Shortened regenerating codes

TL;DR

This paper introduces a new outer bound for exact repair regenerating codes, improving understanding of the trade-offs between storage and repair bandwidth, especially for linear codes.

Contribution

It presents a novel outer bound based on shortened subcodes, providing explicit bounds for linear codes and advancing the theoretical limits of regenerating codes.

Findings

New outer bound for exact repair regenerating codes

Explicit bounds derived for linear codes

Enhanced understanding of storage-bandwidth trade-offs

Abstract

For general exact repair regenerating codes, the optimal trade-offs between storage size and repair bandwith remain undetermined. Various outer bounds and partial results have been proposed. Using a simple chain rule argument we identify nonnegative differences between the functional repair and the exact repair outer bounds. One of the differences is then bounded from below by the repair data of a shortened subcode. Our main result is a new outer bound for an exact repair regenerating code in terms of its shortened subcodes. In general the new outer bound is implicit and depends on the choice of shortened subcodes. For the linear case we obtain explicit bounds.