Shannon and R\'enyi entropy rates of stationary vector valued Gaussian random processes

TL;DR

This paper derives formulas for the Shannon and Rényi entropy rates of stationary vector Gaussian processes using advanced mathematical tools, providing a theoretical foundation for understanding their informational properties.

Contribution

It introduces a novel application of Szeg"o's theorem to compute entropy rates for vector Gaussian processes, extending existing scalar results.

Findings

Explicit formulas for entropy rates of vector Gaussian processes

Application of block matrix Szeg"o's theorem in information theory

Enhanced understanding of entropy in multivariate Gaussian models

Abstract

We derive expressions for the Shannon and R\'enyi entropy rates of stationary vector valued Gaussian random processes using the block matrix version of Szeg\"o's theorem.