Multi-receiver Wiretap Channel with Public and Confidential Messages

TL;DR

This paper characterizes the capacity region of multi-receiver wiretap channels with public and confidential messages, providing bounds and partial solutions for both discrete and Gaussian MIMO models using advanced coding schemes.

Contribution

It offers new inner and outer bounds for the capacity region, including partial characterizations for degraded and general Gaussian MIMO channels using superposition coding, binning, and Gaussian auxiliary variables.

Findings

Inner and outer bounds partially match for degraded channels

Sufficiency of Gaussian auxiliary variables for Gaussian MIMO channels

Partial capacity region characterization for non-degraded Gaussian MIMO channels

Abstract

We study the multi-receiver wiretap channel with public and confidential messages. In this channel, there is a transmitter that wishes to communicate with two legitimate users in the presence of an external eavesdropper. The transmitter sends a pair of public and confidential messages to each legitimate user. While there are no secrecy constraints on the public messages, confidential messages need to be transmitted in perfect secrecy. We study the discrete memoryless multi-receiver wiretap channel as well as its Gaussian multi-input multi-output (MIMO) instance. First, we consider the degraded discrete memoryless channel, and obtain an inner bound for the capacity region by using an achievable scheme that uses superposition coding and binning. Next, we obtain an outer bound, and show that this outer bound partially matches the inner bound, providing a partial characterization for the capacity region of the degraded channel model. Second, we obtain an inner bound for the general, not necessarily degraded, discrete memoryless channel by using Marton's inner bound, superposition coding, rate-splitting and binning. Third, we consider the degraded Gaussian MIMO channel, and show that, to evaluate both the inner and outer bounds, considering only jointly Gaussian auxiliary random variables and channel input is sufficient. Since the inner and outer bounds partially match, these sufficiency results provide a partial characterization of the capacity region of the degraded Gaussian MIMO channel. Finally, we provide an inner bound for the capacity region of the general, not necessarily degraded, Gaussian MIMO multi-receiver wiretap channel.