Multilevel Diversity Coding with Regeneration: Separate Coding Achieves the MBR Point

TL;DR

This paper establishes new bounds on multilevel diversity coding with regeneration, proving that separate coding achieves the minimum-bandwidth-regeneration point and resolving an open question in the field.

Contribution

The paper introduces two new outer bounds on the tradeoffs and confirms the optimality of separate coding at the MBR point.

Findings

Two new outer bounds on optimal tradeoffs

Separate coding achieves the MBR point

Resolves an open question from prior work

Abstract

The problem of multilevel diversity coding with regeneration is considered in this work. Two new outer bounds on the optimal tradeoffs between the normalized storage capacity and repair bandwidth are established, by which the optimality of separate coding at the minimum-bandwidth-regeneration (MBR) point follows immediately. This resolves a question left open in a previous work by Tian and Liu.