Graph-based convolutional and block LDPC codes
Problems of Information Transmission
Construction of nonbinary quasi-cyclic LDPC cycle codes based on singer perfect difference set
IEEE Communications Letters
Large-girth nonbinary QC-LDPC codes of various lengths
IEEE Transactions on Communications
A comparative study of parallel algorithms for the girth problem
AusPDC '12 Proceedings of the Tenth Australasian Symposium on Parallel and Distributed Computing - Volume 127
Low-density parity-check codes based on steiner systems and permutation matrices
Problems of Information Transmission
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A quasi-cyclic (QC) low-density parity-check (LDPC) code can be viewed as the protograph code with circulant permutation matrices (or circulants). In this correspondence, we find all the subgraph patterns of protographs of QC LDPC codes having inevitable cycles of length 2i, i = 6, 7, 8, 9,10, i.e., the cycles that always exist regardless of the shift values of circulants. It is also derived that if the girth of the protograph is 2g, g > 2, its protograph code cannot have the inevitable cycles of length smaller than 6g. Based on these subgraph patterns, we propose new combinatorial construction methods of the protographs, whose protograph codes can have girth larger than or equal to 14 or 18. We also propose a couple of shift value assigning rules for circulants of a QC LDPC code guaranteeing the girth 14.