Lower Bounds on the Sub-Packetization of Optimal-Access MSR Codes for Multiple-Node Repair

TL;DR

This paper derives lower bounds on the sub-packetization levels of optimal-access MSR codes when repairing multiple nodes, extending previous single-node failure bounds and employing generating functions for refined analysis.

Contribution

It generalizes existing bounds for single-node failures to multiple-node failures and introduces generating functions for more precise bounds.

Findings

Established lower bounds for multiple-node failure scenarios.

Extended tight bounds from single-node to multiple-node cases.

Used generating functions for refined analytical bounds.

Abstract

We establish lower bounds on the sub-packetization of optimal-access MSR codes in the context of multiple-node failures. These bounds generalize the tight bounds for single-node failure presented by Balaji et al. (IEEE Transactions on Information Theory, vol. 68, no. 10, 2022). Moreover, we utilize generating functions to provide a more refined analysis, further strengthening these bounds.