Strong Secrecy for Cooperative Broadcast Channels

TL;DR

This paper establishes strong secrecy capacity bounds for cooperative broadcast channels with one-sided cooperation, showing how secrecy constraints impact achievable rates and proposing a coding scheme that is optimal for certain channel types.

Contribution

It introduces a novel inner bound on the secrecy capacity region using channel-resolvability-based coding and likelihood encoding, specifically addressing the impact of secrecy on cooperative broadcast channels.

Findings

Inner bound is tight for semi-deterministic and physically degraded BCs.

Secrecy constraints reduce achievable rates more than typical rate loss.

Sharing only parts of messages via the cooperative link is optimal under secrecy.

Abstract

A broadcast channel (BC) where the decoders cooperate via a one-sided link is considered. One common and two private messages are transmitted and the private message to the cooperative user should be kept secret from the cooperation-aided user. The secrecy level is measured in terms of strong secrecy, i.e., a vanishing information leakage. An inner bound on the capacity region is derived by using a channel-resolvability-based code that double-bins the codebook of the secret message, and by using a likelihood encoder to choose the transmitted codeword. The inner bound is shown to be tight for semi-deterministic and physically degraded BCs and the results are compared to those of the corresponding BCs without a secrecy constraint. Blackwell and Gaussian BC examples illustrate the impact of secrecy on the rate regions. Unlike the case without secrecy, where sharing information about both private messages via the cooperative link is optimal, our protocol conveys parts of the common and non-confidential messages only. This restriction reduces the transmission rates more than the usual rate loss due to secrecy requirements. An example that illustrates this loss is provided.