A New Cooperative Repair Scheme with k + 1 Helper Nodes for (n, k) Hadamard MSR codes with Small Sub-packetization

TL;DR

This paper introduces a new cooperative repair scheme for (n, k) Hadamard MSR codes that significantly reduces sub-packetization levels, improving efficiency in distributed storage systems with multiple node failures.

Contribution

The paper presents a novel cooperative repair scheme that reduces sub-packetization levels by factors of h+1 or 2^m, outperforming previous constructions for (n, k) Hadamard MSR codes.

Findings

Reduces sub-packetization to 2^n under certain conditions

Achieves the lowest known sub-packetization levels for the problem

Improves repair efficiency in distributed storage systems

Abstract

Cooperative repair model is an available technology to deal with multiple node failures in distributed storage systems. Recently, explicit constructions of cooperative MSR codes were given by Ye (IEEE Transactions on Information Theory, 2020) with sub-packetization level $(d-k+h)(d-k+1)^n$. Specifically, the sub-packetization level is $(h+1)2^n$ when $d=k+1$. In this paper, we propose a new cooperative repair scheme by means of the inter-instance and intra-instance pairing inherited from the perfect code which reduces the sub-packetization to $2^n$ when $(h+1)|2^n$ and $(2\ell+1)2^n$ when $h+1=(2\ell+1)2^m$ for $m\ge 0$, $\ell\ge 1$ with $d=k+1$ helper nodes. That is to say, the sub-packetization is $h + 1 $ times or $2^m$ times less than Ye's. It turned out to be the best result so far known.