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

Multi-receiver Wiretap Channel with Public and Confidential Messages