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  3. Entropy of Hidden Markov Processes and Connections to Dynamical Systems
  • Cited by 12
Publisher:
Cambridge University Press
Online publication date:
June 2011
Print publication year:
2011
Online ISBN:
9780511819407
DOI:
https://doi.org/10.1017/CBO9780511819407
Subjects:
Mathematics (general), Mathematics, Communications and Signal Processing, Engineering, Discrete Mathematics Information Theory and Coding
Series:
London Mathematical Society Lecture Note Series (385)
Information

Book description

Hidden Markov processes (HMPs) are important objects of study in many areas of pure and applied mathematics, including information theory, probability theory, dynamical systems and statistical physics, with applications in electrical engineering, computer science and molecular biology. This collection of research and survey papers presents important new results and open problems, serving as a unifying gateway for researchers in these areas. Based on talks given at the Banff International Research Station Workshop, 2007, this volume addresses a central problem of the subject: computation of the Shannon entropy rate of an HMP. This is a key quantity in statistical physics and information theory, characterising the fundamental limit on compression and closely related to channel capacity, the limit on reliable communication. Also discussed, from a symbolic dynamics and thermodynamical viewpoint, is the problem of characterizing the mappings between dynamical systems which map Markov measures to Markov (or Gibbs) measures, and which allow for Markov lifts of Markov chains.

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