A Rate-Distortion Based Secrecy System with Side Information at the Decoders

TL;DR

This paper investigates a lossy source compression secrecy system with side information at decoders, deriving rate-distortion bounds and analyzing secrecy performance in scenarios with correlated side information.

Contribution

It introduces a new rate-distortion framework for secrecy with side information, providing achievable regions and bounds for various correlation cases.

Findings

Derived a general achievable rate-distortion region.

Obtained exact bounds for special side information cases.

Analyzed a binary erasure and symmetric channel example.

Abstract

A secrecy system with side information at the decoders is studied in the context of lossy source compression over a noiseless broadcast channel. The decoders have access to different side information sequences that are correlated with the source. The fidelity of the communication to the legitimate receiver is measured by a distortion metric, as is traditionally done in the Wyner-Ziv problem. The secrecy performance of the system is also evaluated under a distortion metric. An achievable rate-distortion region is derived for the general case of arbitrarily correlated side information. Exact bounds are obtained for several special cases in which the side information satisfies certain constraints. An example is considered in which the side information sequences come from a binary erasure channel and a binary symmetric channel.