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

TL;DR

This paper demonstrates that separate coding strategies using secure regenerating codes can achieve the optimal tradeoff point in multilevel diversity coding with secure regeneration, unifying several related problems.

Contribution

It introduces new outer bounds and a converse proof using an exchange lemma based on Han's subset inequality, establishing the optimality of separate coding at the MBR point.

Findings

Separate coding achieves the MBR point in MDC-SR.

New outer bounds are established for the problem.

The exchange lemma is key to the converse proof.

Abstract

The problem of multilevel diversity coding with secure regeneration (MDC-SR) is considered, which includes the problems of multilevel diversity coding with regeneration (MDC-R) and secure regenerating code (SRC) as special cases. Two outer bounds are established, showing that separate coding of different messages using the respective SRCs can achieve the minimum-bandwidth-regeneration (MBR) point of the achievable normalized storage-capacity repair-bandwidth tradeoff regions for the general MDC-SR problem. The core of the new converse results is an exchange lemma, which can be established using Han's subset inequality.