Multi-receiver Wiretap Channel Research Articles

Relay-Aided Secure Broadcasting for Visible Light Communications

A visible light communication broadcast channel is considered, in which a transmitter luminaire communicates with two legitimate receivers in the presence of an external eavesdropper. A number of trusted cooperative half-duplex relay luminaires are deployed to aid with securing the transmitted data. Transmitters are equipped with single light fixtures, containing multiple light emitting diodes, and receiving nodes are equipped with single photo-detectors, rendering the considered setting as a single-input single-output system. Transmission is amplitude-constrained to maintain operation within the light emitting diodes' dynamic range. Achievable secrecy rate regions are derived under such amplitude constraints for this multi-receiver wiretap channel, first for direct transmission without the relays, and then for multiple relaying schemes: cooperative jamming, decode-and-forward, and amplify-and-forward. Superposition coding with uniform signaling is used at the transmitter and the relays. Further, for each relaying scheme, secure beamforming vectors are carefully designed at the relay nodes in order to hurt the eavesdropper and/or benefit the legitimate receivers. Superiority of the proposed relaying schemes, with secure beamforming, is shown over direct transmission. It is also shown that the best relaying scheme depends on how far the eavesdropper is located from the transmitter and the relays, the number of relays, and their geometric layout.

Secrecy Sum Rates of MIMO Multi-Receiver Wiretap Channels

We consider MIMO multi-receiver wiretap channels where the transmitter sends confidential messages to legitimate receivers in the presence of an external eavesdropper. Since the secrecy sum rate maximization problem is nonconvex, we derive an equivalent alternating optimization problem. We propose an iterative algorithm to find the optimal transmit covariance matrix based on the MIMO BC-MAC duality. We prove that the limit point satisfies the KKT conditions of the original secrecy sum rate maximization problem.

On SDoF of Multi-Receiver Wiretap Channel With Alternating CSIT

We study the problem of secure transmission over a Gaussian multi-input single-output (MISO) two receiver channel with an external eavesdropper, under the assumption that the state of the channel which is available to each receiver is conveyed either perfectly ( $P$ ) or with delay ( $D$ ) to the transmitter. Denoting by $S_{1}$ , $S_{2}$ , and $S_{3}$ , the channel state information at the transmitter (CSIT) of user 1, user 2, and eavesdropper, respectively, the overall CSIT can then alternate between eight possible states, i.e., $(S_{1},S_{2},S_{3}) \in \{P,D\}^{3}$ . We denote by $\lambda _{S_{1} S_{2} S_{3}}$ the fraction of time during which the state $S_{1}S_{2}S_{3}$ occurs. Under these assumptions, we first consider the Gaussian MISO wiretap channel and characterize the secure degrees of freedom (SDoF). Next, we consider the general multi-receiver setup and characterize the SDoF region of fixed hybrid states $PPD$ , $PDP$ , and $DDP$ . We then focus our attention on the symmetric case in which $\lambda _{PDD}=\lambda _{DPD}$ . For this case, we establish bounds on SDoF region. The analysis reveals that alternating CSIT allows synergistic gains in terms of SDoF, and shows that by opposition to encoding separately over different states, joint encoding across the states strictly enables better secure rates. Furthermore, we specialize our results for the two receivers channel with an external eavesdropper to the two-user broadcast channel. We show that the synergistic gains in terms of SDoF by alternating CSIT are not restricted to multi-receiver wiretap channels, and can also be harnessed under broadcast setting.

Multi-Receiver Wiretap Channel With Public and Confidential Messages

We study the multi-receiver wiretap channel (MR-WC) with public and confidential messages. In this channel, there is a transmitter that wishes to communicate with two legitimate users in the presence of an external eavesdropper. The transmitter sends a pair of public and confidential messages to each legitimate user. While there are no secrecy constraints on the public messages, confidential messages need to be transmitted in perfect secrecy. We study the discrete memoryless MR-WC as well as its Gaussian multi-input multi-output (MIMO) counterpart. First, we propose an inner bound for the general, not necessarily degraded, discrete memoryless MR-WC by using Marton's inner bound and rate splitting in conjunction with superposition coding and binning. Second, we specialize this inner bound for the degraded discrete memoryless case. This specialized form of the inner bound can be obtained by using superposition coding and binning only. Next, we obtain an outer bound for the capacity region of the degraded channel, which matches the inner bound for some special cases. Third, we consider the degraded Gaussian MIMO channel, and show that, to evaluate both the inner and outer bounds, considering only jointly Gaussian auxiliary random variables and channel input is sufficient. Similar to the discrete memoryless case, for the Gaussian MIMO case as well, these bounds match for some special cases.

