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IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)

MIMO Gaussian broadcast channels with private and confidential messages and with receiver side information

Rafael F. Schaefer, H. Vincent Poor, Holger Boche

Published Jun 1, 2013• 0 citations
Publisher

Abstract

In this paper the two-receiver MIMO Gaussian broadcast channel with private and confidential messages and receiver side information is studied. In this communication scenario, each receiver is interested in one private and one confidential message having the other private message as side information for decoding available. Each confidential message is exclusively intended for one receiver and must therefore be kept secret from the other receiver. A complete characterization of the secrecy capacity region is established using channel enhancement arguments and an extremal entropy inequality.

DOI
10.1109/spawc.2013.6612132

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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.
This paper considers the problem of the multiple-input multiple-output (MIMO) Gaussian broadcast channel with two receivers (receivers 1 and 2) and two messages: a common message intended for both receivers and a confidential message intended only for receiver 1 but needing to be kept asymptotically perfectly secure from receiver 2. A matrix characterization of the secrecy capacity region is established via a channel enhancement argument. The enhanced channel is constructed by first splitting receiver 1 into two virtual receivers and then enhancing only the virtual receiver that decodes the confidential message. The secrecy capacity region of the enhanced channel is characterized using an extremal entropy inequality previously established for characterizing the capacity region of a degraded compound MIMO Gaussian broadcast channel.
This paper considers the problem of the multiple-input multiple-output (MIMO) Gaussian broadcast channel with two receivers (receivers 1 and 2) and two messages: a common message intended for both receivers and a confidential message intended only for receiver 1 but needing to be kept asymptotically perfectly secure from receiver 2. A matrix characterization of the secrecy capacity region is established via a channel enhancement argument. The enhanced channel is constructed by first splitting receiver 1 into two virtual receivers and then enhancing only the virtual receiver that decodes the confidential message. The secrecy capacity region of the enhanced channel is characterized using an extremal entropy inequality previously established for characterizing the capacity region of a degraded compound MIMO Gaussian broadcast channel. 1
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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 a two-user broadcast channel (BC) with two-degraded message sets where a common message M2is intended for both receivers and a private message M1is intended for receiver one. There is an eavesdropper whose channel is stochastically degraded with respect to both receivers and both messages must be kept confidential from the eavesdropper. However, we do not assume any form of degradedness between the two receivers. We first characterize the capacity region of this class of discrete memoryless BC. Next, we consider the two-user Gaussian MIMO BC with two-degraded message sets and an eavesdropper. We characterize the capacity region for the case where the eavesdropper is only required to be stochastically degraded with respect to receiver one. We make use of the channel enhancement technique as well as an extremal entropy inequality of Liu et al. that was derived using the generalized Costa's entropy power inequality (EPI).