Shannon's secrecy system with informed receivers and its application to systematic coding for wiretapped channels

TL;DR

This paper extends Shannon's secrecy system to scenarios with informed receivers and noisy wiretappers, providing a single-letter characterization of achievable secrecy and efficiency metrics, and analyzing systematic coding performance in wiretap channels.

Contribution

It offers a new framework for analyzing secrecy with side information, including systematic codes, and compares their performance to general codes.

Findings

Single-letter characterization of achievable secrecy region.

Systematic codes' performance is analyzed and compared to general codes.

Examples illustrate the advantages and limitations of systematic coding in wiretap channels.

Abstract

Shannon's secrecy system is studied in a setting, where both the legitimate decoder and the wiretapper have access to side information sequences correlated to the source, but the wiretapper receives both the coded information and the side information via channels that are more noisy than the respective channels of the legitmate decoder, which in turn, also shares a secret key with the encoder. A single--letter characterization is provided for the achievable region in the space of five figures of merit: the equivocation at the wiretapper, the key rate, the distortion of the source reconstruction at the legitimate receiver, the bandwidth expansion factor of the coded channels, and the average transmission cost (generalized power). Beyond the fact that this is an extension of earlier studies, it also provides a framework for studying fundamental performance limits of systematic codes in the presence of a wiretap channel. The best achievable performance of systematic codes is then compared to that of a general code in several respects, and a few examples are given.