Secrecy Capacity of a Class of Broadcast Channels with an Eavesdropper

We study the security of communication between a single transmitter and many receivers in the presence of an eavesdropper for several special classes of broadcast channels. As the first model, we consider the degraded multireceiver wiretap channel where the legitimate receivers exhibit a degradedness order while the eavesdropper is more noisy with respect to all legitimate receivers. We establish the secrecy capacity region of this channel model. Secondly, we consider the parallel multireceiver wiretap channel with a less noisiness order in each subchannel, where this order is not necessarily the same for all subchannels, and hence the overall channel does not exhibit a less noisiness order. We establish the common message secrecy capacity and sum secrecy capacity of this channel. Thirdly, we study a class of parallel multireceiver wiretap channels with two subchannels, two users and an eavesdropper. For channels in this class, in the first (resp., second) subchannel, the second (resp., first) receiver is degraded with respect to the first (resp., second) receiver, while the eavesdropper is degraded with respect to both legitimate receivers in both subchannels. We determine the secrecy capacity region of this channel, and discuss its extensions to arbitrary numbers of users and subchannels. Finally, we focus on a variant of this previous channel model where the transmitter can use only one of the subchannels at any time. We characterize the secrecy capacity region of this channel as well.