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We study the security of communication between a single transmitter andmultiple receivers in a broadcast channel in the presence of an eavesdropper.We consider several special classes of channels. As the first model, weconsider the degraded multi-receiver wiretap channel where the legitimatereceivers exhibit a degradedness order while the eavesdropper is more noisywith respect to all legitimate receivers. We establish the secrecy capacityregion of this channel model. Secondly, we consider the parallel multi-receiverwiretap channel with a less noisiness order in each sub-channel, where thisorder is not necessarily the same for all sub-channels. We establish the commonmessage secrecy capacity and sum secrecy capacity of this channel. Thirdly, westudy a special class of degraded parallel multi-receiver wiretap channels andprovide a stronger result. In particular, we study the case with twosub-channels two users and one eavesdropper, where there is a degradednessorder in each sub-channel such that in the first (resp. second) sub-channel thesecond (resp. first) receiver is degraded with respect to the first (resp.second) receiver, while the eavesdropper is degraded with respect to bothlegitimate receivers in both sub-channels. We determine the secrecy capacityregion of this channel. Finally, we focus on a variant of this previous channelmodel where the transmitter can use only one of the sub-channels at any time.We characterize the secrecy capacity region of this channel as well.

Secrecy Capacity of a Class of Broadcast Channels with an Eavesdropper