An approach to the performance of SPC product codes on the erasure channel

Product codes can be used to correct errors or recover erasures. In this work we consider the simplest form of a product code, this is, the single parity check (SPC) product code. This code has a minimum distance of four and is thus guaranteed to recover all single, double, and triple erasure patterns. The code is actually capable of recovering a higher number of erasure patterns. We count the number of uncorrectable erasure patterns of size n x n with t erasures, for t = 8, 2n-3, 2n-2 and 2n-1, using the relation between erasure patterns and bipartite graphs101SI1128FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP2015/07246-