On the Number of Minimum Stopping Sets and Minimum Codewords of Array LDPC Codes

Abstract

For an odd prime q and an integer m ≤ q, a binary mq × q <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> quasi-cyclic parity-check matrix H(m,q) can be constructed for a class of array LDPC code C(m,q). In this letter, the closed-form formula for the numbers of minimum stopping sets of H(m,q) and minimum codewords of C(m,q) are given for 2 ≤ m ≤ 3 and for (m,q)=(4,5) and (4,7).