Outer bounds for exact repair codes

TL;DR

This paper investigates the limits of exact-repair regenerating codes, providing improved outer bounds that extend previous results and clarify the gap between exact and functional repair rate regions.

Contribution

The paper introduces two new outer bounds for exact-repair regenerating codes, enhancing understanding of their rate regions and extending prior theoretical results.

Findings

New outer bounds for exact-repair codes

Extension of previous bounds by Tian and Sasidharan et al.

Combined bounds lead to further improvements

Abstract

We address the open problem of establishing the rate region for exact-repair regenerating codes for given parameters (n,k,d). Tian determined the rate region for a (4,3,3) code and found that it lies strictly within the functional-repair rate region. Using different methods, Sasidharan, Senthoor and Kumar proved a non-vanishing gap between the functional-repair outer bound and the exact-repair outer bound for codes with k>=3. Our main results are two improved outer bounds for exact-repair regenerating codes. They capture and then extend essential parts in the proofs by Tian and by Sasidharan, Senthoor and Kumar. We show that the bounds can be combined for further improvements.