Further Results on the Stopping Distance of Array LDPC Matrices

Abstract

Given an odd prime q and an integer m ≤ q, an array-based parity-check matrix H(m,q) can be constructed for a quasi-cyclic low-density parity-check (LDPC) code C(m,q). For m = 4 and q ≥ 11, we prove the stopping distance of H(4,q) is 10, which is equal to the minimum Hamming distance of the associated code C(4,q). In addition, a tighter lower bound on the stopping distance of H(m,q) is also given for m > 4 and q ≥ 11.