Secrecy Capacity Region of Some Classes of Wiretap Broadcast Channels

TL;DR

This paper characterizes the secrecy capacity region of certain classes of wiretap broadcast channels with an eavesdropper, providing tight bounds and analyzing the impact of security constraints on channel capacity.

Contribution

It derives new outer and inner bounds for the secrecy capacity region of WBCs, which are tight for specific channel classes, and extends results to parallel channels.

Findings

Tight bounds for deterministic and semi-deterministic BCs with eavesdropper.

Secrecy capacity region for product of inversely less-noisy BCs.

Impact of security constraints on BEC and BSC channel capacities.

Abstract

This work investigates the secrecy capacity of the Wiretap Broadcast Channel (WBC) with an external eavesdropper where a source wishes to communicate two private messages over a Broadcast Channel (BC) while keeping them secret from the eavesdropper. We derive a non-trivial outer bound on the secrecy capacity region of this channel which, in absence of security constraints, reduces to the best known outer bound to the capacity of the standard BC. An inner bound is also derived which follows the behavior of both the best known inner bound for the BC and the Wiretap Channel. These bounds are shown to be tight for the deterministic BC with a general eavesdropper, the semi-deterministic BC with a more-noisy eavesdropper and the Wiretap BC where users exhibit a less-noisiness order between them. Finally, by rewriting our outer bound to encompass the characteristics of parallel channels, we also derive the secrecy capacity region of the product of two inversely less-noisy BCs with a more-noisy eavesdropper. We illustrate our results by studying the impact of security constraints on the capacity of the WBC with binary erasure (BEC) and binary symmetric (BSC) components.