Binary QC-LDPC Codes Based on Whiteman's Generalized Cyclotomy

This study introduces a construction method for QC-LDPC codes, ensuring their absence of four-cycles by utilizing Whiteman's generalized cyclotomic (GC) classes. An analysis of the cycle structure within the Tanner graph for the proposed codes, specifically focusing on cycles with length six, is conducted. Moreover, this paper presents the necessary and sufficient conditions for generating GC-QC-LDPC codes with a minimum girth of eight, based on the analysis. Simulation results demonstrate the superior bit error rate (BER) performance of the constructed QC-LDPC codes over the AWGN channel. Compared to other QC-LDPC codes, QC-LDPC codes constructed using this method have a reduced base matrix size for long code lengths. This attribute augments their suitability for integration within storage systems.