arXiv:1608.06057 · IEEE Information Theory Workshop (ITW)

MIMO Gaussian Broadcast Channels With Common, Private, and Confidential Messages

Ziv Goldfeld, Haim Henri Permuter

Published Sep 1, 2016• 20 citations

Abstract

The two-user multiple-input multiple-output Gaussian broadcast channel with common, private, and confidential messages is considered. The transmitter sends a common message to both users, a confidential message to the User 1 and a private (non-confidential) message to the User 2. The secrecy-capacity region is characterized by showing that certain inner and outer bounds coincide and that the boundary points are achieved by Gaussian inputs, which enables the development of a tight converse. The proof relies on the factorization of upper concave envelopes and a variant of dirty-paper coding (DPC). It is shown that the entire region is exhausted by using DPC to cancel out the signal of the non-confidential message at Receiver 1, thus making DPC against the signal of the confidential message unnecessary. A numerical example illustrates the secrecy-capacity results.

DOI: 10.1109/itw.2016.7606792

Related papers

MIMO Gaussian broadcast channels with confidential and common messages

Ruoheng Liu, Tie Liu, H. Vincent Poor +1 more

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.

arXiv:1001.2806IEEE International Symposium on Information Theory (ISIT)Jun 1, 201044 citations

Transmission of common, public and confidential messages in broadcast channels with multiple antennas

Ersen Ekrem, Şennur Ulukuş

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.

IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC)Sep 1, 20101 citation

The Secrecy Capacity Region of the Gaussian MIMO Broadcast Channel

Ghadamali Bagherikaram, Seyed Abolfazl Motahari, Amir Keyvan Khandani

In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers via a Gaussian multiple-input multiple-output (MIMO) broadcast channel. An eavesdropper also receives the transmitted signal via another MIMO channel. We first consider the discrete memoryless channel and obtain the capacity region of the degraded channel. The secret dirty paper coding (SDPC) region as an achievable rate region for the general discrete channel is introduced. Relying on the results for the discrete channel, we fully characterize the secrecy capacity region of MIMO broadcast channel. It is shown that the SDPC scheme is optimal. The converse part of the proof relies on the generalized Costa's entropy power inequality and a new channel enhancement strategy in which we only need to enhance the channels of the legitimate receivers, and the channel of the eavesdropper remains unchanged.

IEEE Transactions on Information TheoryJan 21, 201349 citations

Secrecy Capacity Region of a Multiple-Antenna Gaussian Broadcast Channel With Confidential Messages

Ruoheng Liu, H. Vincent Poor

Wireless communication is particularly susceptible to eavesdropping due to its broadcast nature. Security and privacy systems have become critical for wireless providers and enterprise networks. This paper considers the problem of secret communication over the Gaussian broadcast channel, where a multiple-antenna transmitter wishes to send independent confidential messages to two users with information-theoretic secrecy. That is, each user would like to obtain its own confidential message in a reliable and safe manner. This communication model is referred to as the multiple-antenna Gaussian broadcast channel with confidential messages (MGBC-CM). Under this communication scenario, a secret dirty-paper coding scheme and the corresponding achievable secrecy rate region are first developed based on Gaussian codebooks. Next, a computable Sato-type outer bound on the secrecy capacity region is provided for the MGBC-CM. Furthermore, the Sato-type outer bound proves to be consistent with the boundary of the secret dirty-paper coding achievable rate region, and hence, the secrecy capacity region of the MGBC-CM is established. Finally, two numerical examples demonstrate that both users can achieve positive rates simultaneously under the information-theoretic secrecy requirement.

IEEE Transactions on Information TheoryFeb 26, 2009266 citations

On the Optimality of Linear Precoding for Secrecy in the MIMO Broadcast Channel

S. Ali. A. Fakoorian, Arnold Lee Swindlehurst

We study the optimality of linear precoding for the two-receiver multiple-input multiple-output (MIMO) Gaussian broadcast channel (BC) with confidential messages. Secret dirty-paper coding (S-DPC) is optimal under an input covariance constraint, but there is no computable secrecy capacity expression for the general MIMO case under an average power constraint. In principle, for this case, the secrecy capacity region could be found through an exhaustive search over the set of all possible matrix power constraints. Clearly, this search, coupled with the complexity of dirty-paper encoding and decoding, motivates the consideration of low complexity linear precoding as an alternative. We prove that for a two-user MIMO Gaussian BC under an input covariance constraint, linear precoding is optimal and achieves the same secrecy rate region as S-DPC if the input covariance constraint satisfies a specific condition, and we characterize the corresponding optimal linear precoders. We then use this result to derive a closed-form sub-optimal algorithm based on linear precoding for an average power constraint. Numerical results indicate that the secrecy rate region achieved by this algorithm is close to that obtained by the optimal S-DPC approach with a search over all suitable input covariance matrices.

IEEE Journal on Selected Areas in CommunicationsAug 23, 201354 citations

On the Optimality of Linear Precoding for Secrecy in the MIMO Broadcast Channel

Arnold Lee Swindlehurst

We study the optimality of linear precoding for the two-receiver multiple-input multiple-output (MIMO) Gaussian broadcast channel (BC) with confidential messages. Secret dirty-paper coding (SDPC) is optimal under an input covariance constraint, but there is no computable secrecy capacity expression for the general MIMO case under an average power constraint. In principle, for this case, the secrecy capacity region could be found through an exhaustive search over the set of all possible matrix power constraints. Clearly, this search, coupled with the complexity of dirty-paper encoding and decoding, motivates the consideration of low complexity linear precoding as an alternative. We prove that for a two-user MIMO Gaussian BC under an input covariance constraint, linear precoding is optimal and achieves the same secrecy rate region as S-DPC if the input covariance constraint satisfies a specific condition, and we characterize the corresponding optimal linear precoders. We then use this result to derive a closed-form sub-optimal algorithm based on linear precoding for an average power constraint. Numerical results indicate that the secrecy rate region achieved by this algorithm is close to that obtained by the optimal S-DPC approach with a search over all suitable input covariance matrices.

arXiv:1304.4627Apr 16, 20132 citations