A Generic Transformation to Enable Optimal Repair in MDS Codes for Distributed Storage Systems

TL;DR

This paper introduces a universal transformation method that converts any nonbinary MDS code into a more repair-efficient version, optimizing repair bandwidth and access for all or selected nodes with minimal sub-packetization increase.

Contribution

The authors present a generic transformation technique that enhances repair properties of existing MDS codes while maintaining their core parameters and only modestly increasing sub-packetization.

Findings

Transforms any nonbinary MDS code to have optimal repair for selected nodes.

Enables all-node repair optimality through iterative application of the transformation.

Maintains original code parameters with minimal sub-packetization increase.

Abstract

We propose a generic transformation that can convert any nonbinary $(n=k+r,k)$ maximum distance separable (MDS) code into another $(n,k)$ MDS code over the same field such that 1) some arbitrarily chosen $r$ nodes have the optimal repair bandwidth and the optimal rebuilding access, 2) for the remaining $k$ nodes, the normalized repair bandwidth and the normalized rebuilding access (over the file size) are preserved, 3) the sub-packetization level is increased only by a factor of $r$. Two immediate applications of this generic transformation are then presented. The first application is that we can transform any nonbinary MDS code with the optimal repair bandwidth or the optimal rebuilding access for the systematic nodes only, into a new MDS code which possesses the corresponding repair optimality for all nodes. The second application is that by applying the transformation multiple times, any nonbinary $(n,k)$ scalar MDS code can be converted into an $(n,k)$ MDS code with the optimal repair bandwidth and the optimal rebuilding access for all nodes, or only a subset of nodes, whose sub-packetization level is also optimal.