Construction And Design Of Spatially-coupled LDPC Codes Based On Finite Fields

Spatially-coupled low-density parity-check(SC-LDPC)codes,originally known as LDPC convolutional codes,have received much attention due to their excellent thresholds.It has been proved that for binary memoryless symmetric(BMS)channels,the maximum a posteriori probability(MAP)threshold of a regular LDPC block ensemble can be approached by the belief propagation(BP)threshold of an ensemble generated by spatially coupling a collection of the original LDPC block ensembles.This is called the threshold saturation phenomenon.Quasi-cyclic LDPC(QC-LDPC)codes have been standardized for various communication systems,due to their low complexity and highly parallelizable encoding and decoding.Due to the merits of both QC-LDPC codes and SC-LDPC codes,this paper theoretically studies the construction of SC-LDPC codes with quasi-cyclic structure over arbitrary finite fields.Such codes are called SC-QC-LDPC codes(Spatially-Coupled Quasi-Cyclic LDPC,SC-QC-LDPC).The SC-QC-LDPC code constructed in this paper is a deterministic construction based on finite field,which avoids time-consuming computer search and ensures that the girth of Tanner graph of the parity-check matrix is at least 6,which generally guarantees the excellent performance of the code.The specific content is as follows:(1)The basic principle of LDPC code and the basic structure of SC-LDPC code.Firstly,for an important factor affecting the performance of LDPC codes—girth,a general method for constructing SC-LDPC codes based on finite field is proposed.The girth of Tanner graph corresponding to the parity-check matrix is at least 6.Then,based on the general method and combining with the characteristics of RS codes,the construction method of RS codes SC-LDPC codes is given.(2)The construction of binary and non-binary SC-LDPC codes based on finite field are studied.Firstly,based on the basic structure of SC-LDPC codes and QC-LDPC codes,a general method for constructing binary and non-binary SC-QC-LDPC codes is proposed.The proposed method is based on the array dispersion of the modified basis matrix satisfying 2 x 2 submatrix constraint on the finite field GF(q).The girth of Tanner graph corresponding to the parity-check matrix is at least 6.Then,based on the general method,three specific methods for constructing binary and non-binary SC-QC-LDPC codes are proposed.From these methods,six classes of binary SC-QC-LDPC codes and non-binary SC-QC-LDPC codes are constructed.(3)The construction of SC-LDPC code based on RS code is studied.Firstly,based on the universal parity-check matrix of a special subclass RS codes,the construction of basis matrix and masking matrix is given.From the general method in(2),the girth of Tanner graph corresponding to the parity-check matrix of SC-LDPC codes is at least 6.Then,for structured SC-LDPC codes based on RS codes,the structure of basis matrix and masking matrix is given.From the general method in(2),the girth of Tanner graph corresponding to the parity-check matrix of SC-LDPC codes is at least 6.