Erasure codes with symbol locality and group decodability for distributed storage

TL;DR

This paper introduces group decodable erasure codes for distributed storage that combine local repairability with efficient group decoding, providing bounds on their minimum distance and conditions for optimality.

Contribution

It proposes a new family of erasure codes called group decodable codes, establishing bounds on their minimum distance and demonstrating their optimality under certain field size conditions.

Findings

Established an upper bound on the minimum distance of GDCs.

Proved the bound is achievable with sufficiently large field size.

Designed codes with combined local repairability and group decodability.

Abstract

We introduce a new family of erasure codes, called group decodable code (GDC), for distributed storage system. Given a set of design parameters {\alpha; \beta; k; t}, where k is the number of information symbols, each codeword of an (\alpha; \beta; k; t)-group decodable code is a t-tuple of strings, called buckets, such that each bucket is a string of \beta symbols that is a codeword of a [\beta; \alpha] MDS code (which is encoded from \alpha information symbols). Such codes have the following two properties: (P1) Locally Repairable: Each code symbol has locality (\alpha; \beta-\alpha + 1). (P2) Group decodable: From each bucket we can decode \alpha information symbols. We establish an upper bound of the minimum distance of (\alpha; \beta; k; t)-group decodable code for any given set of {\alpha; \beta; k; t}; We also prove that the bound is achievable when the coding field F has size |F| > n-1 \choose k-1.