Repairing Reed-Solomon Codes With Multiple Erasures

TL;DR

This paper extends the trace collection technique for Reed-Solomon codes to efficiently repair multiple erasures, improving repair bandwidth in distributed storage systems.

Contribution

It introduces a novel method to repair two and three erasures in Reed-Solomon codes using trace collection, building on prior single-erasure techniques.

Findings

Effective repair of two erasures demonstrated

Effective repair of three erasures demonstrated

Improved repair bandwidth over naive methods

Abstract

Despite their exceptional error-correcting properties, Reed-Solomon codes have been overlooked in distributed storage applications due to the common belief that they have poor repair bandwidth: A naive repair approach would require the whole file to be reconstructed in order to recover a single erased codeword symbol. In a recent work, Guruswami and Wootters (STOC'16) proposed a single-erasure repair method for Reed-Solomon codes that achieves the optimal repair bandwidth amongst all linear encoding schemes. Their key idea is to recover the erased symbol by collecting a sufficiently large number of its traces, each of which can be constructed from a number of traces of other symbols. We extend the trace collection technique to cope with two and three erasures.