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The heat channel is defined by a linear time-varying (LTV) filter with additive white Gaussian noise (AWGN) at the filter output. The continuous-time LTV filter is related to the heat kernel of the quantum mechanical harmonic oscillator, so…
Optimization methods aimed at estimating the capacities of a general Gaussian channel are developed. Specifically evaluation of classical capacity as maximum of the Holevo information is pursued over all possible Gaussian encodings for the…
The I-MMSE formula connects two important quantities in information theory and estimation theory: the mutual information and the minimum mean-squared error (MMSE). It states that in a scalar Gaussian channel, the derivative of the mutual…
The capacity of multiple-input multiple-output additive white Gaussian noise channels is investigated under peak amplitude constraints on the norm of the input vector. New insights on the capacity-achieving input distribution are presented.…
A recent result of the authors shows a so-called I-MMSE-like relationship that, for the two-user Gaussian interference channel, an I-MMSE relationship holds in the limit, as n $\to \infty$, between the interference and the interfered-with…
This paper explores the two-user Gaussian interference channel through the lens of a natural deterministic channel model. The main result is that the deterministic channel uniformly approximates the Gaussian channel, the capacity regions…
The minimum mean square error of the estimation of a non Gaussian signal where observed from an additive white Gaussian noise channel's output, is analyzed. First, a quite general time-continuous channel model is assumed for which the…
The minimum mean-square error of the estimation of a signal where observed from the additive white Gaussian noise (WGN) channel's output, is analyzed. It is assumed that the channel input's signal is composed of a (normalized) sum of N…
In this paper, we revisit the problem of finding the average capacity of the Gaussian feedback channel. First, we consider the problem of finding the average capacity of the analog Gaussian noise channel where the noise has an arbitrary…
This paper deals with arbitrarily distributed finite-power input signals observed through an additive Gaussian noise channel. It shows a new formula that connects the input-output mutual information and the minimum mean-square error (MMSE)…
The capacity of a deterministic multiple-input multiple-output (MIMO) channel under the peak and average power constraints is investigated. For the identity channel matrix, the approach of Shamai et al. is generalized to the higher…
We address the capacity of a discrete-time memoryless Gaussian channel, where the channel state information (CSI) is neither available at the transmitter nor at the receiver. The optimal capacity-achieving input distribution at low…
In this paper, a new and general version of Gaussian channel in presence of two-sided state information correlated to the channel input and noise is considered. Determining a general achievable rate for the channel and obtaining the…
Recent outer bounds on the capacity region of Gaussian interference channels are generalized to $m$-user channels with $m>2$ and asymmetric powers and crosstalk coefficients. The bounds are again shown to give the sum-rate capacity for…
Many of the classical and recent relations between information and estimation in the presence of Gaussian noise can be viewed as identities between expectations of random quantities. These include the I-MMSE relationship of Guo et al.; the…
In this paper we consider the classical capacity problem for Gaussian measurement channels without imposing any kind of threshold condition. We prove Gaussianity of the average state of the optimal ensemble in general and discuss the…
The full solution of the optimization problem giving the Gaussian capacity of the single-mode fiducial Gaussian quantum channel is provided. Since it was shown that the Gaussian capacity of an arbitrary (phase-sensitive or insensitive)…
Unveiling a fundamental link between information theory and estimation theory, the I-MMSE relationship by Guo, Shamai and Verdu~\cite{gu05}, together with its numerous extensions, has great theoretical significance and various practical…
This paper investigates a channel estimator based on Gaussian mixture models (GMMs) in the context of linear inverse problems with additive Gaussian noise. We fit a GMM to given channel samples to obtain an analytic probability density…
The scalar additive Gaussian noise channel has the "single crossing point" property between the minimum-mean square error (MMSE) in the estimation of the input given the channel output, assuming a Gaussian input to the channel, and the MMSE…