Progress on High-rate MSR Codes: Enabling Arbitrary Number of Helper Nodes

TL;DR

This paper introduces a new construction for high-rate MSR codes that supports any number of helper nodes with polynomial sub-packetization, broadening the applicability of bandwidth-efficient distributed storage repair.

Contribution

It extends existing MSR code constructions to support arbitrary helper node counts with polynomial sub-packetization, building on recent code designs.

Findings

Supports all helper node counts d as a design parameter

Maintains polynomial sub-packetization for all d

Broadens parameter sets for known MSR code constructions

Abstract

This paper presents a construction for high-rate MDS codes that enable bandwidth-efficient repair of a single node. Such MDS codes are also referred to as the minimum storage regenerating (MSR) codes in the distributed storage literature. The construction presented in this paper generates MSR codes for all possible number of helper nodes $d$ as $d$ is a design parameter in the construction. Furthermore, the obtained MSR codes have polynomial sub-packetization (a.k.a. node size) $\alpha$. The construction is built on the recent code proposed by Sasidharan et al. [1], which works only for $d = n-1$, i.e., where all the remaining nodes serve as the helper nodes for the bandwidth-efficient repair of a single node. The results of this paper broaden the set of parameters where the constructions of MSR codes were known earlier.