QC-LDPC Code Complete Algebraic Design Method

Low-density parity check code(LDPC, low-density parity-check codes),as a result of a natural parallel decoding algorithm and approaching Shannon's capacity limit performance, is becoming an optional error correction with good performance and a good execution code category in high-speed mobile communication systems. Design of complete algebraic structure of LDPC codes with good performance is of great significance in practice.This paper studied the complete algebraic structure of Quasi-Cyclic LDPC(QC-LDPC) code,the main work has the following several aspects:1?This paper proposes a completely algebraic structure design method of regular QC-LDPC codes, the parity check matrix H is decomposed into the base matrix and shift matrix. Base Matrix formed by t=3 Steiner system of Combinatorial mathematics, full shift matrix formed by finite field additive group, Under the effect of generalized Hadamard product, we get a sparse shift matrix from base matrix and shift matrix. whose extended matrix defines an regular QC-LDPC code. Because of complete algebraic structure,the QC-LDPC codes perform better in occupying hardware resources and hardware implementation as well as the error performance.2?This paper describes the principle of base matrix based on the Steiner system of t = 2 and t 33,puts forward the design of multiple base matrix, the matrix are excluding four cycle.This paper also summarizes the basic principles of finite field additive group and multiply group, make them effective mathem-atical tool for design of full elements shift matrix.Under the design framework,we constructed a variety of parameters QC-LDPC codes are met girth of 6, the simulation results and analysis are given. For 1/2 rate,column weight of three is a kind of typical QC-LDPC codes, there's almost no completely algebraic s cheme design code(3,6) rules, using the design method proposed in this paper, the design of(3,6) QC-LDPC code is completely algebraic structure.And the s imulation results show that compared with other published algebraic structure,theregular(3,6)QC-LDPC proposed in this paper has better performance.,.when bit error rate at 610-. Its performance close to the Shannon limit of less than 1.9d B.3?we design an algorithm which statistics the six cycle number in check matrix when it is absence of four cycle and have constant row weight.The Algorithm is independent of the design scheme of the matrix,flexible and practical.Using the algorithm to calculate the number of six cycle in several kinds of matrix in this paper, through the analysis,we analyzed. the shift values influence on short loop number, and impact on ber performance.