A Lattice-Based Systematic Recursive Construction of Quasi-Cyclic LDPC Codes.

This paper presents a low-complexity recursive and systematic method to construct good well-structured low-density parity-check (LDPC) codes. The method is based on a recursive application of a partial Kronecker product operation on a given γ × q, q ≥ 3 a prime, integer lattice L(γ × q). The (n - 1)- fold product of L(γ × q) by itself, denoted Ln(γ × q), represents a regular quasi-cyclic (QC) LDPC code, denoted Cγxqn, of high rate and girth 6. The minimum distance of Cγxq1 is equal to that of the core code Cγxq1 introduced by L(γ x q). The support of the minimum weight codewords in Cγ×qn are characterized by the support of the same type of codewords in Cγ×q1. From performance perspective the constructed codes compete with the pseudorandom LDPC codes. [ABSTRACT FROM AUTHOR]