Constructing $(h,d)$ cooperative MSR codes with sub-packetization $(d-k+h)(d-k+1)^{\lceil n/2 \rceil}$

TL;DR

This paper presents explicit constructions of optimal cooperative MDS array codes for multi-node failure repair with a novel sub-packetization level, improving upon recent existing codes in the field.

Contribution

The paper introduces a new class of cooperative MDS array codes with a specific sub-packetization level, enhancing repair efficiency for multiple node failures.

Findings

Constructed explicit optimal MDS array codes for cooperative repair.

Achieved a sub-packetization level of $(d-k+h)(d-k+1)^{ ceil n/2 ceil}$.

Improved upon recent code constructions by Liu et al.

Abstract

We address the multi-node failure repair challenges for MDS array codes. Presently, two primary models are employed for multi-node repairs: the centralized model where all failed nodes are restored in a singular data center, and the cooperative model where failed nodes acquire data from auxiliary nodes and collaborate amongst themselves for the repair process.This paper focuses on the cooperative model, and we provide explicit constructions of optimal MDS array codes with $d$ helper nodes under this model. The sub-packetization level of our new codes is $(d-k+h)(d-k+1)^{\lceil n/2 \rceil}$ where $h$ is the number of failed nodes, $k$ the number of information nodes and $n$ the code length. This improves upon recent constructions given by Liu \emph{et al.} (IEEE Transactions on Information Theory, Vol. 69, 2023).