Related papers: Markov Capacity for Factor Codes with an Unambiguo…
This paper considers the derivative of the entropy rate of a hidden Markov process with respect to the observation probabilities. The main result is a compact formula for the derivative that can be evaluated easily using Monte Carlo…
We study joint source-channel coding over Markov channels through the empirical coordination framework. More specifically, we aim at determining the empirical distributions of source and channel symbols that can be induced by a coding…
The main result of this paper is an edge-coloured version of Tutte's $f$-factor theorem. We give a necessary and sufficient condition for an edge-coloured graph $G^c$ to have a properly coloured $f$-factor. We state and prove our result in…
Recently, a strong exponential character bound has been established in [3] for all elements $g \in \mathbf{G}^F$ of a finite reductive group $\mathbf{G}^F$ which satisfy the condition that the centraliser $C_{\mathbf{G}}(g)$ is contained in…
We revisit the source coding problem for a Markov chain under the assumption that the transmission times and how fast the Markov chain transitions its state happen at the same time-scale. Specifically, we assume that the transmission of…
In this paper, we are concerned with sufficient conditions for the existence of a $\{P_{2},P_{2k+1}\}$-factor. We prove that for $k\geq 3$, there exists $\varepsilon_{k}>0$ such that if a graph $G$ satisfies $\sum_{0\leq j\leq…
We study topological mixing properties and the maximal equicontinuous factor of rank-one subshifts as topological dynamical systems. We show that the maximal equicontinuous factor of a rank-one subshift is finite. We also determine all the…
We present an algorithm for tests generation tools based on symbolic execution. The algorithm is supposed to help in situations, when a tool is repeatedly failing to cover some code by tests. The algorithm then provides the tool a necessary…
We consider the application of the factor graph framework for symbol detection on linear inter-symbol interference channels. Based on the Ungerboeck observation model, a detection algorithm with appealing complexity properties can be…
In this paper, we investigate some properties on capacity factors, which were proposed to investigate the link failure problem from network coding. A capacity factor (CF) of a network is an edge set, deleting which will cause the maximum…
Let $\sigma:\boldsymbol{\Sigma}\to\boldsymbol{\Sigma}$ be the left shift acting on $ \boldsymbol{\Sigma} $, a one-sided Markov subshift on a countable alphabet. Our intention is to guarantee the existence of $\sigma$-invariant Borel…
The optimal zero delay coding of a finite state Markov source is considered. The existence and structure of optimal codes are studied using a stochastic control formulation. Prior results in the literature established the optimality of…
In this paper, we study Markov chains (MC) on topological spaces within the framework of the operator approach. We extend the Markov operator from the space of countably additive measures to the space of finitely additive measures. Cesaro…
We study limit theorems for partial sums of instantaneous functions of a homogeneous Markov chain on a general state space. The summands are heavy-tailed and the limits are stable distributions. The conditions imposed on the transition…
A rateless code encodes a finite length information word into an infinitely long codeword such that longer prefixes of the codeword can tolerate a larger fraction of errors. A rateless code achieves capacity for a family of channels if, for…
In distributed communication, each transmitter prepares an ensemble of channel codes. To encode a message, a transmitter chooses a channel code individually without sharing the coding choice with other transmitters or with the receiver.…
We consider general Markov chains with discrete time in an arbitrary measurable (phase) space and homogeneous in time. Markov chains are defined by the classical transition function which within the framework of the operator treatment…
This article develops a general framework for Laplace duality between positive Markov processes in which the one-dimensional Laplace transform of one process can be represented through that of another. We show that a process admits a…
We study multifractal decompositions based on Birkhoff averages for sequences of functions belonging to certain classes of symbolically continuous functions. We do this for an expanding interval map with countably many branches, which we…
We obtain an upper escape rate function for a continuous time minimal symmetric Markov chain, defined on a locally finite weighted graph. This upper rate function is given in terms of volume growth with respect to an adapted path metric and…