MDS Array Codes With Small Sub-packetization Levels and Small Repair Degrees

TL;DR

This paper introduces a transformation method to convert MSR codes into MDS array codes with small sub-packetization levels and near-optimal repair bandwidth, enhancing practicality for various code parameters.

Contribution

A generic transformation that creates MDS array codes with small sub-packetization and near-optimal repair bandwidth from existing MSR codes.

Findings

Successfully applied the transformation to three known MSR codes.

Produced MDS array codes with small sub-packetization and support for small repair degrees.

Codes work efficiently for both small and large parameters.

Abstract

High-rate minimum storage regenerating (MSR) codes are known to require a large sub-packetization level, which can make meta-data management difficult and hinder implementation in practical systems. A few maximum distance separable (MDS) array code constructions have been proposed to attain a much smaller sub-packetization level by sacrificing a bit of repair bandwidth. However, to the best of our knowledge, only one construction by Guruswami et al. can support the repair of a failed node without contacting all the surviving nodes. This construction is certainly of theoretical interest but not yet practical due to its requirement for very large code parameters. In this paper, we propose a generic transformation that can convert any $(\overline{n}, \overline{k})$ MSR code with a repair degree of $\overline{d}<\overline{n}-1$ into another $(n=s\overline{n},k)$ MDS array code that supports $d<n-1$ with a small sub-packetization level and $(1+\epsilon)$-optimal repair bandwidth (i.e., $1+\epsilon$ times the optimal value) under a specific condition. We obtain three MDS array codes with small sub-packetization levels and $(1+\epsilon)$-optimal repair bandwidth by applying this transformation to three known MSR codes. All the new MDS array codes have a small repair degree of $d<n-1$ and work for both small and large code parameters.