On the Existence of Optimal Exact-Repair MDS Codes for Distributed Storage

TL;DR

This paper proves the existence of bandwidth-optimal exact-repair MDS codes for distributed storage, using interference alignment and vector linear codes to achieve minimal repair bandwidth for various parameters.

Contribution

It demonstrates the existence of exact-repair MDS codes that attain the minimum repair bandwidth for all admissible parameters, expanding the theoretical understanding of regenerating codes.

Findings

Existence of exact-repair MDS codes matching the cutset bound.

Use of interference alignment techniques in code construction.

Applicable for all parameters with k<n and k<=d<=n-1.

Abstract

The high repair cost of (n,k) Maximum Distance Separable (MDS) erasure codes has recently motivated a new class of codes, called Regenerating Codes, that optimally trade off storage cost for repair bandwidth. In this paper, we address bandwidth-optimal (n,k,d) Exact-Repair MDS codes, which allow for any failed node to be repaired exactly with access to arbitrary d survivor nodes, where k<=d<=n-1. We show the existence of Exact-Repair MDS codes that achieve minimum repair bandwidth (matching the cutset lower bound) for arbitrary admissible (n,k,d), i.e., k<n and k<=d<=n-1. Our approach is based on interference alignment techniques and uses vector linear codes which allow to split symbols into arbitrarily small subsymbols.