In this paper, some affine and rational functions are applied to define a class of LDPC codes, called RLDPC codes, which can be classified in two types, type-I and type-II, depending on being equivalent or not with APM-LDPC codes, respectively. Then, for each type, some explicit methods are provided to generate RLDPC codes with girth at least 6. While, cyclotomic cosets are used to generate type-I RLDPC codes, normal and diameter RLDPC codes are proposed as a class of type-II RLDPC codes which are analyzed for the existence of 4-cycles. Finally, simulation results show that the constructed type-II RLDPC codes outperform the randomly constructed QC LDPC codes, APM-LDPC codes and the LDPC codes based on PEG.

本文利用仿射函数和有理函数定义了一类LDPC码，称为RLDPC码，根据与APM-LDPC码是否等价，可以分为I类和II类两类。 ， 分别。然后，对于每种类型，提供一些显式方法来生成周长至少为 6 的 RLDPC 码。同时，使用分圆陪集来生成 I 类 RLDPC 码、法线和直径RLDPC 码被提议为一类 II 型 RLDPC 码，分析其是否存在 4 个周期。最后，仿真结果表明，构造的II型RLDPC码优于随机构造的QC LDPC码、APM-LDPC码和基于PEG的LDPC码。