Private Broadcasting Over Independent Parallel Channels

We study broadcasting of two confidential messages to two groups of receivers over independent parallel subchannels. One group consists of an arbitrary number of receivers, interested in a common message, whereas the other group has only one receiver. Each message must be confidential from the receiver(s) in the other group. Each of the subchannels is assumed to be degraded in a certain fashion. While corner points of the capacity region of this setup were characterized in earlier works, we establish the complete capacity region, and show the optimality of a superposition coding technique. For Gaussian channels, we establish the optimality of a Gaussian input distribution by applying an extremal information inequality. By extending our coding scheme to block-fading channels, we demonstrate significant performance gains over a baseline time-sharing scheme.