基于环路分类的围长至少为10的QC-LDPC码显式构造方法

Explicit construction of QC-LDPC codes with girth at least ten based on cycle classification

对于围长至少为10的(3,L)-规则准循环(QC)低密度奇偶校验(LDPC)码,现有的显式构造法在参数选取上不够灵活。针对该问题,提出一种基于环路分类的显式构造方法。该方法在构造过程中,首先在循环置换矩阵(CPM)尺寸为无穷大的假设下,考虑各种长度小于10的环路形状导致的等式约束,以渐进方式确定出QC-LDPC码对应的指数矩阵中的每个元素的取值下界;然后根据指数矩阵确定出CPM尺寸的连续取值下界。这种方法允许L任意取值,允许CPM尺寸在一个门限以上任意取值。仿真结果表明,对于L=5,新码与Tanner提出的围长为12的(3,5)-规则QC-LDPC码的译码性能几乎一致。

For the construction of(3,L)-regular quasi-cyclic(QC)low-density parity-check codes with girth at least ten,the existing explicit methods are not flexible in the selection of parameters.As to this problem,this paper proposed a novel explicit method on the basis of cycle classification.In the construction procedure,it considered all equation constraints governing all cycles with lengths smaller than ten for the case of an infinite circulant-permutation-matrix(CPM)size.Then,it determined all elements within an exponent matrix for a QC-LDPC code as lower bounded progressively.Finally,it determined a lower bound above which CPM size could vary consecutively based on the entries within the exponent matrix.The new approach enables both an arbitrary L and an arbitrary CPM size above a certain lower bound.Simulation results show that,for L=5,the new codes perform as well as Tanner’s(3,5)-regular QC-LDPC codes with girth 12.