Related papers: An Elementary Proof of a Classical Information-The…
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…
Two familiar notions of correlation are rediscovered as the extreme operating points for distributed synthesis of a discrete memoryless channel, in which a stochastic channel output is generated based on a compressed description of the…
In recent years, there has been an upswing of interest in estimating information from data emerging in a lot of areas beyond communications. This paper aims at estimating the information between two random phenomena by using consolidated…
An expression is derived characterizing the set of admissible rate pairs for simultaneous transmission of classical and quantum information over a given quantum channel, generalizing both the classical and quantum capacities of the channel.…
This paper introduces time into information theory, gives a more accurate definition of information, and unifies the information in cognition and Shannon information theory. Specially, we consider time as a measure of information, giving a…
The transmission of classical information over a classical channel gave rise to the classical capacity theorem with the optimal rate in terms of the classical mutual information. Despite classical information being a subset of quantum…
Mutual information is one of the essential building blocks of information theory. Yet, it is only finitely defined for distributions with fast decaying tails on a countable joint alphabet of two random elements. The unboundedness of mutual…
A simple proof for the Shannon coding theorem, using only the Markov inequality, is presented. The technique is useful for didactic purposes, since it does not require many preliminaries and the information density and mutual information…
We determine the amount of information contained in a time series of price returns at a given time scale, by using a widespread tool of the information theory, namely the Shannon entropy, applied to a symbolic representation of this time…
We describe how to analyze the wide class of non stationary processes with stationary centered increments using Shannon information theory. To do so, we use a practical viewpoint and define ersatz quantities from time-averaged probability…
A model of quantum noisy channel with input encoding by a classical random vector is described. An equation of optimality is derived to determine a complete set of wave functions describing quantum decodings based on quasi-measurements…
In this letter, we investigate the mutual information rate (MIR) achieved by an independent identically distributed (IID) Gaussian input on the intensity-driven signal transduction channel. Specifically, the asymptotic expression of the…
The concept of Shannon entropy of random variables was generalized to measurable functions in general, and to simple functions with finite values in particular. It is shown that the information measure of a function is related to the time…
The applications of the general formulae of channel capacity developed in the quantum information theory to evaluation of information transmission capacity of optical channel are interesting subjects. In this review paper, we will point out…
The capacity of a classical-quantum channel (or in other words the classical capacity of a quantum channel) is considered in the most general setting, where no structural assumptions such as the stationary memoryless property are made on a…
Information theory is a practical and theoretical framework developed for the study of communication over noisy channels. Its probabilistic basis and capacity to relate statistical structure to function make it ideally suited for studying…
In this paper we show how \emph{the metric theory of tensor products} developed by Grothendieck perfectly fits in the study of channel capacities, a central topic in \emph{Shannon's information theory}. Furthermore, in the last years…
We consider the estimation of a signal from the knowledge of its noisy linear random Gaussian projections, a problem relevant in compressed sensing, sparse superposition codes or code division multiple access just to cite few. There has…
Many of the traditional results in information theory, such as the channel coding theorem or the source coding theorem, are restricted to scenarios where the underlying resources are independent and identically distributed (i.i.d.) over a…
Fundamental relations between information and estimation have been established in the literature for the continuous-time Gaussian and Poisson channels, in a long line of work starting from the classical representation theorems by Duncan and…