Related papers: A simpler derivation of the coding theorem
We present a simplification of Jensen's proof of his Coding Theorem (even in the case where 0# exists). The proof avoids Jensen's split into cases according to whether or not 0# exists. In addition, the paper contains self-contained proofs…
We prove a martingale triangular array generalization of the Chow-Birnbaum-Marshall's inequality. The result is used to derive a strong law of large numbers for martingale triangular arrays whose rows are asymptotically stable in a certain…
Telling apart the cause and effect between two random variables with purely observational data is a challenging problem that finds applications in various scientific disciplines. A key principle utilized in this task is the algorithmic…
Coinduction refers to both a technique for the definition of infinite streams, so-called codata, and a technique for proving the equality of coinductively specified codata. This article first reviews coinduction in declarative programming.…
The optimal causal coding of a partially observed Markov process is studied, where the cost to be minimized is a bounded, non-negative, additive, measurable single-letter function of the source and the receiver output. A structural result…
The paper establishes an analog Whittaker-Shannon-Kotelnikov sampling theorem with fast decreasing coefficient, as well as a new modification of the corresponding interpolation formula applicable for general type non-vanishing bounded…
The output of a discrete Markov source is to be encoded instantaneously by a variable-rate encoder and decoded by a finite-state decoder. Our performance measure is a linear combination of the distortion and the instantaneous rate.…
In estimating the complexity of objects, in particular of graphs, it is common practice to rely on graph- and information-theoretic measures. Here, using integer sequences with properties such as Borel normality, we explain how these…
We consider the entropy of sums of independent discrete random variables, in analogy with Shannon's Entropy Power Inequality, where equality holds for normals. In our case, infinite divisibility suggests that equality should hold for…
This simple note lays out a few observations which are well known in many ways but may not have been said in quite this way before. The basic idea is that when comparing two different Markov chains it is useful to couple them is such a way…
In this correspondence we present a new proof of Holevo's coding theorem for transmitting classical information through quantum channels, and its strong converse. The technique is largely inspired by Wolfowitz's combinatorial approach using…
A proof of the continuous martingale convergence theorem is provided. It relies on a classical martingale inequality and the almost sure convergence of a uniformly bounded non-negative super-martingale, after a truncation argument.
In quantum Shannon theory, the way information is encoded and decoded takes advantage of the laws of quantum mechanics, while the way communication channels are interlinked is assumed to be classical. In this Letter we relax the assumption…
Linear information and rank inequalities as, for instance, Ingleton inequality, are useful tools in information theory and matroid theory. Even though many such inequalities have been found, it seems that most of them remain undiscovered.…
We obtain a mathematically simple characterization of all functionals coinciding with the von Neumann reduced entropy on pure states based on the Khinchin-Faddeev axiomatization of Shannon entropy and give a physical interpretation of the…
Renyi's "thinning" operation on a discrete random variable is a natural discrete analog of the scaling operation for continuous random variables. The properties of thinning are investigated in an information-theoretic context, especially in…
A great number of articles widen a known scientific result $P(a)$ (such as: a theorem, an inequality, or a math/physics/chemical etc. proposition or formula) by a simple recurrence procedure and using, in the proof, the proposition $P(a)$…
We give a proof of a Martingale Representation Theorem using the methods of nonstandard analysis.
The idea of the restricted mean has been used to establish a significantly improved version of Markov's inequality that does not require any new assumptions. The result immediately extends on Chebyshev's inequalities and Chernoff's bound.…
We give trade-offs between classical communication, quantum communication, and entanglement for processing information in the Shannon-theoretic setting. We first prove a unit-resource capacity theorem that applies to the scenario where only…