Type‐II quasi‐cyclic low‐density parity‐check codes from Sidon sequences

Abstract

From Sidon sequences, two explicit methods for constructing (2J, 2L)-regular type-II quasi-cyclic (QC) low-density parity-check (LDPC) codes are proposed without four cycles. The advantage of the new methods is two-fold: (i) compared with the existing lower bound of circulant permutation matrix (CPM) sizes above which type-II QC-LDPC codes exist without four cycles, the novel constructions enable much tighter lower bounds; and (ii) the codes constructed by the first method perform almost as well as type-II QC-LDPC codes from perfect cyclic difference set, while possessing a much more flexible CPM sizes.