Partial MDS Codes with Regeneration
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Partial MDS (PMDS) and sector-disk (SD) codes are classes of erasure correcting 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. In the event of a node failure, these codes reduce both, the number of servers that have to be contacted as well as the amount of network traffic required for the repair process. The constructions require significantly smaller field size than the only other construction known in literature. Further, we present a PMDS code construction that allows for efficient repair for patterns of node failures that exceed the local erasure correction capability of the code and thereby invoke repair across different local groups.
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