Recoverability study of SPC product codes under erasure decoding

Product codes are powerful codes that can be used to correct errors or recover erasures. The simplest form of a product code is that where every row and every column is terminated by a single parity bit referred to as 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. Judging the code performance based on its minimum distance is very pessimistic because the code is actually capable of recovering many higher erasure patterns. Kousa [IEEE Trans. Commun. 50 (Jan) (2002) 7] develops a novel approach for deriving an upper bound on the post-decoding erasure rate for the SPC product code with iterative decoding. We derive a formula for finding the number of unrecoverable basic pattern and the number of recoverable pattern generated from the unrecoverable basic pattern. The results are compared with that of Kousa [IEEE Trans. Commun. 50 (Jan) (2002) 7].