A repair scheme for a distributed storage system based on multivariate polynomials

TL;DR

This paper extends existing repair schemes for distributed storage systems from Reed-Solomon codes to Reed-Muller codes, utilizing multivariate polynomials to enable efficient recovery from multiple node failures.

Contribution

It introduces a novel repair scheme based on multivariate polynomials for Reed-Muller codes, allowing recovery of multiple node failures under certain conditions.

Findings

The scheme repairs any single node failure.

The scheme can repair multiple node failures.

It generalizes previous Reed-Solomon based methods.

Abstract

A distributed storage system stores data across multiple nodes, with the primary objective of enabling efficient data recovery even in the event of node failures. The main goal of an exact repair scheme is to recover the data from a failed node by accessing and downloading information from the rest of the nodes. In a groundbreaking paper, ~\cite{GW} developed an exact repair scheme for a distributed storage system that is based on Reed-Solomon codes, which depend on single-variable polynomials. In these notes, we extend the repair scheme to the family of distributed storage systems based on Reed-Muller codes, which are linear codes based on multivariate polynomials. The repair scheme we propose repairs any single node failure and multiple node failures, provided the positions satisfy certain conditions.