Research On ADMM Decoding Algorithms For Non-binary LDPC Codes

Low density parity check(LDPC)codes are a good class of error correcting codes whose error correcting performance can approach the Shannon limit.In recent years,LDPC codes have received considerable attention.The non-binary LDPC codes can be obtained by generalizing the binary LDPC codes to the finite field with more than two symbols.Compared with binary LDPC codes,non-binary LDPC codes have better anti-burst noise performance and are more suitable for multiple phase modulation.From the viewpoint of speeding up the convergence rate and reducing the computational complexity,the ADMM decoding and the ADMM penalized decoding algorithms for nonbinary LDPC codes are thoroughly investigate in this thesis.The main research works are summarized as follows:1.The basic principle of non-binary LDPC codes and both maximum likelihood decoding algorithm and linear programming decoding algorithm for non-binary LDPC codes are summarized.The basic principle of Alternating Direction Method of Multipliers(ADMM)is described.The ADMM decoding algorithm and the ADMM penalized decoding algorithm for non-binary LDPC codes are discussed in detail.The word error rate performance of the ADMM penalized decoding algorithm for non-binary LDPC codes is greatly improved compared with ADMM decoding algorithm.2.The existing ADMM decoding algorithms for non-binary LDPC codes are implemented with flooding scheduling.This scheduling scheme makes the ADMM decoding converge slowly.In order to improve the convergence rate,two layered scheduling schemes are designed in this thesis,which are called the horizontal layered(HL)scheduling and the vertical layered(VL)scheduling.Simulation results show that these two layered scheduling schemes for ADMM decoding and ADMM penalized decoding exhibit better word error rate performance and faster convergence rates when compared to the flooding scheduling scheme.In addition,the performance of the VL scheduling is better than that of the HL scheduling.3.The ADMM penalized decoding algorithm for non-binary LDPC codes needs to be solved by double-layer ADMM.The outer iteration of ADMM is used to solve the decoding problem,and the inner iteration of ADMM is used to solve the European projection operation on the relaxed code polytope.Therefore,the complexity of the ADMM penalized decoding algorithm for non-binary LDPC codes is high.By determining the invalid projection operation in decoding and omitting these invalid projections,the inner iteration of ADMM can be omitted,a reduced-complexity ADMM penalized decoding algorithm for non-binary LDPC codes is proposed.Simulation results show that compared with the existing ADMM penalized decoding algorithm,the proposed ADMM penalized decoding algorithm for nonbinary LDPC codes has a shorter average decoding time in the case of comparable error performance.