Abstract
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.
Highlights
Rapid advances in wireless technology are quickly moving us toward a pervasively connected world in which a vast array of wireless devices, from iPhones to biosensors, seamlessly communicate with one another
We study the problem of secret communication over the multiple-input multiple-output (MIMO) Gaussian broadcast channel with two receivers
The main result of this paper is a precise characterization of the secrecy capacity region of the MIMO Gaussian broadcast channel, summarized in the following theorem
Summary
Rapid advances in wireless technology are quickly moving us toward a pervasively connected world in which a vast array of wireless devices, from iPhones to biosensors, seamlessly communicate with one another. The problem of communicating two confidential messages over the two-receiver MIMO Gaussian broadcast channel was first considered in [12], where it was shown that under the average total power constraint, secret dirty-paper coding (S-DPC) based on double binning [13] achieves the secrecy capacity region for the MISO case. Theorem 1: The secrecy capacity region Cs(H1, H2, S) of the MIMO Gaussian broadcast channel (1) with confidential messages W1 (intended for receiver 1 but needing to be kept secret from receiver 2) and W2 (intended for receiver 2 but needing to be kept secret from receiver 1) under the matrix power constraint (2) is given by the set of nonnegative rate pairs (R1, R2) such that.
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