利用几何图形构造不含小环的LDPC码

对低密度奇偶校验(low-density parity-check,LDPC)码的Tanner图和几何图形之间的关系进行分析后,提出了一种规则的(3,k)LDPC码的构造方法,该方法基于三维点阵实现。通过在一个三维的点阵中构造线,并合理地选择斜率来消除点阵中的三角形结构,从而使得所造的码的圈长为8,三维点阵高度的选择通过一个搜索算法实现,该方法简单有效。在AWGN信道上进行仿真,结果表明利用提出的构造方法所构造的LDPC码具有良好的性能。

Construction of LDPC codes without small cycles based on geometry

By analyzing the relationship between the Tanner graph of LDPC codes and geometry,a construction of(3,k) regular LDPC codes based on 3-D grid is proposed.By selection of line slope,triangles are removed from the lattice,which leads to the girth of the point-line incident matrix no smaller than eight, the height of lattice is obtained by a searching algorithm,and the construction is simple and efficient.Simulation result shows that the codes consturcted under the construction perform well over AWGN channel.