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This paper studies the classification of high-dimensional Gaussian signals from low-dimensional noisy, linear measurements. In particular, it provides upper bounds (sufficient conditions) on the number of measurements required to drive the probability of misclassification to zero in the low-noise regime, both for random measurements and designed ones. Such bounds reveal two important operational regimes that are a function of the characteristics of the source: 1) when the number of classes is less than or equal to the dimension of the space spanned by signals in each class, reliable classification is possible in the low-noise regime by using a one-vs-all measurement design; 2) when the dimension of the spaces spanned by signals in each class is lower than the number of classes, reliable classification is guaranteed in the low-noise regime by using a simple random measurement design. Simulation results both with synthetic and real data show that our analysis is sharp, in the sense that it is able to gauge the number of measurements required to drive the misclassification probability to zero in the low-noise regime. [ABSTRACT FROM PUBLISHER]

This paper considers the problem of filter design with secrecy constraints, where two legitimate parties (Alice and Bob) communicate in the presence of an eavesdropper (Eve) over a Gaussian multiple-input-multiple-output (MIMO) wiretap channel. This problem involves designing, subject to a power constraint, the transmit and the receive filters which minimize the mean-squared error (MSE) between the legitimate parties whilst assuring that the eavesdropper MSE remains above a certain threshold. We consider a general MIMO Gaussian wiretap scenario, where the legitimate receiver uses a linear zero-forcing (ZF) filter and the eavesdropper receiver uses either a ZF or an optimal linear Wiener filter. We provide a characterization of the optimal filter designs by demonstrating the convexity of the optimization problems. We also provide generalizations of the filter designs from the scenario where the channel state is known to all the parties to the scenario where there is uncertainty in the channel state. A set of numerical results illustrates the performance of the novel filter designs, including the robustness to channel modeling errors. In particular, we assess the efficacy of the designs in guaranteeing not only a certain MSE level at the eavesdropper, but also in limiting the error probability at the eavesdropper. We also assess the impact of the filter designs on the achievable secrecy rates. The penalty induced by the fact that the eavesdropper may use the optimal nonlinear receive filter rather than the optimal linear one is also explored in the paper. [ABSTRACT FROM PUBLISHER]