Multi-Receiver Wiretap Channel With Public and Confidential Messages

We study the multi-receiver wiretap channel (MR-WC) 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 MR-WC as well as its Gaussian multi-input multi-output (MIMO) counterpart. First, we propose an inner bound for the general, not necessarily degraded, discrete memoryless MR-WC by using Marton's inner bound and rate splitting in conjunction with superposition coding and binning. Second, we specialize this inner bound for the degraded discrete memoryless case. This specialized form of the inner bound can be obtained by using superposition coding and binning only. Next, we obtain an outer bound for the capacity region of the degraded channel, which matches the inner bound for some special cases. 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. Similar to the discrete memoryless case, for the Gaussian MIMO case as well, these bounds match for some special cases.