This work investigates the secrecy capacity region of the Wiretap Broadcast Channel (WBC) where an encoder communicates two private messages over a Broadcast Channel (BC) while keeping both messages secret from the eavesdropper. Our main result is the derivation of a novel outer bound and an inner bound on the secrecy capacity region of this setting. These results allow us to characterize the capacity region for three non-degraded classes of WBCs: the deterministic and the semi-deterministic WBC with a more noisy eavesdropper, and the WBC when users exhibit less noisiness order between them.
This work investigates the secrecy capacity region of the Wiretap Broadcast Channel (WBC) where an encoder communicates two private messages over a Broadcast Channel (BC) while keeping both messages secret from the eavesdropper. Our main result is the derivation of a novel outer bound and an inner bound on the secrecy capacity region of this setting. These results allow us to characterize the capacity region for three non-degraded classes of WBCs: the deterministic and the semi-deterministic WBC with a more noisy eavesdropper, and the WBC when users exhibit less noisiness order between them.
This paper investigates the secrecy capacity of the wiretap broadcast channel (WBC) with an external eavesdropper where a source wishes to communicate two private messages over a broadcast channel (BC) while keeping them secret from the eavesdropper. We derive a nontrivial outer bound on the secrecy capacity region of this channel which, in absence of security constraints, reduces to the best known outer bound to the capacity of the standard BC. An inner bound is also derived, which follows the behavior of both the best known inner bound for the BC and the wiretap channel. These bounds are shown to be tight for the deterministic BC with a general eavesdropper, the semideterministic BC with a more noisy eavesdropper, and the wiretap BC where users exhibit a less noisiness order between them. Finally, by rewriting our outer bound to encompass the characteristics of parallel channels, we also derive the secrecy capacity region of the product of two inversely less noisy BCs with a more noisy eavesdropper. We illustrate our results by studying the impact of security constraints on the capacity of the WBC with binary erasure and binary symmetric components.
This work investigates the secrecy capacity region of a class of Wiretap Broadcast Channel (WBC) where a source wishes to send two independent messages to two receivers in the presence of an external eavesdropper. We focus on the class of parallel WBC and more precisely on the product of two reversely less-noisy BC with a more noisy eavesdropper. We fully characterize the capacity region of such a setting through a novel powerful outer bound that relies on a careful single letter expression, followed by a non-trivial equivalent formulation of the resulting rate region. This outer bound turns out to be tight with the inner bound we derive for the setting under study.
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.
We study the security of communication between a single transmitter and multiple receivers in a broadcast channel in the presence of an eavesdropper. We consider several special classes of channels. As the first model, we consider the degraded multi-receiver 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 multi-receiver wiretap channel with a less noisiness order in each sub-channel, where this order is not necessarily the same for all sub-channels. We establish the common message secrecy capacity and sum secrecy capacity of this channel. Thirdly, we study a special class of degraded parallel multi-receiver wiretap channels and provide a stronger result. In particular, we study the case with two sub-channels two users and one eavesdropper, where there is a degradedness order in each sub-channel such that in the first (resp. second) sub-channel 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 sub-channels. We determine the secrecy capacity region of this channel. Finally, we focus on a variant of this previous channel model 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.
We study the security of communication between a single transmitter and multiple receivers in a broadcast channel in the presence of an eavesdropper. We consider several special classes of channels. As the first model, we consider the degraded multi-receiver 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 multi-receiver wiretap channel with a less noisiness order in each sub-channel, where this order is not necessarily the same for all sub-channels. We establish the common message secrecy capacity and sum secrecy capacity of this channel. Thirdly, we study a special class of degraded parallel multi-receiver wiretap channels and provide a stronger result. In particular, we study the case with two sub-channels two users and one eavesdropper, where there is a degradedness order in each sub-channel such that in the first (resp. second) sub-channel 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 sub-channels. We determine the secrecy capacity region of this channel.
In this paper, bounds to the secrecy capacity region for the general 3-receiver broadcast channel with 3 degraded message sets, are presented for confidential messages sent to be kept secret from one of the receivers. This model is a more general model than 2-receiver broadcast channels with confidential messages with an external wiretapper, and recently studied 3-receiver degraded broadcast channels with confidential messages, since the conditions on the receivers are general and wiretapper receives the common message. Wyner’s code partitioning combined with double-binning is used to show achievable rate tuples. Error probability analysis and equivocation calculation are also provided. The proof for the outer bound is shown for three cases: the general case; under the condition that receiver 1 is less noisy than receiver 3, the wiretapper; and under the condition that both receivers 1 and 2 are less noisy than the wiretapper, where the inner and outer bounds coincide, giving the secrecy capacity of the special case of a 3-receiver BC with 2 degraded message sets. I.