Research On LDCP Codes Linear Programming Decoding Algorithms Based On BADMM

Low density parity check(LDPC)code is a linear block code with a sparse parity check matrix.LDPC code has been widely used in the field of wireless communications due to its decoding performance approaching the Shannon limit.Belief Propagation(BP)algorithm is currently the most widely used decoding algorithm for LDPC codes,and its main dilemma is that there is high bit error floor when SNR is high.In recent years,the linear programming(LP)decoding algorithm has been developed.It has approximate maximum likelihood(ML)decoding performance and a low error floor.But the main problem is that LP decoding methods are high decoding complexity and slow convergence speed.In view of the above disadvantages of the existing LP decoding algorithm,this paper proposes a LP decoding algorithm called Bregman alternating direction multiplier method(BADMM).BADMM decoder has two advantages: low complexity and fast convergence.The simulation results show that the proposed BADMM algorithm has faster convergence speed than the existing LP decoding algorithm.The main contents and innovations of this article are summarized as follows:1.The basic principles and decoding methods of the LDPC code are introduced.The concept,representation and classification of LDPC codes are given.Three decoding algorithms of LDPC codes are mainly introduced: ML decoding algorithm,BP decoding algorithm and LP decoding algorithm.Finally,three different lengths of codewords are selected to simulate the decoding performance of the BP decoding algorithm,and it is concluded that the BP decoding algorithm will have a bit error floor when the SNR is high.2.For LDPC codes,ADMM decoding algorithm with lower complexity each iteration is proposed.A framework of ADMM algorithm is introduced.Based on Feldman's basic polytope LP decoding model,the LP decoding algorithm based on ADMM algorithm is introduced.In order to reduce the computational complexity of the projection part of the ADMM decoding algorithm,a method is proposed that does not need to be sorted.The cut search algorithm(CSA)reduces the computational complexity of the algorithm in each iteration.3.To further improve the convergence speed of the above mentioned ADMM decoding algorithm,we combine the Bregman divergence idea and ADMM decoding framework,then propose a BADMM decoding algorithm with fast convergence characteristics and low complexity.In this algorithm,Bregman divergence is added to each updated variable,which accelerates the convergence of the algorithm.The simulation results show that compared with the ADMM algorithm,the proposed BADMM algorithm can reduce the average number of iterations significantly without reducing the decoding performance.In order to further improve the decoding performance of the BADMM algorithm in the low SNR region,an improved BADMM algorithm is proposed by adding a penalty function to the objective function.Simulation results show that the proposed has similar decoding performance in low SNR and BP decoding.