Research On Construction And Decoding Algorithm Of Nonbinary Low-Density Parity-Check Codes

In this paper, the methods to reduce the complexity of decoding algorithm and design the construction methods of nonbinary LDPC codes with low encoding complexity are studied.In the study of decoding algorithms of nonbinary LDPC codes, the Sum-Product algorithm of nonbinary LDPC codes based on belief propagation is summarized at first. Then the Sum-Product decoding algorithm of nonbinary LDPC codes based on log-likelihood ratios is analyzed in detail and an improved algorithm with low complexity is proposed based on the linear approach method. The Extended-Min-Sum algorithm which has lower computational complexity is carefully studied and an improved algorithm based on sorting and truncation method is proposed. The simulation results show that the proposed algorithms not only have low computational complexity but also have outstanding performance. In the study of LDPC codes construction, the available design methods are compared and introduced at first. Then the construction methods of nonbinary quasi-cyclic LDPC codes in the Galois Field are discussed and some methods are proposed. Subsequently, three construction methods of LDPC codes are proposed based on RS codes according to the characteristic of parity check matrix of RS codes. Finally, the simulation results show that the proposed construction methods have linear encoding complexity and are suitable for constructing the middle and short nonbinary LDPC codes with outstanding performance. All the algorithms in this paper are simulated using Matlab. The simulation results show that the proposed algorithms can effectively reduce the complexity of construction methods and decoding algorithms of nonbinary LDPC codes.