Research On Linear Programming Decoding Of Non-binary LDPC Code Based On The Decomposition Of Check Node's Degree

The Low Density Parity Check(LDPC)code is one of the best channel coding schemes at present,which is a hot topic in the field of channel coding and is widely used in various kinds of communication systems.Compared with the binary LDPC code,the non-binary LDPC code has the advantages of better error correction performance and stronger anti-burst error capability.However,the disadvantages of the high complexity of the decoder of nonbinary LDPC code and large hardware implementation cost have hindered its wide application.After deeply researching the linear programming(LP)decoding algorithm and the alternating direction method of multiplier(ADMM)of non-binary LDPC codes,a nonbinary LDPC code LP decoding method based on the decomposition of check node's degree is proposed,and applies ADMM method to solve it.Simulation results show that the proposed ADMM-LP method based on degree decomposition is less complex and more efficient in decoding than traditional LP decoding methods.The main content of the paper are as follows:(1)In this thesis,the concepts and details of channel coding,LP decoding algorithms and non-binary LDPC code are clearly introduced.Two main construction methods of nonbinary LDPC codes,Belief Propagation(BP)decoding algorithms for non-binary LDPC codes,and Fast-Fourier-Transformation Q-ary Sum-product algorithm(FFT-QSPA)are given.(2)Based on Maximum Likelihood(ML)decoding criterion,the algorithmic process of LP decoding of non-binary LDPC codes is given.The relaxation method of LP decoding,the construction of polytope,the features of the algorithms and the decoding model complexity are discussed.The basic principle and iterative framework of ADMM algorithm are clearly given.The convergence and termination conditions of ADMM algorithm are summarized.The ADMM algorithm is used to solve the LP decoding model.Error performance of LP decoding model using BP algorithm and ADMM algorithm are compared through simulation.(3)In order to reduce the complexity of LP decoding method,a non-binary LDPC code LPdecoding algorithm based on the decomposition of check node's degree is proposed.The algorithm does not require Euclidean projection on a polytope,thereby reducing the computational complexity of each iteration in the decoding process,and the decoding algorithm can be executed in parallel in each iteration.The simulation results show that the LP decoding algorithm based on the decomposition of check node's degree proposed in the paper can reduce the decoding time compared with the existing LP decoding algorithm without reducing the error performance.The paper also studies the LP decoding problem with penalty function,and applied the ADMM algorithm to solve it,which further improved the decoding performance of the decoder.