Related papers: Markov Capacity for Factor Codes with an Unambiguo…
In this paper, we utilize the framework of Markov processes to attain a more probabilistic perspective on the theory of transfer operators. In doing so, we establish a functional central limit theorem (FLCT) for an $O(N)$ model associated…
Let G be a block matrix function with one diagonal block A being positive definite and the off diagonal blocks complex conjugates of each other. Conditions are obtained for G to be factorable (in particular, with zero partial indices) in…
This paper deals with the multiplicative finite-field matrix channel, a discrete memoryless channel whose input and output are matrices (over a finite field) related by a multiplicative transfer matrix. The model considered here assumes…
Variable-order Markov models generate sequences over a finite alphabet by conditioning each symbol on the longest available suffix of the generated history. Regular constraints, by contrast, describe finite-horizon control requirements by…
We prove that, for all binary-input symmetric memoryless channels, polar codes enable reliable communication at rates within $\epsilon > 0$ of the Shannon capacity with a block length, construction complexity, and decoding complexity all…
We provide a sufficient criterion for the unique parameter identification of combinatorially symmetric Hidden Markov Models based on the structure of their transition matrix. If the observed states of the chain form a zero forcing set of…
We give necessary and sufficient conditions for the group of a rational maximal bifix code $Z$ to be isomorphic with the $F$-group of $Z\cap F$, when $F$ is recurrent and $Z\cap F$ is rational. The case where $F$ is uniformly recurrent,…
We propose a new definition of metastability of Markov processes on countable state spaces. We obtain sufficient conditions for a sequence of processes to be metastable. In the reversible case these conditions are expressed in terms of the…
Directed and undirected graphical models, also called Bayesian networks and Markov random fields, respectively, are important statistical tools in a wide variety of fields, ranging from computational biology to probabilistic artificial…
Markov chains are convenient means of generating realizations of networks with a given (joint or otherwise) degree distribution, since they simply require a procedure for rewiring edges. The major challenge is to find the right number of…
The $\{K_2,C_n\}$-factor of a graph is a spanning subgraph whose each component is either $K_2$ or $C_n$. In this paper, a sufficient condition with regard to tight toughness, isolated toughness and binding number bounds to guarantee the…
The two most popular types of graphical model are directed models (Bayesian networks) and undirected models (Markov random fields, or MRFs). Directed and undirected models offer complementary properties in model construction, expressing…
We investigate the maximum size of graph families on a common vertex set of cardinality $n$ such that the symmetric difference of the edge sets of any two members of the family satisfies some prescribed condition. We solve the problem…
We consider a model of communication via a fully quantum jammer channel with quantum jammer, quantum sender and quantum receiver, which we dub quantum arbitrarily varying channel (QAVC). Restricting to finite dimensional user and jammer…
We give a necessary and sufficient criterion when a normal CP-map on a von Neumann algebra admits a restriction to a maximal commutative subalgebra. We apply this result to give a far reaching generalization of Rebolledo's sufficient…
In this paper, we propose a model for large scale fading channels via markov process. We exploit the channel delay profile and the dependency between channel states via a first order autoregressive model that cast insight to the channel…
Several types of graphs with different conditional independence interpretations --- also known as Markov properties --- have been proposed and used in graphical models. In this paper we unify these Markov properties by introducing a class…
In this paper we investigate the local limit theorem for additive functionals of a nonstationary Markov chain with finite or infinite second moment. The moment conditions are imposed on the individual summands and the weak dependence…
In his influential work Choquet systematically studied capacities on Boolean algebras in a topological space, and gave a probabilistic interpretation for completely monotone (and completely alternating) capacities. Beyond complete…
We derive a single-letter upper bound to the mismatched-decoding capacity for discrete memoryless channels. The bound is expressed as the mutual information of a transformation of the channel, such that a maximum-likelihood decoding error…