A precise matrix characterization of the capacity-equivocation region of the multiple-input multiple-output (MIMO) Gaussian wiretap channel is established. This characterization is obtained via a connection to the problem of simultaneously communicating a private and a confidential messages over a MIMO Gaussian broadcast channel, for which the secrecy capacity region can be established using previous results on the secrecy capacity of the MIMO Gaussian wiretap channel.
A precise matrix characterization of the capacity-equivocation region of the multiple-input multiple-output (MIMO) Gaussian wiretap channel is established. This characterization is obtained via a connection to the problem of simultaneously communicating a private and a confidential messages over a MIMO Gaussian broadcast channel, for which the secrecy capacity region can be established using previous results on the secrecy capacity of the MIMO Gaussian wiretap channel.
This paper presents two new results on multiple-input multiple-output (MIMO) Gaussian broadcast channels with confidential messages. First, the MIMO Gaussian wiretap channel is revisited. A matrix characterization of the capacity-equivocation region is provided, which extends the previous result on the secrecy capacity to the more general imperfect secrecy setting. Next, the MIMO Gaussian broadcast channel with two receivers and three independent messages: a common message intended for both receivers, and two confidential messages each intended for one of the receivers but needing to be kept asymptotically perfectly secret from the other, is considered. A precise characterization of the capacity region is provided, generalizing the previous results which considered only two out of three possible messages.
We study the Gaussian multiple-input multiple-output (MIMO) wiretap channel, which consists of a transmitter, a legitimate user, and an eavesdropper. In this channel, the transmitter sends a common message to both the legitimate user and the eavesdropper. Moreover, the legitimate user receives a private message, which is desired to be kept hidden as much as possible from the eavesdropper. We obtain the entire capacity-equivocation region of the Gaussian MIMO wiretap channel. This region contains all achievable common message, private message, and private message's equivocation rates. This capacity-equivocation region is equal to the capacity region of a Gaussian MIMO broadcast channel where the transmitter sends a common message to both the legitimate user and the eavesdropper, a public message to the legitimate user on which there is no secrecy constraint, and a confidential message to the legitimate user which needs to kept perfectly secret from the eavesdropper.
We study the Gaussian multiple-input multiple-output (MIMO) wiretap channel, which consists of a transmitter, a legitimate user, and an eavesdropper. In this channel, the transmitter sends a common message to both the legitimate user and the eavesdropper. In addition to this common message, the legitimate user receives a private message, which is desired to be kept hidden as much as possible from the eavesdropper. We obtain the entire capacity-equivocation region of the Gaussian MIMO wiretap channel. This region contains all achievable common message, private message, and private message's equivocation (secrecy) rates. In particular, we show the sufficiency of jointly Gaussian auxiliary random variables and channel input to evaluate the existing single-letter description of the capacity-equivocation region due to Csiszar-Korner.
We study the Gaussian multiple-input multiple-output (MIMO) wiretap channel, which consists of a transmitter, a legitimate user, and an eavesdropper. In this channel, the transmitter sends a common message to both the legitimate user and the eavesdropper. In addition to this common message, the legitimate user receives a private message, which is desired to be kept hidden as much as possible from the eavesdropper. We obtain the entire capacity-equivocation region of the Gaussian MIMO wiretap channel. This region contains all achievable common message, private message, and private message's equivocation (secrecy) rates. In particular, we show the sufficiency of jointly Gaussian auxiliary random variables and channel input to evaluate the existing single-letter description of the capacity-equivocation region due to Csiszar–Korner.
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.
We study secure communication in which a transmitter wants to send confidential messages to an arbitrary number of receivers in the presence of an external eavesdropper. We consider two classes of Gaussian channels: the Gaussian single-input single-output (SISO) multi-receiver wiretap channel and the degraded Gaussian multiple-input multiple-output (MIMO) multi-receiver wiretap channel. These two channels belong to the class of degraded multi-receiver wiretap channels. In previous literature the secrecy capacity regions of these two channels were established under the conservative joint secrecy constraint. Thus, we focus our work on the less conservative individual secrecy constraint, which is characterized by a higher throughput. We establish the individual secrecy capacity region for these two cases. The achievability follows from the individual secrecy capacity established for the discrete memoryless degraded wiretap channels where coding is performed using Gaussian signals. On the other hand, the converse is established by adapting the techniques used for formulating the joint secrecy capacity region to the individual secrecy constraint.