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Entropy of Hidden Markov Processes and Connections to Dynamical Systems

Papers from the Banff International Research Station Workshop

Brian Marcus (University of British Columbia, Vancouver) Karl Petersen (University of North Carolina, Chapel Hill) Tsachy Weissman (Stanford University, California)

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English
Cambridge University Press
26 May 2011
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.

Edited by:   , , , ,
Imprint:   Cambridge University Press
Country of Publication:   United Kingdom
Volume:   v. 385
Dimensions:   Height: 226mm,  Width: 150mm,  Spine: 15mm
Weight:   400g
ISBN:   9780521111133
ISBN 10:   0521111137
Series:   London Mathematical Society Lecture Note Series
Pages:   278
Publication Date:  
Audience:   Professional and scholarly ,  Undergraduate
Format:   Paperback
Publisher's Status:   Active

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.

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