Locally Repairable Codes

TL;DR

This paper introduces locally repairable codes (LRCs) for distributed storage, achieving a balance between repair efficiency, data rate, and reliability, with explicit constructions based on Reed-Solomon codes.

Contribution

It characterizes the fundamental trade-off between locality, code distance, and storage capacity, and provides optimal, explicit LRC constructions achieving high data rates.

Findings

Existence of optimal LRCs that meet the trade-off bounds.

A randomized code construction using locality-aware flow-graph gadgets.

An explicit LRC construction based on Reed-Solomon codes.

Abstract

Distributed storage systems for large-scale applications typically use replication for reliability. Recently, erasure codes were used to reduce the large storage overhead, while increasing data reliability. A main limitation of off-the-shelf erasure codes is their high-repair cost during single node failure events. A major open problem in this area has been the design of codes that {\it i)} are repair efficient and {\it ii)} achieve arbitrarily high data rates. In this paper, we explore the repair metric of {\it locality}, which corresponds to the number of disk accesses required during a {\color{black}single} node repair. Under this metric we characterize an information theoretic trade-off that binds together locality, code distance, and the storage capacity of each node. We show the existence of optimal {\it locally repairable codes} (LRCs) that achieve this trade-off. The achievability proof uses a locality aware flow-graph gadget which leads to a randomized code construction. Finally, we present an optimal and explicit LRC that achieves arbitrarily high data-rates. Our locality optimal construction is based on simple combinations of Reed-Solomon blocks.