Construction of Quasi-Cyclic LDPC Codes via Masking With Successive Cycle Elimination

In this letter, we study the construction of quasi-cyclic (QC) low-density parity-check (LDPC) codes by array dispersion and masking. We first propose a class of arrays of circulant permutation matrices (CPMs) of arbitrary size obtained by dispersion. Based on this class of arrays of CPMs, a class of QC-LDPC codes is constructed. For these resulting codes, we analyze their cycle structure and derive the numbers, which indicate how many cycles pass through each CPM in their parity-check matrices. Following the indication numbers with the order from largest to smallest, we replace the corresponding CPMs with zero matrices (ZMs) of the same size one by one until a targeted masking termination condition is satisfied. Then, the resultant arrays of CPMs and ZMs give a large class of QC-LDPC codes. Numerical results show that the codes constructed perform well over the additive white Gaussian noise (AWGN) channel when decoded with the sum-product algorithm.