For information transmission a discrete time channel with independent additive Gaussian noise is used. There is also another channel with independent additive Gaussian noise (the feedback channel), and the transmitter observes without delay all outputs of the forward channel via that channel. Transmission of nonexponential number of messages is considered (i.e. transmission rate equals zero) an...

Observations where additive noise is present can for many models be grouped into a compound observation matrix, adhering to the same type of model. There are many ways the observations can be stacked, for instance vertically, horizontally, or quadratically. An estimator for the spectrum of the underlying model can be formulated for each stacking scenario in the case of Gaussian noise. We compar...

The problem of minimax detection of Gaussian random signal vector in White Gaussian additive noise is considered. It is supposed that an unknown vector $\boldsymbol{\sigma}$ of the signal vector intensities belong to the given set ${\mathcal E}$. It is investigated when it is possible to replace the set ${\mathcal E}$ by a smaller set ${\mathcal E}_{0}$ without loss of quality (and, in particul...

We assume that Eve and Bob are connected to Alice with additive white Gaussian noise, and their noises are correlated. We mathematically formulate the correlation between their noises, and optimize Eve’s strategy. We give a necessarily and sufficient condition to generate the agreed secure key between Alice and Bob even with the Eve’s optimal strategy. Further, in this setting, we give a concre...

For each of the lattices A,(n 2 I), D,,(n 2 2), EC, E,, E,, and their duals a very fast algorithm is given for finding the closest lattice point to an arbitrary point. If these lattices are used for vector quantizing of uniformly distributed data, the algorithm finds the min imum distortion lattice point. If the lattices are used as codes for a Gaussian channel, the algorithm performs max imum ...

| This paper considers a class of nonGaussian noise modeled as a combination of a white Gaussian process and a shot noise process as suggested by Bello and Esposito [1]. With this noise model as input of a quadrature demodulator, the noise output vector is shown to have circular symmetry. In the particular case of Rayleigh distribution for the noise envelope amplitude, the symbol error probabil...

In this paper we establish lower and upper Gaussian bounds for the solutions to the heat and wave equations driven by an additive Gaussian noise, using the techniques of Malliavin calculus and recent density estimates obtained by Nourdin and Viens in [19]. In particular, we deal with the one-dimensional stochastic heat equation in [0, 1] driven by the space-time white noise, and the stochastic ...

We study the effect of a non-Gaussian noise on interstate switching activated primarily by Gaussian noise. Even weak non-Gaussian noise can strongly change the switching rate. The effect is determined by all moments of the noise distribution. It is expressed in a closed form in terms of the noise characteristic functional. The analytical results are compared with the results of simulations for ...