Outer Bounds on the Storage-Repair Bandwidth Tradeoff of Exact-Repair Regenerating Codes

TL;DR

This paper derives three outer bounds on the storage-repair bandwidth tradeoff for exact-repair regenerating codes, providing new characterizations and tighter bounds in specific parameter regimes, including linear codes.

Contribution

It introduces three novel outer bounds on the ER tradeoff, improving existing bounds and characterizing the tradeoff for certain parameters and code classes.

Findings

Establishes a non-vanishing gap between ER and FR tradeoffs.

Provides a tight outer bound for linear ER codes when k=d=n-1.

Characterizes the ER tradeoff for (n,k=3,d=n-1) using improved layered codes.

Abstract

In this paper, three outer bounds on the normalized storage-repair bandwidth (S-RB) tradeoff of regenerating codes having parameter set $\{(n,k,d),(\alpha,\beta)\}$ under the exact-repair (ER) setting are presented. The first outer bound is applicable for every parameter set $(n,k,d)$ and in conjunction with a code construction known as {\em improved layered codes}, it characterizes the normalized ER tradeoff for the case $(n,k=3,d=n-1)$. It establishes a non-vanishing gap between the ER and functional-repair (FR) tradeoffs for every $(n,k,d)$. The second bound is an improvement upon an existing bound due to Mohajer et al. and is tighter than the first bound, in a regime away from the Minimum Storage Regeneraing (MSR) point. The third bound is for the case of $k=d$, under the linear setting. This outer bound matches with the achievable region of {\em layered codes} thereby characterizing the normalized ER tradeoff of linear ER codes when $k=d=n-1$.