Partial MDS Codes with Regeneration

TL;DR

This paper introduces new partial MDS and sector-disk codes with local regeneration, reducing repair bandwidth and contact points, and requiring smaller field sizes than previous methods, enhancing erasure correction efficiency.

Contribution

It presents novel constructions of PMDS and SD codes with local and global regeneration, improving repair efficiency and reducing field size compared to existing literature.

Findings

Codes achieve bandwidth-optimal local regeneration

Construction requires significantly smaller field size

Supports repair of complex failure patterns across local groups

Abstract

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 with local regeneration 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 construction of PMDS codes with global regeneration which allow to efficiently repair patterns of node failures that exceed the local erasure correction capability of the code and thereby invoke repair across different local groups.