An Explicit, Coupled-Layer Construction of a High-Rate MSR Code with Low Sub-Packetization Level, Small Field Size and All-Node Repair

TL;DR

This paper introduces an explicit, layered MSR code construction with low sub-packetization, small field size, and uniform node repair, improving upon prior designs by reducing field size requirements.

Contribution

It presents a novel layered MSR code construction with low sub-packetization and small field size, adaptable to different repair degrees, using scalar or vector MDS codes as building blocks.

Findings

Constructed MSR codes with near-ideal rate and low sub-packetization.

Achieved repair with minimal data download uniformly across nodes.

Extended construction to cases with fewer helper nodes, maintaining efficiency.

Abstract

This paper presents an explicit construction for an $((n,k,d=n-1), (\alpha,\beta))$ regenerating code over a field $\mathbb{F}_Q$ operating at the Minimum Storage Regeneration (MSR) point. The MSR code can be constructed to have rate $k/n$ as close to $1$ as desired, sub-packetization given by $r^{\frac{n}{r}}$, for $r=(n-k)$, field size no larger than $n$ and where all code symbols can be repaired with the same minimum data download. The construction modifies a prior construction by Sasidharan et. al. which required far larger field-size. A building block appearing in the construction is a scalar MDS code of block length $n$. The code has a simple layered structure with coupling across layers, that allows both node repair and data recovery to be carried out by making multiple calls to a decoder for the scalar MDS code. While this work was carried out independently, there is considerable overlap with a prior construction by Ye and Barg. It is shown here that essentially the same architecture can be employed to construct MSR codes using vector binary MDS codes as building blocks in place of scalar MDS codes. The advantage here is that computations can now be carried out over a field of smaller size potentially even over the binary field as we demonstrate in an example. Further, we show how the construction can be extended to handle the case of $d<(n-1)$ under a mild restriction on the choice of helper nodes.