Exact-MSR Codes for Distributed Storage with Low Repair Complexity

TL;DR

This paper introduces two new exact-MSR code constructions for distributed storage that simplify data repair to basic operations, support arbitrary parameters, and reduce repair complexity, enhancing efficiency in data recovery.

Contribution

The paper presents the first exact-MSR codes with arbitrary parameters and low repair complexity, using linearized polynomials over extension fields.

Findings

Data repair avoids matrix inversion, using only additions, multiplications, and cyclic shifts.

The first construction supports arbitrary code parameters with a sufficiently large base field.

Repair complexity is lower compared to existing exact-MSR codes.

Abstract

In this paper, we propose two new constructions of exact-repair minimum storage regenerating (exact-MSR) codes. For both constructions, the encoded symbols are obtained by treating the message vector over GF(q) as a linearized polynomial and evaluating it over an extension field GF(q^m). For our exact-MSR codes, data repair does not need matrix inversion, and can be implemented by additions and multiplications over GF$(q)$ as well as cyclic shifts when a normal basis is used. The two constructions assume a base field of GF(q) (q>2) and GF(2), respectively. In contrast to existing constructions of exact-MSR codes, the former construction works for arbitrary code parameters, provided that $q$ is large enough. This is the first construction of exact-MSR codes with arbitrary code parameters, to the best of our knowledge. In comparison to existing exact-MSR codes, while data construction of our exact-MSR codes has a higher complexity, the complexity of data repair is lower. Thus, they are attractive for applications that need a small number of data reconstructions along with a large number of data repairs.