Wyner's wiretap channel is extended to parallel broadcast channels and fading channels with multiple receivers. In the first part of the paper, we consider the setup of parallel broadcast channels with one sender, multiple intended receivers, and one eavesdropper. We study the situations where the sender broadcasts either a common message or independent messages to the intended receivers. We derive upper and lower bounds on the common-message-secrecy capacity, which coincide when the users are reversely degraded. For the case of independent messages we establish the secrecy sum-capacity when the users are reversely degraded. In the second part of the paper we apply our results to fading channels: perfect channel state information of all intended receivers is known globally, whereas the eavesdropper channel is known only to her. For the common message case, a somewhat surprising result is proven: a positive rate can be achieved independently of the number of intended receivers. For independent messages, an opportunistic transmission scheme is presented that achieves the secrecy sum-capacity in the limit of large number of receivers. Our results are stated for a fast fading channel model. Extensions to the block fading model are also discussed.
Wyner's wiretap channel is extended to parallel broadcast channels and fading channels with multiple receivers. In the first part of the paper, we consider the setup of parallel broadcast channels with one sender, multiple intended receivers, and one eavesdropper. We study the situations where the sender broadcasts either a common message or independent messages to the intended receivers. We derive upper and lower bounds on the common-message-secrecy capacity, which coincide when the users are reversely degraded. For the case of independent messages we establish the secrecy sum-capacity when the users are reversely degraded. In the second part of the paper we apply our results to fading channels: perfect channel state information of all intended receivers is known globally, whereas the eavesdropper channel is known only to her. For the common message case, a somewhat surprising result is proven: a positive rate can be achieved independently of the number of intended receivers. For independent messages, an opportunistic transmission scheme is presented that achieves the secrecy sum-capacity in the limit of large number of receivers. Our results are stated for a fast fading channel model. Extensions to the block fading model are also discussed.
We study a problem of broadcasting confidential messages to multiple receivers under an information-theoretic secrecy constraint. Two scenarios are considered: 1) all receivers are to obtain a common message; and 2) each receiver is to obtain an independent message. Moreover, two models are considered: parallel channels and fast-fading channels. For the case of reversely degraded parallel channels, one eavesdropper, and an arbitrary number of legitimate receivers, we determine the secrecy capacity for transmitting a common message, and the secrecy sum-capacity for transmitting independent messages. For the case of fast-fading channels, we assume that the channel state information of the legitimate receivers is known to all the terminals, while that of the eavesdropper is known only to itself. We show that, using a suitable binning strategy, a common message can be reliably and securely transmitted at a rate independent of the number of receivers. We also show that a simple opportunistic transmission strategy is optimal for the reliable and secure transmission of independent messages in the limit of large number of receivers.
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, we consider secure broadcasting over fast fading channels. Assuming imperfect main channel state information (CSI) at the transmitter, we first provide an upper and a lower bounds on the ergodic secrecy capacity when a common message is broadcasted to multiple legitimate receivers in the presence of one eavesdropper. For this case, we show that the secrecy rate is limited by the legitimate receiver having, on average, the worst main channel link. Then, we present an expression for the achievable secrecy sum-rate when each legitimate receiver is interested in an independent message. The special cases of high SNR, perfect and no-main CSI are also analyzed. Numerical results are presented to illustrate the obtained results for the case of independent but not necessarily identically distributed Rayleigh fading channels.
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.
In this paper, we investigate the problem of secure broadcasting over block-fading channels with limited channel knowledge at the transmitter. More particularly, we analyze the effect of having imperfect channel state information (CSI) via a finite rate feedback on the throughput of a broadcast channel where the transmission is intended for multiple legitimate receivers in the presence of an eavesdropper. First, we partially characterize the ergodic secrecy capacity of the system when the source broadcasts the same information to all the receivers, i.e., common message transmission. Then, we look at the independent messages case, where the transmitter broadcasts multiple independent messages to the legitimate receivers. For this case, we present lower and upper bounds on the ergodic secrecy sum-capacity. In both scenarios, we show that the proposed lower and upper bounds coincide asymptotically as the capacity of the feedback links becomes large, hence, fully characterizing the secrecy capacity in this case.