Equality in the Matrix Entropy-Power Inequality and Blind Separation of Real and Complex sources

The matrix version of the entropy-power inequality for real or complex coefficients and variables is proved using a transportation argument that easily settles the equality case. An application to blind source extraction is given.Comment: 5 pages, in Proc. 2019 IEEE International Symposium on Information Theory (ISIT 2019), Paris, France, July 7-12, 201

The Capacity of Single-Server Weakly-Private Information Retrieval

A private information retrieval (PIR) protocol guarantees that a user can privately retrieve files stored in a database without revealing any information about the identity of the requested file. Existing information-theoretic PIR protocols ensure perfect privacy, i.e., zero information leakage to the servers storing the database, but at the cost of high download. In this work, we present weakly-private information retrieval (WPIR) schemes that trade off perfect privacy to improve the download cost when the database is stored on a single server. We study the tradeoff between the download cost and information leakage in terms of mutual information (MI) and maximal leakage (MaxL) privacy metrics. By relating the WPIR problem to rate-distortion theory, the download-leakage function, which is defined as the minimum required download cost of all single-server WPIR schemes for a given level of information leakage and a fixed file size, is introduced. By characterizing the download-leakage function for the MI and MaxL metrics, the capacity of single-server WPIR is fully described.Comment: To appear in IEEE Journal of Selected Areas in Information Theory (JSAIT), Special Issue on Privacy and Security of Information Systems, 202

Soft Guessing Under Log-Loss Distortion Allowing Errors

This paper deals with the problem of soft guessing under log-loss distortion (logarithmic loss) that was recently investigated by [Wu and Joudeh, IEEE ISIT, pp. 466--471, 2023]. We extend this problem to soft guessing allowing errors, i.e., at each step, a guesser decides whether to stop the guess or not with some probability and if the guesser stops guessing, then the guesser declares an error. We show that the minimal expected value of the cost of guessing under the constraint of the error probability is characterized by smooth R\'enyi entropy. Furthermore, we carry out an asymptotic analysis for a stationary and memoryless source

A Simple Derivation of the Refined Sphere Packing Bound Under Certain Symmetry Hypotheses

A judicious application of the Berry-Esseen theorem via suitable Augustin information measures is demonstrated to be sufficient for deriving the sphere packing bound with a prefactor that is $\mathit{\Omega}\left(n^{-0.5(1-E_{sp}'(R))}\right)$ for all codes on certain families of channels -- including the Gaussian channels and the non-stationary Renyi symmetric channels -- and for the constant composition codes on stationary memoryless channels. The resulting non-asymptotic bounds have definite approximation error terms. As a preliminary result that might be of interest on its own, the trade-off between type I and type II error probabilities in the hypothesis testing problem with (possibly non-stationary) independent samples is determined up to some multiplicative constants, assuming that the probabilities of both types of error are decaying exponentially with the number of samples, using the Berry-Esseen theorem.Comment: 20 page