Degraded Compound Multi-Receiver Wiretap Channels

We study the degraded compound multi-receiver wiretap channel (DCMRWC). DCMRWC consists of two groups of users and a group of eavesdroppers, where, if we pick an arbitrary user from each group of users and an arbitrary eavesdropper, they satisfy a certain Markov chain. We study two different communication scenarios for this channel. In the first scenario, the transmitter wants to send a confidential message to users in the first (stronger) group and a different confidential message to users in the second (weaker) group, where both messages need to be kept confidential from the eavesdroppers. For this scenario, we assume that there is only one eavesdropper. We obtain the secrecy capacity region for the discrete memoryless channel model, the parallel channel model, and the Gaussian parallel channel model. For the Gaussian multiple-input multiple-output (MIMO) channel model, we obtain the secrecy capacity region when there is only one user in the second group. In the second scenario we study, the transmitter sends a confidential message to users in the first group which needs to be kept confidential from the second group of users and the eavesdroppers. Moreover, the transmitter sends a different confidential message to users in the second group which needs to be kept confidential only from the eavesdroppers. For this scenario, we do not put any restriction on the number of eavesdroppers. As in the first scenario, we obtain the secrecy capacity region for the discrete memoryless channel model, the parallel channel model, and the Gaussian parallel channel model. For the Gaussian MIMO channel model, we establish the secrecy capacity region when there is only one user in the second group.

The Secrecy Capacity Region of the Gaussian MIMO Multi-Receiver Wiretap Channel

In this paper, we consider the Gaussian multiple-input multiple-output (MIMO) multi-receiver wiretap channel in which a transmitter wants to have confidential communication with an arbitrary number of users in the presence of an external eavesdropper. We derive the secrecy capacity region of this channel for the most general case. We first show that even for the single-input single-output (SISO) case, existing converse techniques for the Gaussian scalar broadcast channel cannot be extended to this secrecy context, to emphasize the need for a new proof technique. Our new proof technique makes use of the relationships between the minimum-mean-square-error and the mutual information, and equivalently, the relationships between the Fisher information and the differential entropy. Using the intuition gained from the converse proof of the SISO channel, we first prove the secrecy capacity region of the degraded MIMO channel, in which all receivers have the same number of antennas, and the noise covariance matrices can be arranged according to a positive semi-definite order. We then generalize this result to the aligned case, in which all receivers have the same number of antennas; however, there is no order among the noise covariance matrices. We accomplish this task by using the channel enhancement technique. Finally, we find the secrecy capacity region of the general MIMO channel by using some limiting arguments on the secrecy capacity region of the aligned MIMO channel. We show that the capacity achieving coding scheme is a variant of dirty-paper coding with Gaussian signals.

Secure broadcasting using multiple antennas

We consider three different secure broadcasting scenarios: i) Broadcast channels with common and confidential messages (BCC), ii) multi-receiver wiretap channels with public and confidential messages, and iii) compound wiretap channels. The BCC is a broadcast channel with two users, where in addition to the common message sent to both users, a private message, which needs to be kept hidden as much as possible from the other user, is sent to each user. In this model, each user treats the other user as an eavesdropper. The multi-receiver wiretap channel is a broadcast channel with two legitimate users and an external eavesdropper, where the transmitter sends a pair of public and confidential messages to each legitimate user. Although there is no secrecy concern about the public messages, the confidential messages need to be kept perfectly secret from the eavesdropper. The compound wiretap channel is a compound broadcast channel with a group of legitimate users and a group of eavesdroppers. In this model, the transmitter sends a common confidential message to the legitimate users, and this confidential message needs to be kept perfectly secret from all eavesdroppers. In this paper, we provide a survey of the existing information-theoretic results for these three forms of secure broadcasting problems, with a closer look at the Gaussian multiple-input multiple-output (MIMO) channel models. We also present the existing results for the more general discrete memory-less channel models, as they are often the first step in obtaining the capacity results for the corresponding Gaussian MIMO channel models.

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.