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arXiv:2205.06412 · IEEE International Symposium on Information Theory (ISIT)

Optimal Order of Encoding for Gaussian MIMO Multi-Receiver Wiretap Channel

Yue Qi, Mojtaba Vaezi

Published Jun 26, 2022• 2 citations
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Abstract

The Gaussian multiple-input multiple-output (MIMO) multi-receiver wiretap channel is studied in this paper. The base station broadcasts confidential messages to K intended users while keeping the messages secret from an eavesdropper. The capacity of this channel has already been characterized by applying dirty-paper coding and stochastic encoding. However, K factorial encoding orders may need to be enumerated for that, which makes the problem intractable. We prove that there exists one optimal encoding order and reduced the K factorial times to a one-time encoding. The optimal encoding order is proved by forming a secrecy weighted sum rate (WSR) maximization problem. The optimal order is the same as that for the MIMO broadcast channel without secrecy constraint, that is, the weight of users’ rate in the WSR maximization problem determines the optimal encoding order. Numerical results verify the optimal encoding order.

DOI
10.1109/isit50566.2022.9834739

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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.
This paper considers the problem of secret communication over a two-receiver multiple-input multiple-output (MIMO) Gaussian broadcast channel. The transmitter has two independent messages, each of which is intended for one of the receivers but needs to be kept asymptotically perfectly secret from the other. It is shown that, surprisingly, under a matrix power constraint, both messages can be simultaneously transmitted at their respective maximal secrecy rates. To prove this result, the MIMO Gaussian wiretap channel is revisited and a new characterization of its secrecy capacity is provided via a new coding scheme that uses artificial noise (an additive prefix channel) and random binning.
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 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.
This paper considers the problem of secret communication over a two-receiver multiple-input multiple-output (MIMO) Gaussian broadcast channel. The transmitter has two independent, confidential messages and a common message. Each of the confidential messages is intended for one of the receivers but needs to be kept perfectly secret from the other, and the common message is intended for both receivers. It is shown that a natural scheme that combines secret dirty-paper coding with Gaussian superposition coding achieves the secrecy capacity region. To prove this result, a channel-enhancement approach and an extremal entropy inequality of Weingarten et al. are used.