Exact enumeration of dominant unrecoverable erasure patterns in SPCPC schemes

Abstract EN

Single Parity Check Product Codes (SPCPC) are simple yet powerful error detection and erasure recovery codes.

When used for erasure recovery, they are capable of recovering any pattern of up to 3 erasures, and most of the higher order patterns.

Previous studies have developed upper bounds for the performance of such codes.

However, these bounds are very loose and do not accurately characterize the performance of SPCPC.

This paper introduces a novel paradigm for exactly enumerating the number of unrecoverable erasure patterns for some of the dominant terms in the bound, namely for the cases of 6, 7, and 8 erasures in any M × N matrix.

In addition, this new technique determines the number of post-decoding unrecoverable erasures in a given pattern exactly.

As a result, the bound on the post-decoding erasure rate is tightened.

This framework is extendable to cases with more than 8 erasures and, hence, can be used to develop an analytical model or an algorithm that would ultimately solve the problem exactly or further improve the bound.