Abstract
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.
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