Distributed Consensus ADMM Algorithm And Its Application On RS Decoding

The distributed system has good reliability and can be calculated in parallel.As a result,the distributed system has attracted the attention of many scholars.This thesis studies how the Alternating Direction Method of Multipliers(ADMM),which is a classic optimization algorithm,can achieve better reliability on distributed systems.This thesis will also apply the distributed algorithm obtained from the research to solve the RS(Reed-Solomon)decoding problem.As a type of multi-ary code with strong error correction capability and60 years of development since its proposal,RS code is widely used in the fields of satellite communication and optical communication.This thesis combines RS decoding with a decentralized and centralized distributed system to make the RS decoding system have better reliability and higher decoding efficiency.The main work of this thesis is as follows:1.Established a consensus ADMM algorithm model suitable for centralized architecture and a consensus ADMM algorithm model suitable for decentralized architecture.2.Conventional linear programming decoding algorithms for binary codes cannot be applied to RS decoding for multi-ary codes,and traditional decoding algorithms cannot perform distributed calculations.This thesis derives the linear programming decoding model of the RS code from the maximum likelihood decoding model of the RS code,and uses the decentralized consensus ADMM algorithm to solve the linear programming decoding problem.This thesis proposes an RS decoding method using the decentralized consensus ADMM algorithm.The simulation results show that the decoding performance of the RS decoding method using the decentralized consensus ADMM algorithm proposed in this thesis is much better than that of the hard decision algorithm.At the same time,the decoder system based on the decentralized architecture has good reliability and parallel computing capabilities.3.In view of the long decoding time of the RS decoding method using the decentralized consensus ADMM algorithm,this thesis models the RS decoding problem using the centralized consensus ADMM algorithm.The simulation results show that under the same signal-to-noise ratio,the decoding time of the RS decoding method using the centralized consensus ADMM algorithm is nearly 100 times shorter than that of the RS decoding method using the decentralized consensus ADMM algorithm.