PMDS Array Codes With Small Sub-packetization, Small Repair Bandwidth/Rebuilding Access

TL;DR

This paper introduces new PMDS array code constructions that achieve smaller sub-packetization levels and reduced repair bandwidth and rebuilding access, improving efficiency for data recovery in distributed storage systems.

Contribution

The paper presents two novel PMDS array code constructions with two global parities, supporting arbitrary local parities with near-optimal repair bandwidth and reduced sub-packetization, plus a three-global parity code with similar benefits.

Findings

Supports arbitrary local parities with near-optimal repair bandwidth

Achieves significantly smaller sub-packetization levels

Requires smaller finite fields than existing codes

Abstract

Partial maximum distance separable (PMDS) codes are a kind of erasure codes where the nodes are divided into multiple groups with each forming an MDS code with a smaller code length, thus they allow repairing a failed node with only a few helper nodes and can correct all erasure patterns that are information-theoretically correctable. However, the repair of a failed node of PMDS codes still requires a large amount of communication if the group size is large. Recently, PMDS array codes with each local code being an MSR code were introduced to reduce the repair bandwidth further. However, they require extensive rebuilding access and unavoidably a significant sub packetization level. In this paper, we first propose two constructions of PMDS array codes with two global parities that have smaller sub-packetization levels and much smaller finite fields than the existing one. One construction can support an arbitrary number of local parities and has $(1+\epsilon)$-optimal repair bandwidth (i.e., $(1+\epsilon)$ times the optimal repair bandwidth), while the other one is limited to two local parities but has significantly smaller rebuilding access and its sub packetization level is only $2$. In addition, we present a construction of PMDS array code with three global parities, which has a smaller sub-packetization level as well as $(1+\epsilon)$-optimal repair bandwidth, the required finite field is significantly smaller than existing ones.