Low Complexity Bounds on a Class of Irregular LDPC Belief-Propagation Decoding Thresholds

This paper investigates about the usefulness of a recently published low complexity upper bound on belief-propagation decoding thresholds for a class of irregular low-density parity-check (LDPC) codes. In particular, the class considered is characterized by variable node degree distributions lambda(x) of minimum degree i(1) > 2: being, in this case, lambda'(0) = lambda(2) = 0, this is useful to design LDPC codes presenting a linear minimum distance growth with the block length with probability 1, as shown in Di et al.'s 2006 paper. These codes unfortunately cannot reach capacity under iterative decoding, since the achievement of capacity requires lambda(2) not equal 0. However, in this latter case, the block error probability might converge to a constant, as shown in the aforementioned paper.