Local Codes with Addition Based Repair

TL;DR

This paper introduces a new class of locally repairable codes that use only addition operations for repairing single node failures, achieving near-optimal and optimal distances relative to the Singleton-like bound.

Contribution

The paper constructs two families of addition-based repair codes, one nearly optimal and one optimal, advancing the design of efficient repair algorithms for distributed storage.

Findings

First family attains distance one less than the Singleton-like upper bound.

Second family attains the Singleton-like upper bound.

Codes enable repair using only addition operations.

Abstract

We consider the complexities of repair algorithms for locally repairable codes and propose a class of codes that repair single node failures using addition operations only, or codes with addition based repair. We construct two families of codes with addition based repair. The first family attains distance one less than the Singleton-like upper bound, while the second family attains the Singleton-like upper bound.