Explicit Constructions of Short QC-LDPC Codes Free of Small Cycles and with Large Column Weight

Three new explicit constructions are proposed for quasi-cyclic (QC) low-density parity-check (LDPC) codes free of 4-cycles and 6-cycles with large column weights. The exponent matrices for these new methods are completely defined by two sequences of integers. The first sequence is an arithmetic sequence starting from zero with the common difference being one, and the second is a special sequence composed of integers satisfying the greatest-common-divisor (GCD) constraint. The new methods can produce rather small circulant sizes for many categories of row weights, while the existing explicit methods can only provide relatively large circulant sizes, thus the up-to-date smallest circulant sizes being nearly halved. Compared with the recently proposed symmetrical construction which relies upon extensive search, the new explicit constructions have similar or better decoding performance, possess extremely low description complexity and need no computer search. © 2024 Chinese Institute of Electronics. All rights reserved.