Research On Decoding Algorithm Based On ADMM For Low-density Parity-check Codes

At present,low-density parity-check(LDPC)codes have received much attention by many researchers due to their flexible structure,lower decoding complexity and good performance approaching Shannon limit.The linear programming(LP)decoding algorithm for LDPC codes has the maximum likelihood certificate property,but its disadvantage is the high decoding complexity.Barman et al.presented an iterative LP decoding algorithm based on the alternating direction method of multipliers(ADMM).This algorithm can effectively reduce the LP decoding complexity for LDPC codes,while its decoding performance is worse than the belief propagation(BP)decoding algorithm.In order to solve this problem,Liu et al.designed an ADMM penalized decoding algorithm by introducing a penalty term to the objective function of the LP decoding model,which can make pseudocodewords more costly than codewords.In order to accelerate the decoding speed and improve the decoding performance,the ADMM decoding algorithm for LDPC codes are thoroughly investigated in this dissertation.The main research results are summarized as follows:1.In order to improve the ADMM penalized decoding performance for LDPC codes,two improved penalty functions are designed for ADMM penalized decoding algorithm by increasing the slope of the penalty function at the points near x(28)0 and x(28)1.These two improved penalty functions can punish pseudocodewords more quickly and thus increase the decoding speed.Compare with the existing penalty functions,the ADMM penalized decoding algorithm based on the improved penalty functions can achieve better decoding performance with faster decoding speed.2.To increase the ADMM penalized decoding speed further,through decreasing the number of Euclidean projections,two kinds of layered scheduling ADMM penalized decoding methods are designed based on the improved penalty function by exploiting horizontal layered scheduling and vertical layered scheduling strategies,respectively.Compared with the existing ADMM penalized decoding algorithms,the designed two decoding algorithms obtain better decoding performance with the less average number of iterations.3.In order to reduce the average number of iterations for LDPC codes decoding,an early termination(ET)method of the ADMM penalized decoding is proposed by making a thorough analysis of the change rule of the number of satisfied parity-check constraints in ADMM penalized decoding for LDPC codes.The proposed method can detect the error codewords at an early stage of decoding and then the decoding process is stopped,which saves the unnecessary decoding iterations.Compared with the existing stopping methods of ADMM penalized decoding,the proposed ET method can almost lose no decoding performance and meanwhile reduces the average number of iterations of ADMM penalized decoding at low signal-to-noise rations.4.By tracking the changing rate of hard decisions message during every two iterations of the ADMM penalized decoding,an efficient ET criterion is proposed to improve the convergence rate of ADMM penalized decoding for LDPC codes.Simulation experiments show that the proposed ET method can reduce the average number of iterations significantly at low signal-to-noise ratios with a negligible performance degradation.