Entropy of Hidden Markov Processes and Connections to Dynamical Systems

Erscheinungsjahr 2016
ISBN: 978-0-521-11113-3
Verlag: Cambridge University Press

Buch, Englisch, Band 385, 278 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 410 g

Reihe: London Mathematical Society Lecture Note Series

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.

Autoren/Hrsg.

Marcus, Brian

Petersen, Karl

Weissman, Tsachy

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Informationstheorie, Kodierungstheorie
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Mathematik | Informatik EDV | Informatik Daten / Datenbanken Informationstheorie, Kodierungstheorie

Inhaltsverzeichnis

1. Hidden Markov processes in the context of symbolic dynamics Mark Boyle and Karl Petersen; 2. On the preservation of Gibbsianess under symbol amalgamation Jean-René Chazottes and E. Ugalde; 3. A note on a complex Hilbert metric with application to domain of analyticity for entropy rate of hidden Markov processes Guangyue Han, Brian Marcus and Yuval Peres; 4. Bounds on the entropy rate of binary hidden Markov processes Erik Ordentlich and Tsachy Weissman; 5. Entropy rate for hidden Markov chains with rare transitions Yuval Peres and Anthony Quas; 6. The capacity of finite-state channels in the high-noise regime Henry Pfister; 7. Computing entropy rates for hidden Markov processes Mark Pollicott; 8. Factors of Gibbs measures for full shifts Mark Pollicott and Thomas Kempton; 9. Thermodynamics of hidden Markov processes Evgeny Verbitskiy.

Über Autor(innen)

Weissman, Tsachy
Tsachy Weissman is an Associate Professor of Electrical Engineering at Stanford University and at the Technion. He is a recipient of the joint Information Theory – Communication Society best paper award, a Horev Fellowship for Leaders in Science and Technology and the Henry Taub Prize for excellence in research. He currently serves as Associate Editor of Shannon Theory for the IEEE Transactions on Information Theory.

Petersen, Karl
Karl Petersen is a Professor of Mathematics at the University of North Carolina, Chapel Hill. He has previously written the book Ergodic Theory (Cambridge University Press, 1983) and numerous research papers.

Marcus, Brian
Brian Marcus is a Professor in the Department of Mathematics at the University of British Columbia. He is a Fellow of the IEEE and was co-recipient of the Leonard G. Abraham Prize Paper Award of the IEEE Communications Society in 1993. He has published over 60 research papers and holds 12 US patents.

Brian Marcus is a Professor in the Department of Mathematics at the University of British Columbia. He is a Fellow of the IEEE and was co-recipient of the Leonard G. Abraham Prize Paper Award of the IEEE Communications Society in 1993. He has published over 60 research papers and holds 12 US patents.

Karl Petersen is a Professor of Mathematics at the University of North Carolina, Chapel Hill. He has previously written the book Ergodic Theory (Cambridge University Press, 1983) and numerous research papers.

Tsachy Weissman is an Associate Professor of Electrical Engineering at Stanford University and at the Technion. He is a recipient of the joint Information Theory - Communication Society best paper award, a Horev Fellowship for Leaders in Science and Technology and the Henry Taub Prize for excellence in research. He currently serves as Associate Editor of Shannon Theory for the IEEE Transactions on Information Theory.