Partial MDS Codes with Local Regeneration

Abstract

Partial MDS (PMDS) and sector-disk (SD) codes are classes of erasure codes that combine locality with strong erasure correction capabilities. We construct PMDS and SD codes where each local code is a bandwidth-optimal regenerating MDS code. The constructions require significantly smaller field size than the only other construction known in literature.

A Construction of Maximally Recoverable Codes with Order-Optimal Field Size

“…For the sake of completeness, we would like to mention that aside from PMDS codes, there are other codes with locality that can recover from predetermined erasure patterns beyond the minimum Hamming distances [7], [12], [18], [24], [30]. As an example, sector-disk (SD) codes [30] with (r, δ) a -locality can correct δ − 1 disk erasures together with any additional h sector erasures, where h denotes the number of global parity-check symbols.…”