基于伪辛空间的LDPC码的构造

Construction of LDPC Codes Based on Pseudo-symplectic Space

基于有限域Fq上的(2v+2)维伪辛空间,根据子空间的包含关系,选取(m,0,0,1)型全迷向子空间,构造出了点集和线集并定义了点、线之间的关联关系,根据图论知识构造出所对应的二分图的关联矩阵,得到LDPC码的校验矩阵,最终构造出LDPC码C(ν+1,2ν+2,q),求得围长为8,最小距离为2q+2.对码C(ν+1,2ν+2,q)取固定参数,利用子空间的包含关系,得到LDPC码C(3,6,2)的校验矩阵,求得码率,并对码进行了译码仿真,发现码C(3,6,2)比相同参数的随机码的码率高.

The low density parity check(LDPC) code is presented based on the subspaces of type(m,0,0,1) in the(2v+2)-pseudo-symplectic space F;through the inclusion relationships of subspace. The point set and the line set are constructed and the association relationship between points and lines is defined. The incidence matrix of the bipartite graph can be obtained. Let the incidence matrix be the check matrix, then the low density parity check code C(ν+1,2ν+2,q) is constructed with girth 8 and minimum distance 2q+2. Take the concrete parameters, the code C(3,6,2) is presented and simulated in decoding whose code rate is higher than that of most random codes.