Artificial neural network is an important method to solve the decoding problem in this thesis.Firstly,the basic structure of artificial neural network,activation function,cost function and back propagation algorithm are explained.This thesis introduces introduces the more mature neural network model,in which the feedforward neural network and the recurrent neural network are the main structures of the BCH code and RS code decoding neural network.Finally,the experimental tool Tensorflow is introduced.3.Firstly,the method of decoding with multi-layer perceptron is introduced.The method has high complexity and bad error correction performance.Then this thesis introduces the belief propagation decoding algorithm and the belief propagation neural network decoding based on the Tanner graph structure.Because of the large estimation error in the output of the network,this thesis designs a one-dimensional convolutional neural network for BCH codes to reduce the estimation error,and expounds the design idea and principle of the network structure.Tensorflow verifies that the improved scheme proposed in this thesis has a lower frame error rate than the belief propagation decoding network.4.Since RS code is a kind of M-ary code,the decoding neural network of the binary BCH code is not suitable for the M-ary RS code.In this thesis,a neural network decoding method for RS code is proposed.The decoding neural network consists of two parts: the noise reduction neural network and the error correction neural network.Firstly,a recurrent neural network for M-ary RS codes is designed to realize the noise reduction function of RS codewords for channel reception.Then a codeword rearrangement multiplier is designed to make the recursive neural network better.In the sequence relationship in the codeword,a multi-level residual neural network is designed to realize the error correction function of the noise-reducing RS codeword.Finally,the specific model of the noise-reduction neural network and the error-correction neural network is determined via experiments.The decoding neural network of RS code is obtained,and the error frame rate experiment is carried out.The results show that the proposed method can complete the decoding of RS code and has a better error correction performance than the traditional decoding method.