Repairing Generalized Reed-Muller Codes

TL;DR

This paper extends optimal repair schemes to Generalized Reed-Muller codes, achieving near-minimal bandwidth for single and multiple failure repairs in distributed storage systems.

Contribution

It generalizes Guruswami and Wooters' repair scheme from Reed-Solomon to GRM codes, improving repair bandwidth and extending to multiple failure scenarios.

Findings

Bandwidth approaches lower bound for small subfields

Effective repair scheme for multiple failures

Enhanced repair efficiency in distributed storage

Abstract

In distributed storage systems, both the repair bandwidth and locality are important repair cost metrics to evaluate the performance of a storage code. Recently, Guruswami and Wooters proposed an optimal linear repair scheme based on Reed-Solomon codes for a single failure, improved the bandwidth of the classical repair scheme. In this paper, we consider the repair bandwidth of Generalized Reed-Muller (GRM) codes, which have good locality property. We generalize Guruswami and Wooters' repairing scheme to GRM codes for single failure, which has nontrivial bandwidth closing to the lower bound when the subfield is small. We further extend the repair scheme for multiple failures in distributed and centralized repair models, and compute the expectation of bandwidth by considering different erasure-patterns.