On the First Separating Redundancy of Array LDPC Codes

Abstract

Given an odd prime q and an integer m ≤ q, a binary mq × q² quasi-cyclic parity-check matrix H(m, q) can be constructed for an array low-density parity-check (LDPC) code C(m, q). In this letter, we investigate the first separating redundancy of C(m, q). We prove that H(m, q) is 1-separating for any pair of (m, q), from which we conclude that the first separating redundancy of C(m, q) is upper bounded by mq. Then we show that our upper bound on the first separating redundancy of C(m, q) is tighter than the general deterministic and constructive upper bounds in the literature. For m = 2, we further prove that the first separating redundancy of C(2, q) is 2q for any odd prime q. For m ≥ 3, we conjecture that the first separating redundancy of C(m, q) is mq for any fixed m and sufficiently large q.