Structure Design Of GC-LDPC Codes Based On Finite Field

Low density parity check(LDPC)codes is a kind of practical error correcting code with performance approaching Shannon limit,which has been adopted by many communication industry standards including 5G.In the parity check matrix of LDPC codes,the existence of cycles will have a significant impact on the error correction performance,it is also one of the research hotspots of LDPC codes.GC-LDPC codes is a special kind of LDPC codes.Due to its special structure,it has great performance on AWGN channel.This paper mainly studies the construction of GC-LDPC codes with good performance.The main works and innovations of this paper are described as follows:Firstly,a shift matrix is constructed based on galois field.QC-LDPC code constructed based on such a shift matrix will not have 4-girth structure in its parity check matrix.Combining the matrix structure of GC-LDPC codes with the shift matrix,a codeword without 4-cycle is constructed.Secondly,according to the structure characteristics of cycle,a matrix with an inevitable girth with size at least 20 is designed.This matrix is used as the model matrix of the local matrix R in GC LDPC code base matrix.The model matrix of global matrix X is constructed by the matrix with column weight of 1.In this way,the model matrix of GC LDPC code base matrix with column weight 3 is obtained.The base matrix of GC-LDPC code with girth 6 is obtained by filling the complete model matrix with the shift value matrix based on finite field.Then,on this basis,the search algorithm is used to further eliminate the 6-girth and 8-girth.Then,balanced incomplete block design(BIBD)is applied to the design of local matrix and global matrix of base matrix of GC-LDPC code.By adding the corresponding full element matrix to the global matrix,the GC-LDPC code with column weight of 6 is generated,and different code rates are achieved by adjusting the incidence matrix of BIBD.Simulation results show that the GC-LDPC code constructed in this method have good performance over AWGN channel.Finally,a search algorithm based on difference matrix is proposed to construct shift value matrixs with column weight of 6 and without 4-cycle and 6-cycle.On this basis,QC-LDPC code with half-rate and column weight 6 is constructed.