相关论文: Shannon capacity, Chess, DNA and Umbrellas

The accessible information quantifies the amount of classical information that can be extracted from an ensemble of quantum states. Analogously, the informational power quantifies the amount of classical information that can be extracted by…

New sufficient conditions for determining in closed form the capacity region of point-to-point memoryless two-way channels (TWCs) are derived. The proposed conditions not only relax Shannon's condition which can identify only TWCs with a…

The theory of graphons is an important tool in understanding properties of large networks. We investigate a power-law random graph model and cast it in the graphon framework. The distinctively different structures of the limit graph are…

We consider the use of the well-known dual capacity bounding technique for deriving upper bounds on the capacity of indecomposable finite-state channels (FSCs) with finite input and output alphabets. In this technique, capacity upper bounds…

We present a problem relating measurements and information theory in spin foam models. In the three dimensional case of quantum gravity we can compute probabilities of spin network graphs and study the behaviour of the Shannon entropy…

We establish the ultimate limits to the compression of sequences of identically prepared qubits. The limits are determined by Holevo's information quantity and are attained through use of the optimal universal cloning machine, which finds…

Chess graphs encode the moves that a particular chess piece can make on an $m\times n$ chessboard. We study through these graphs through the lens of chip-firing games and graph gonality. We provide upper and lower bounds for the gonality of…

We discuss weak and strong links (`virtual connections') in the Shannon game. General properties of these links are discussed, leading to a method to find all links of given size by a suitably pruned exhaustive search. This is applied to…

We consider the maximum cut and maximum independent set problems on random regular graphs in the infinite-size limit, and calculate the energy densities achieved by QAOA for high degrees up to $d=100$. Such an analysis is possible because…

The concept of optimal communication channels shapes our understanding of wave-based communication. Its analysis, however, always pertains to specific communication-domain geometries, without a general theory of scaling laws or fundamental…

A tournament is a complete directed graph. It is well known that every tournament contains at least one vertex v such that every other vertex is reachable from v by a path of length at most 2. All such vertices v are called *kings* of the…

This paper addresses information design in a workhorse model of network games, where agents have linear best responses, the information designer maximizes a quadratic objective, and the payoff-relevant state follows a multivariate Gaussian…

What is the optimal number of independent observations from which a sparse Gaussian Graphical Model can be correctly recovered? Information-theoretic arguments provide a lower bound on the minimum number of samples necessary to perfectly…

We provide a simple physical interpretation, in the context of the second law of thermodynamics, to the information inequality (a.k.a. the Gibbs' inequality, which is also equivalent to the log-sum inequality), asserting that the relative…

We consider the problem of recovering a subhypergraph based on an observed adjacency tensor corresponding to a uniform hypergraph. The uniform hypergraph is assumed to contain a subset of vertices called as subhypergraph. The edges…

This paper studies the Shannon regime for the random displacement of stationary point processes. Let each point of some initial stationary point process in $\R^n$ give rise to one daughter point, the location of which is obtained by adding…

The maximal clique problem, to find the maximally sized clique in a given graph, is classically an NP-complete computational problem, which has potential applications ranging from electrical engineering, computational chemistry,…

Whereas Shannon entropy is related to the growth rate of multinomial coefficients, we show that the quadratic entropy (Tsallis 2-entropy) is connected to their $q$-deformation; when $q$ is a prime power, these $q$-multinomial coefficients…

It is well known that orthogonal coding can be used to approach the Shannon capacity of the power-constrained AWGN channel without a bandwidth constraint. This correspondence describes a semi-orthogonal variation of pulse position…

In this paper, we characterize the information-theoretic capacity scaling of wireless ad hoc networks with $n$ randomly distributed nodes. By using an exact channel model from Maxwell's equations, we successfully resolve the conflict in the…