Erasure Correcting Capability of SPC Product Codes

Abstract

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. A detailed mathematical analysis has been carried out for erasure pattern of the SPC product code. 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 post decoding rate is calculated for SPC product code. Our results are in good agreement with Kousa (2002). Simulation results show that the error correcting capability of the SPC product code is beyond the minimum distance