Research On Linear Programming Decoding Algorithm Based On ADMM For RS Codes

With the advent of the 5G era,the public's awareness and expectations of communication technology have gradually begun to increase.As one of the most important research fields in communication technology,channel coding technology has also gradually developed and expanded to provide guarantee for the reliability of information transmission.RS code is a special M-ary code in channel coding.Because of its strong error correction ability,RS code is favored by researchers and communication engineers,and is widely used in optical communication and satellite communication.As a traditional optimization model,linear programming has matured and is widely used in various fields.It provides a new idea for error correction code decoding.In this paper,by studying the linear programming decoding algorithm and RS code,we find that almost all existing linear programming decoding is performed on binary codes.However,because RS is a M-ary code,conventional linear programming decoding cannot be used to solve it.In view of this,this paper uses a special construction method to convert the RS binary code check matrix into a brand new binary check matrix,and uses the ternary check idea to transform the decoding problem into a linear programming problem..Finally,the ADMM algorithm is used to solve the problem.It can be seen from the simulation results that the linear programming decoding performance of the RS code proposed in this paper is higher than that of hard decision decoding,and it is a suboptimal decoding algorithm close to ML decoding.The main work of this article is as follows:1.First,the algebraic structure of RS codes and the concept of Galois field are briefly introduced,and the definitions of linear block codes and cyclic codes are given.The emphasis is on the generation of RS codes and traditional hard-decision decoding algorithms.2.Linear programming is an important method to solve RS code decoding in this paper.First,the basic structure of linear programming is given.The ADMM algorithm is briefly explained.Starting from maximum likelihood decoding,the basic model of linear programming decoding is derived,and the performance of LP decoding is simulated,which proves that the decoding method is a suboptimal decoding algorithm close to ML decoding.3.For the M-ary RS code,a creative method is proposed to transform the multi-ary check matrix of the RS code into a binary check matrix,and use the idea of ternary check to relax the decoding of the RS code.It is a linear programming problem and is solved using the ADMM algorithm.4.Since the RS code is a high-density code,the number of non-zero elements in the binary check matrix constructed using the construction method of this article is too large,which leads to the decoding convergence to the fractional digital word.In view of this,it is proposed to perform elementary row transformation on the check matrix,reduce the number of non-zero elements in the matrix,and analyze the introduction of auxiliary variables in the ternary check idea.A new introduction method is proposed,which greatly reduces the auxiliary The number of variables.Compared with the traditional algorithm,it is found that the introduction method greatly improves the LP decoding performance.