Mallows has conjectured that among distributions which are Gaussian but for occasional contamination by additive noise, the one having least Fisher information has (two-sided) geometric contamination. A very similar problem arises in estimation of a non-negative vector parameter in Gaussian white noise when it is known also that most, i.e. (1 − ǫ), components are zero. We provide a partial asym...

In this paper, we give the white noise calculus for the Fermion system and prove the Fock expansion for any continuous linear operators from the space of test functionals to the space of generalized functionals. As an application of the Fock expansion, we give a necessary and sufficient condition for implementability of Bogoliubov automorphisms on Z2-invariant subalgebra of canonical anti-commu...

Many communication systems are bandwidthexpanding : the transmitted signal occupies a bandwidth larger than the symbol rate. The sampling theorems of Kotelnikov, Shannon, Nyquist et al. [1] shows that in order to represent a bandlimited signal, it is necessary to sample at what is popularly referred to as the Shannon or Nyquist rate. However, in many systems, the required sampling rate is very ...

The automatic estimation of machine translation (MT) output quality is an active research area due to its many potential applications (e.g. aiding human translation and post-editing, re-ranking MT hypotheses, MT system combination). Current approaches to the task rely on supervised learning methods for which high-quality labelled data is fundamental. In this framework, quality estimation (QE) h...

For the purpose of various synchronization tasks (including carrier phase, time, frequency, and frame synchronization), one may add a known pilot sequence, typically a pseudo-noise sequence, to the unknown data sequence. This approach is known as a spread-spectrum pilot technique or as a superimposed pilot sequence technique. In previous work, we applied the superimposed pilot sequence techniqu...

h a digital fiber optic transmission system, during photodetection process, a shot noise is produced that is neither stationary nor independent of the digital message. The evaluation of the average error probability in the presence of such a message-dependent shot noise, of additive Gaussian noise, and of intersymbol interference is considered. Two methods of calculation are outlined: an exhaus...

In several sensory pathways, input stimuli project to sparsely active downstream populations that have more neurons than incoming axons. Here, we address the computational benefits of expansion and sparseness for clustered inputs, where different clusters represent behaviorally distinct stimuli and intracluster variability represents sensory or neuronal noise. Through analytical calculations an...

We consider chaos expansion in generalized random variable spaces exp(S)ρ,H and exp(S)−ρ,H based on fractional white noise space, which correspond to the ones studied in [6]. Generalized stochastic processes with values in these spaces are proven to have a series expansion, and different Wick products are discussed. AMS Mathematics Subject Classification (2000): 60H40, 60G20, 60G15.

Using the geometric properties of Sobolev spaces of integer order and a duality condition, the covariance operators of a generalized random field and its dual can be factorized. Via this covariance factorization, a representation of the generalized random field is obtained as a stochastic equation driven by generalized white noise. This stochastic equation becomes a differential equation under ...

We define a class of “algebraic” random matrix channels for which one can generically compute the limiting Shannon transform using numerical techniques and often enumerate the low SNR series expansion coefficients in closed form. We describe this class, the coefficient enumeration techniques and compare theory with simulations.