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Measuring the relationship between any pair of variables is a rich and active area of research that is central to scientific practice. In contrast, characterizing the common information among any group of variables is typically a…
"Bounds on information combining" are entropic inequalities that determine how the information (entropy) of a set of random variables can change when these are combined in certain prescribed ways. Such bounds play an important role in…
Understanding the entanglement dynamics in quantum many-body systems under steady-state transport conditions is an actively pursued challenging topic. Hydrodynamic equations, akin to transport equations for charge or heat, would be of great…
This paper introduces \texttt{infotheory}: a package written in C++ and usable from Python and C++, for multivariate information theoretic analyses of discrete and continuous data. This package allows the user to study the relationship…
The max-relative entropy and the conditional min-entropy it induces have become central to one-shot information theory. Both may be expressed in terms of a conic program over the positive semidefinite cone. Recently, it was shown that the…
The problem of lossless data compression with side information available to both the encoder and the decoder is considered. The finite-blocklength fundamental limits of the best achievable performance are defined, in two different versions…
Matrix completion is a fundamental problem that comes up in a variety of applications like the Netflix problem, collaborative filtering, computer vision, and crowdsourcing. The goal of the problem is to recover a k-by-n unknown matrix from…
The information convex allows us to look into certain information-theoretic constraints in two-dimensional topological orders. We provide a derivation of the topological contribution $\ln d_a$ to the von Neumann entropy, where $d_a$ is the…
The problem of mismatched decoding for discrete memoryless channels is addressed. A mismatched cognitive multiple-access channel is introduced, and an inner bound on its capacity region is derived using two alternative encoding methods:…
In private information delivery (PID) problem, there are $K$ messages stored across $N$ servers, each capable of storing $M$ messages and a user. Servers want to convey one of the $K$ messages to the user without revealing the identity…
Learning-to-communicate (LTC) in partially observable environments has received increasing attention in deep multi-agent reinforcement learning, where the control and communication strategies are jointly learned. Meanwhile, the impact of…
Intervals in binary or n-ary relations or other discrete structures generalize the concept of interval in a linearly ordered set. Join-irreducible partitions into intervals are characterized in the lattice of all interval decompositions of…
We address three outstanding problems in information theory. Problem one is the definition of a non-negative decomposition of the information conveyed by two or more sources about a target variable into the specific contribution of each…
We are assisting at a growing interest in the development of learning architectures with application to digital communication systems. Herein, we consider the detection/decoding problem. We aim at developing an optimal neural architecture…
In this paper, we take a unified approach for network information theory and prove a coding theorem, which can recover most of the achievability results in network information theory that are based on random coding. The final single-letter…
Any measurement is intended to provide information on a system, namely knowledge about its state. However, we learn from quantum theory that it is generally impossible to extract information without disturbing the state of the system or its…
We introduce an algebraic concept of the frame for abstract conditional independence (CI) models, together with basic operations with respect to which such a frame should be closed: copying and marginalization. Three standard examples of…
The decoupling technique is a fundamental tool in quantum information theory with applications ranging from quantum thermodynamics to quantum many body physics to the study of black hole radiation. In this work we introduce the notion of…
A new algorithm to compute cylindrical algebraic decompositions (CADs) is presented, building on two recent advances. Firstly, the output is truth table invariant (a TTICAD) meaning given formulae have constant truth value on each cell of…
Scientific and commercial data is often incomplete. Recovery of the missing information is an important pre-processing step in data analysis. Real-world data can in many cases be represented as a superposition of two or more different types…