Achieving Secrecy Capacity of the Wiretap Channel and Broadcast Channel with a Confidential Component

TL;DR

This paper demonstrates that polar codes can achieve the secrecy capacity of general wiretap channels and extend to broadcast channels with confidential messages, achieving their entire capacity region.

Contribution

It introduces a polar coding scheme that achieves the secrecy capacity of general wiretap channels and extends to broadcast channels with confidential messages.

Findings

Polar codes achieve the secrecy capacity of general wiretap channels.

The scheme extends to broadcast channels with confidential messages.

Entire capacity region of broadcast channels with confidential messages is achieved.

Abstract

The wiretap channel model of Wyner is one of the first communication models with both reliability and security constraints. Capacity-achieving schemes for various models of the wiretap channel have received considerable attention in recent literature. In this paper, we show that capacity of the general (not necessarily degraded or symmetric) wiretap channel under a "strong secrecy constraint" can be achieved using a transmission scheme based on polar codes. We also extend our construction to the case of broadcast channels with confidential messages defined by Csisz{\'a}r and K{\"orner}, achieving the entire capacity region of this communication model.