Abstract
This paper presents fundamental limits associated with compressive classification of Gaussian mixture source models. In particular, we offer an asymptotic characterization of the behavior of the (upper bound to the) misclassification probability associated with the optimal Maximum-A-Posteriori (MAP) classifier that depends on quantities that are dual to the concepts of diversity gain and coding gain in multi-antenna communications. The diversity, which is shown to determine the rate at which the probability of misclassification decays in the low noise regime, is shown to depend on the geometry of the source, the geometry of the measurement system and their interplay. The measurement gain, which represents the counterpart of the coding gain, is also shown to depend on geometrical quantities. It is argued that the diversity order and the measurement gain also offer an optimization criterion to perform dictionary learning for compressive classification applications.

Abstract
This paper investigates power allocation strategies over a bank of independent parallel Gaussian wiretap channels where a legitimate transmitter and a legitimate receiver communicate in the presence of an eavesdropper and a friendly jammer. We give algorithms to compute the optimal power allocation strategy of the jammer in the degraded scenario. We also give an algorithm to compute power allocations strategies of the jammer in a general scenario, leading to significant performance gains in relation to isotropic jamming. Additionally, we provide a set of results that cast further insight into the problem. In our scenario, which is applicable to current OFDM communications systems, we demonstrate that the proposed jammer power allocation strategy can lead to considerable secrecy gains.

Abstract
We characterize the minimum number of measurements needed to drive to zero the minimum mean squared error (MMSE) of Gaussian mixture model (GMM) input signals in the low-noise regime. The result also hints at almost phasetransition optimal recovery procedures based on a classification and reconstruction approach.

Abstract
This paper puts forth projections designs for compressive classification of Gaussian mixture models. In particular, we capitalize on the asymptotic characterization of the behavior of an (upper bound to the) misclassification probability associated with the optimal Maximum-A-Posteriori (MAP) classifier, which depends on quantities that are dual to the concepts of the diversity gain and coding gain in multi-antenna communications, to construct measurement designs that maximize the diversity-order of the measurement model. Numerical results demonstrate that the new measurement designs substantially outperform random measurements. Overall, the analysis and the designs cast geometrical insight about the mechanics of compressive classification problems.

Abstract
A transmission between two agents, Alice and Bob, over a set of parallel sub-channels is overheard by a third agent Eve, through a second set of parallel sub-channels. All sub-channels are flat with random and independent gains and additive white Gaussian noise (AWGN). Alice splits the total amount of available power among the sub-channels, with the purpose of maximizing the communication rate to Bob, under reliability and secrecy constraints. To this end, two schemes are considered. In one case the secret message is encoded with a single wiretap code and then split among the sub-channels. In the latter case the secret message is first split into a number of sub-messages, each separately encoded and transmitted on a different sub-channel. The achievable secrecy rates under a constraint on the secrecy outage probability (SOP) are derived and closed form expressions for Rayleigh fading sub-channels are obtained. In order to limit the complexity of resources optimization (power and rates) we also consider suboptimal solutions based on the selection of active sub-channels over which power is split either equally or according to a waterfilling algorithm with respect to the Alice-Bob channel.

Abstract
This paper puts forth new recovery guarantees for the source separation problem in the presence of side information, where one observes the linear superposition of two source signals plus two additional signals that are correlated with the mixed ones. By positing that the individual components of the mixed signals as well as the corresponding side information signals follow a joint Gaussian mixture model, we characterise necessary and sufficient conditions for reliable separation in the asymptotic regime of low-noise as a function of the geometry of the underlying signals and their interaction. In particular, we show that if the subspaces spanned by the innovation components of the source signals with respect to the side information signals have zero intersection, provided that we observe a certain number of measurements from the mixture, then we can reliably separate the sources, otherwise we cannot. We also provide a number of numerical results on synthetic data that validate our theoretical findings.