$\epsilon$-MSR Codes: Contacting Fewer Code Blocks for Exact Repair

TL;DR

This paper introduces $\\epsilon$-MSR codes that enable exact repair of code blocks by contacting fewer blocks, reducing the repair complexity while maintaining optimal storage and error correction, with practical implementation benefits.

Contribution

The paper constructs $\\epsilon$-MSR codes that require fewer contacted code blocks for repair, with linear field size and balanced load distribution, improving upon prior designs.

Findings

Fewer code blocks needed for repair contact.

Linear field size in code length.

Balanced load among contacted blocks.

Abstract

$\epsilon$-Minimum Storage Regenerating ($\epsilon$-MSR) codes form a special class of Maximum Distance Separable (MDS) codes, providing mechanisms for exact regeneration of a single code block in their codewords by downloading slighly sub-optimal amount of information from the remaining code blocks. The key advantage of these codes is a significantly lower sub-packetization that grows only logarithmically with the length of the code, while providing optimality in storage and error-correcting capacity. However, from an implementation point of view, these codes require each remaining code block to be available for the repair of any single code block. In this paper, we address this issue by constructing $\epsilon$-MSR codes that can repair a failed code block by contacting a fewer number of available code blocks. When a code block fails, our repair procedure needs to contact a few compulsory code blocks and is free to choose any subset of available code blocks for the remaining choices. Further, our construction requiresa field size linear in code length and ensures load balancing among the contacted code blocks in terms of information downloaded from them for a single repair.