Related papers: Information-Theoretic Extensions of the Shannon-Ny…
In this paper, we propose to use Brownian motions to model families of continuous-time multiuser Gaussian channels without bandwidth limit. It turns out that such a formulation allows parallel translation of many fundamental notions and…
In this paper, we consider single- and multi-user Gaussian channels with feedback under expected power constraints and with non-vanishing error probabilities. In the first of two contributions, we study asymptotic expansions for the…
Dual to the usual noisy channel coding problem, where a noisy (classical or quantum) channel is used to simulate a noiseless one, reverse Shannon theorems concern the use of noiseless channels to simulate noisy ones, and more generally the…
Starting with the Wigner distribution formulation for beam wave propagation in H\"{o}lder continuous non-Gaussian random refractive index fields we show that the wave beam regime naturally leads to the white-noise scaling limit and…
Biochemical signal transduction, a form of molecular communication, can be modeled using graphical Markov channels with input-modulated transition rates. Such channel models are strongly non-Gaussian. In this paper we use a linear noise…
The most natural way to describe an information-carrying system containing a specific noise is an additive white Gaussian-noise (AWGN) channel. In bosonic quantum systems (especially the Gaussian case), although the classical information…
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…
This article serves as a brief introduction to the Shannon information theory. Concepts of information, Shannon entropy and channel capacity are mainly covered. All these concepts are developed in a totally combinatorial flavor. Some issues…
In this paper we address a fundamental question in communication, that is, in the presence of various noise scenarios such as white/colored Gaussian noise and impulsive -type noises, how to efficiently and accurately transmit a set of…
The amount of information lost in sub-Nyquist sampling of a continuous-time Gaussian stationary process is quantified. We consider a combined source coding and sub-Nyquist reconstruction problem in which the input to the encoder is a noisy…
In our companion paper [1], an information identity decomposition has been derived, which can be interpreted as a law of conservation of information flows in feedback systems. In this paper, we further investigate this decomposition result…
This paper quantifies the intuitive observation that adding noise reduces available information by means of non-linear strong data processing inequalities. Consider the random variables $W\to X\to Y$ forming a Markov chain, where $Y=X+Z$…
Diffusion models have attracted a lot of attention in recent years. These models view speech generation as a continuous-time process. For efficient training, this process is typically restricted to additive Gaussian noising, which is…
In the first part of this thesis, we discuss the algebraic approach to classical and quantum physics and develop information theoretic concepts within this setup. In the second part, we discuss the uncertainty principle in quantum…
The feedback capacity of the stationary Gaussian additive noise channel has been open, except for the case where the noise is white. Here we find the feedback capacity of the stationary first-order moving average additive Gaussian noise…
We provide a model to study memory effects in quantum Gaussian channels with additive classical noise over an arbitrary number of uses. The correlation among different uses is introduced by contiguous two-mode interactions. Numerical…
We present the continuous wavelet transform (WT) of white Gaussian noise and establish a connection to the theory of Gaussian analytic functions. Based on this connection, we propose a methodology that detects components of a signal in…
In information theory, the link between continuous information and discrete information is established through well-known sampling theorems. Sampling theory explains, for example, how frequency-filtered music signals are reconstructible…
With the use of Hida's white noise space theory space theory and spaces of stochastic distributions, we present a detailed analytic continuation theory for classes of Gaussian processes, with focus here on Brownian motion. For the latter,…
Starting from Shannon's celebrated 1948 channel coding theorem, we trace the evolution of channel coding from Hamming codes to capacity-approaching codes. We focus on the contributions that have led to the most significant improvements in…