Exact Regeneration Codes for Distributed Storage Repair Using Interference Alignment

TL;DR

This paper introduces explicit, deterministic Exact-MSR codes for distributed storage that use interference alignment to achieve optimal repair bandwidth for certain parameters, improving repair efficiency without loss of optimality.

Contribution

The paper presents a new class of Exact-MSR codes using interference alignment, providing explicit constructions that match the optimal repair bandwidth for specific parameters.

Findings

Exact-MSR codes can regenerate any failed node exactly.

The codes achieve the cutset lower bound on repair bandwidth.

Constructive schemes require finite field size at most 2(n-k).

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. On one end of this spectrum of Regenerating Codes are Minimum Storage Regenerating (MSR) codes that can match the minimum storage cost of MDS codes while also significantly reducing repair bandwidth. In this paper, we describe Exact-MSR codes which allow for any failed nodes (whether they are systematic or parity nodes) to be regenerated exactly rather than only functionally or information-equivalently. We show that Exact-MSR codes come with no loss of optimality with respect to random-network-coding based MSR codes (matching the cutset-based lower bound on repair bandwidth) for the cases of: (a) k/n <= 1/2; and (b) k <= 3. Our constructive approach is based on interference alignment techniques, and, unlike the previous class of random-network-coding based approaches, we provide explicit and deterministic coding schemes that require a finite-field size of at most 2(n-k).