Security Embedding Codes

TL;DR

This paper introduces a coding scheme for securely embedding a high-security message within a low-security message, achieving optimal secrecy capacity without sacrificing overall communication rate, applicable to Gaussian channels and wiretap scenarios.

Contribution

It proposes a novel coding scheme combining rate splitting, superposition coding, nested binning, and channel prefixing to achieve the secrecy capacity region in security embedding problems.

Findings

Achieves the secrecy capacity region in various scenarios.

High-security message embedded at full rate without rate loss.

Extends results to wiretap channel II with perfect security embedding.

Abstract

This paper considers the problem of simultaneously communicating two messages, a high-security message and a low-security message, to a legitimate receiver, referred to as the security embedding problem. An information-theoretic formulation of the problem is presented. A coding scheme that combines rate splitting, superposition coding, nested binning and channel prefixing is considered and is shown to achieve the secrecy capacity region of the channel in several scenarios. Specifying these results to both scalar and independent parallel Gaussian channels (under an average individual per-subchannel power constraint), it is shown that the high-security message can be embedded into the low-security message at full rate (as if the low-security message does not exist) without incurring any loss on the overall rate of communication (as if both messages are low-security messages). Extensions to the wiretap channel II setting of Ozarow and Wyner are also considered, where it is shown that "perfect" security embedding can be achieved by an encoder that uses a two-level coset code.