Secure Symmetrical Multilevel Diversity Coding

TL;DR

This paper extends Symmetrical Multilevel Diversity Coding to include security constraints against eavesdroppers, demonstrating that superposition coding remains optimal for minimizing total transmission rate in the secure setting.

Contribution

It characterizes the entire admissible rate region for secure SMDC and proves superposition coding's optimality under security constraints.

Findings

Complete characterization of the secure SMDC rate region.

Superposition coding achieves the minimum sum rate.

Connection established to secure coding over a three-layer wiretap network.

Abstract

Symmetrical Multilevel Diversity Coding (SMDC) is a network compression problem introduced by Roche (1992) and Yeung (1995). In this setting, a simple separate coding strategy known as superposition coding was shown to be optimal in terms of achieving the minimum sum rate (Roche, Yeung, and Hau, 1997) and the entire admissible rate region (Yeung and Zhang, 1999) of the problem. This paper considers a natural generalization of SMDC to the secure communication setting with an additional eavesdropper. It is required that all sources need to be kept perfectly secret from the eavesdropper as long as the number of encoder outputs available at the eavesdropper is no more than a given threshold. First, the problem of encoding individual sources is studied. A precise characterization of the entire admissible rate region is established via a connection to the problem of secure coding over a three-layer wiretap network and utilizing some basic polyhedral structure of the admissible rate region. Building on this result, it is then shown that superposition coding remains optimal in terms of achieving the minimum sum rate for the general secure SMDC problem.