On the Achievability Region of Regenerating Codes for Multiple Erasures

TL;DR

This paper advances the understanding of exact repair in distributed storage by constructing new codes that achieve optimal points for multiple failures, improving existing layered codes, and explicitly characterizing the best achievable repair regions.

Contribution

It introduces improved layered code constructions for exact repair of multiple failures and determines the optimal repair tradeoff region for certain parameters.

Findings

Achieved new interior points for exact repair of multiple failures.

Proved the optimality of a specific point on the functional repair tradeoff.

Explicitly characterized the best achievable repair region using space-sharing.

Abstract

We study the problem of centralized exact repair of multiple failures in distributed storage. We describe constructions that achieve a new set of interior points under exact repair. The constructions build upon the layered code construction by Tian et al., designed for exact repair of single failure. We firstly improve upon the layered construction for general system parameters. Then, we extend the improved construction to support the repair of multiple failures, with varying number of helpers. In particular, we prove the optimality of one point on the functional repair tradeoff of multiple failures for some parameters. Finally, considering minimum bandwidth cooperative repair (MBCR) codes as centralized repair codes, we determine explicitly the best achievable region obtained by space-sharing among all known points, including the MBCR point.