Reasearch On ADMM Decoding Algorithm Of LDPC Codes

As the key technology of communication physical layer,channel coding plays an important role in the development of communication system in recent years.As a linear block code with sparse check matrix,low-density parity-check(LDPC)can has the performance of approaching shannon limit.As a classical decoding algorithm of LDPC,belief propagation(BP)has good performance,but there is an error floor phenomenon in the high signal-to-noise ratio(SNR)region.In order to overcome this phenomenon and improve performance,the decoding algorithm based on mathematical programming(MP)has been widely studied in the field of error correcting coding.The alternating direction method of multipliers(ADMM)is used as a method to solve large-scale optimization,and it can be used to solve MP decoding problem with linear time complexity.It has better performance and lower error floor than BP algorithm.In this dissertation,we do the following optimization for LDPC decoding problem:1.Aiming at the problem of false flat layer in BP decoding,first,we proposed a hybrid decoding of BP and ADMM for LDPC codes based on cylic redundancy check(CRC).At the decoding end,BP and ADMM serial hybrid decoding scheme is used.At the encoding end,CRC-LDPC is used,and the corresponding decoding end uses CRC and parity joint check.When the joint check fails,the soft information corresponding to the failed sequence is sent to the second level decoder.The simulation results show that the performance of hybrid decoding is improved by 0.2d B compared with BP decoding.2.In order to solve the problem of excessive auxiliary variables in the degree decomposition of check nodes,an arbitrary degree decomposition algorithm of check nodes is proposed.This scheme reduces the number of auxiliary variables by replacing high check nodes with fewer low check nodes.Compared with the 3-degree decomposition scheme of check node,this scheme is more flexible,and the calculation time required for one iteration is shorter.Finally,the ADMM algorithm based on 4-degree decomposition of check node is verified by simulation.Finally,the ADMM algorithm based on the parity node 4-degree decomposition is verified by simulation.Based on the algorithm of parity node degree decomposition,a parity matrix expansion scheme based on parity node degree decomposition is proposed,and the feasibility of the scheme is verified by simulation.3.For the problem of too many iterations of ADMM algorithm,the NS-ADMM algorithm based on degree decomposition is proposed.Firstly,the ADMM algorithm message passing model based on check node decomposition is derived.The definition and calculation method of check node residuals are given in the message passing model.Finally,a node scheduling strategy based on the principle of maximization of check node residuals is proposed,and variable nodes are updated by this strategy.Simulation shows that under the scheme of hybrid degree decomposition of check nodes,compared with the ADMM algorithm without node scheduling,the iteration times of the ADMM algorithm using node scheduling strategy is only 15% of that of the ADMM algorithm with high signal-to-noise ratio.