MDS Array Codes With (Near) Optimal Repair Bandwidth for All Admissible Repair Degrees

TL;DR

This paper introduces a new class of MSR array codes that achieve near-optimal repair bandwidth for all admissible repair degrees, with reduced sub-packetization and field size, improving flexibility and efficiency in distributed storage systems.

Contribution

It presents a novel (n, k) MSR code construction valid for any repair degree d>k, with smaller sub-packetization and field size, and extends to near-optimal repair bandwidth for d=n-1.

Findings

Supports any repair degree d>k

Achieves $(1+b5)$-optimal repair bandwidth for d=n-1

Reduces sub-packetization level and field size compared to existing codes

Abstract

Abundant high-rate (n, k) minimum storage regenerating (MSR) codes have been reported in the literature. However, most of them require contacting all the surviving nodes during a node repair process, resulting in a repair degree of d=n-1. In practical systems, it may not always be feasible to connect and download data from all surviving nodes, as some nodes may be unavailable. Therefore, there is a need for MSR code constructions with a repair degree of d<n-1. Up to now, only a few (n, k) MSR code constructions with repair degree d<n-1 have been reported, some have a large sub-packetization level, a large finite field, or restrictions on the repair degree d. In this paper, we propose a new (n, k) MSR code construction that works for any repair degree d>k, and has a smaller sub-packetization level or finite field than some existing constructions. Additionally, in conjunction with a previous generic transformation to reduce the sub-packetization level, we obtain an MDS array code with a small sub-packetization level and $(1+\epsilon)$-optimal repair bandwidth (i.e., $(1+\epsilon)$ times the optimal repair bandwidth) for repair degree d=n-1. This code outperforms some existing ones in terms of either the sub-packetization level or the field size.