Cooperative Local Repair in Distributed Storage

TL;DR

This paper explores cooperative local repair in erasure-correcting codes for distributed storage, providing bounds, explicit constructions, and analysis of such codes, including Hadamard/Simplex codes, to improve repair efficiency.

Contribution

It introduces a generalized class of codes supporting cooperative local repair, with bounds and explicit constructions, advancing the design of efficient distributed storage codes.

Findings

Established bounds on the trade-off between minimum distance and dimension.

Provided explicit constructions of codes with cooperative local repair.

Analyzed the cooperative repair properties of Hadamard/Simplex codes.

Abstract

Erasure-correcting codes, that support local repair of codeword symbols, have attracted substantial attention recently for their application in distributed storage systems. This paper investigates a generalization of the usual locally repairable codes. In particular, this paper studies a class of codes with the following property: any small set of codeword symbols can be reconstructed (repaired) from a small number of other symbols. This is referred to as cooperative local repair. The main contribution of this paper is bounds on the trade-off of the minimum distance and the dimension of such codes, as well as explicit constructions of families of codes that enable cooperative local repair. Some other results regarding cooperative local repair are also presented, including an analysis for the well-known Hadamard/Simplex codes.