New Construction of QC-LDPC Codes Based on Full-Length Row-Multiplier

This paper proposes a new explicit construction method for quasi-cyclic (QC) low-density parity-check (LDPC) codes without 4-cycles and 6-cycles with large column weights. Two integer sequences entirely define the exponent matrix of the new method. The first sequence is an arithmetic sequence starting from 0 with a tolerance of 1, and the second sequence is a special sequence composed of integers that meet the constraint of the greatest common divisor (GCD). The existing explicit method can only provide a variety of row weight types with large circulant size. Compared with the recently proposed symmetric structure method based on computer search, the new explicit construction method has better decoding performance, extremely low description complexity, and does not require computer search.