Construction of QC-LDPC Codes with Product-like Exponent Matrices Based on Rectangular Area

This paper proposes a novel algorithm for constructing girth-8 quasi-cyclic (QC) LDPC codes with product-like (PL) exponent matrices, termed PL-QC-LDPC codes. To simplify the analysis of cycles in the Tanner graph of PL-QC-LDPC codes, we introduce the rectangular area (RA) and present an efficient semi-search RA algorithm to determine the minimum size of circulant permutation matrices (CPMs) in the exponent matrix. Moreover, search depth is employed to balance the trade-off between search complexity and optimization of the minimum CPM-size. Numerical results demonstrate that our proposed method, combined with masking method, can achieve smaller CPM-size and lower error floor than the greatest common divisor (GCD) method.