Related papers: On Matched Metric and Channel Problem
In this paper we establish some criteria to decide when a discrete memoryless channel admits a metric in such a way that the maximum likelihood decoding coincides with the nearest neighbour decoding. In particular we prove a conjecture…
Necessary and sufficient conditions for approximation of a general channel by a general source are proved. For the special case in which the channel input is deterministic, which corresponds to source simulation, we prove a stronger…
We consider the problem of communicating over a channel for which no mathematical model is specified, and the achievable rates are determined as a function of the channel input and output sequences known a-posteriori, without assuming any…
Evaluating the channel capacity is one of many key problems in information theory. In this work we derive rather-mild sufficient conditions under which the capacity is finite and achievable. These conditions are derived for generic,…
Two quantum channels are called compatible if they can be obtained as marginals from a single broadcasting channel; otherwise they are incompatible. We derive a characterization of the compatibility relation in terms of concatenation and…
A generalized word in two positive definite matrices A and B is a finite product of nonzero real powers of A and B. Symmetric words in positive definite A and B are positive definite, and so for fxed B, we can view a symmetric word, S(A,B),…
Properties of metrics and pairs consisting of left and right connections are studied on the bimodules of differential 1-forms. Those bimodules are obtained from the derivation based calculus of an algebra of matrix valued functions, and an…
When dealing with certain mathematical problems, it is sometimes necessary to show that some function induces a metric on a certain space. When this function is not a well renowned example of a distance, one has to develop very particular…
Let M be a complete metric space. It is proved that if the space or scalar-valued bounded continuous functions on M admits an isometric shift, then M is separable.
A finite number of rational functions are compatible if they satisfy the compatibility conditions of a first-order linear functional system involving differential, shift and q-shift operators. We present a theorem that describes the…
The classical Cauchy completion of a metric space (by means of Cauchy sequences) as well as the completion of a uniform space (by means of Cauchy filters) are well-known to rely on the symmetry of the metric space or uniform space in…
The execution of sequential programs allows them to be represented using mathematical functions formed by the composition of statements following one after the other. Each such statement is in itself a partial function, which allows only…
Achievable and converse bounds for general channels and mismatched decoding are derived. The direct (achievable) bound is derived using random coding and the analysis is tight up to factor 2. The converse is given in term of the achievable…
We prove general results about separation and weak$^\#$-convergence of boundedly finite measures on separable metric spaces and Souslin spaces. More precisely, we consider an algebra of bounded real-valued, or more generally a $*$-algebra…
Using the frame formalism we determine some possible metrics and metric-compatible connections on the noncommutative differential geometry of the real quantum plane. By definition a metric maps the tensor product of two 1-forms into a…
In the first part of the paper we consider binary input channels that are not necessarily stationary and show how positive rates can be achieved using codes constrained to be within predetermined dictionaries. We use a…
A metric is formal if all products of harmonic forms are again harmonic. The existence of a formal metric implies Sullivan formality of the manifold, and hence formal metrics can exist only in presence of a very restricted topology. We show…
We settle the equivalence between the problem of hitting a polyhedral set by the orbit of a linear map and the intersection of a regular language and a language of permutations of binary words (the permutation filter realizability problem).…
We establish common fixed point theorems for two pairs of weakly compatible self-mappings using an auxiliary function of two variables. Unlike classical results, our theorems do not assume continuity of the mappings and require completeness…
Let $f \colon X \rightarrow Y$ be a resolvable-measurable mapping of a metrizable space $X$ to a regular space $Y$. Then $f$ is piecewise continuous. Additionally, for a metrizable completely Baire space $X$, it is proved that $f$ is…