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2 results

6 - Tensorization and Information Rates
from Part I - Information Measures
Yury Polyanskiy, Massachusetts Institute of Technology, Yihong Wu, Yale University, Connecticut
Book:

Information Theory

Published online:

09 January 2025

Print publication:

02 January 2025, pp 106-114
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Summary

In Chapter 6 we start with explaining the important property of mutual information known as tensorization (or single-letterization), which allows one to maximize and minimize mutual information between two high-dimensional vectors. Next, we extend the information measures discussed in previous chapters for random variables to random processes by introducing the concepts of entropy rate (for a stochastic process) and mutual information rate (for a pair of stochastic processes).

On the entropy for semi-Markov processes
Part of
Valerie Girardin, Nikolaos Limnios
Journal:

Journal of Applied Probability / Volume 40 / Issue 4 / September 2003

Published online by Cambridge University Press:

14 July 2016, pp. 1060-1068

Print publication:

September 2003
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The aim of this paper is to define the entropy of a finite semi-Markov process. We define the entropy of the finite distributions of the process, and obtain explicitly its entropy rate by extending the Shannon–McMillan–Breiman theorem to this class of nonstationary continuous-time processes. The particular cases of pure jump Markov processes and renewal processes are considered. The relative entropy rate between two semi-Markov processes is also defined.

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