Weakly Secure Symmetric Multilevel Diversity Coding

TL;DR

This paper investigates weakly secure symmetric multilevel diversity coding, characterizing when superposition coding is optimal and proposing joint coding strategies that can achieve better rates under certain security constraints.

Contribution

It provides a complete characterization of superposition coding optimality in weakly secure SMDC and introduces new joint coding strategies for improved rate performance.

Findings

Superposition coding is optimal under certain security conditions.

Two joint coding strategies can outperform superposition coding.

Specific security constraints allow for optimal rate region achievement with proposed strategies.

Abstract

Multilevel diversity coding is a classical coding model where multiple mutually independent information messages are encoded, such that different reliability requirements can be afforded to different messages. It is well known that {\em superposition coding}, namely separately encoding the independent messages, is optimal for symmetric multilevel diversity coding (SMDC) (Yeung-Zhang 1999). In the current paper, we consider weakly secure SMDC where security constraints are injected on each individual message, and provide a complete characterization of the conditions under which superposition coding is sum-rate optimal. Two joint coding strategies, which lead to rate savings compared to superposition coding, are proposed, where some coding components for one message can be used as the encryption key for another. By applying different variants of Han's inequality, we show that the lack of opportunity to apply these two coding strategies directly implies the optimality of superposition coding. It is further shown that under a set of particular security constraints, one of the proposed joint coding strategies can be used to construct a code that achieves the optimal rate region.