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Article: Analyticity of entropy rate of hidden Markov chains

TitleAnalyticity of entropy rate of hidden Markov chains
Authors
KeywordsAnalyticity
Entropy
Entropy Rate
Hidden Markov Chain
Hidden Markov Process
Issue Date2006
PublisherIEEE. The Journal's web site is located at http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?puNumber=18
Citation
IEEE Transactions On Information Theory, 2006, v. 52 n. 12, p. 5251-5266 How to Cite?
AbstractWe prove that under mild positivity assumptions the entropy rate of a hidden Markov chain varies analytically as a function of the underlying Markov chain parameters. A general principle to determine the domain of analyticity is stated. An example is given to estimate the radius of convergence for the entropy rate. We then show that the positivity assumptions can be relaxed, and examples are given for the relaxed conditions. We study a special class of hidden Markov chains in more detail: binary hidden Markov chains with an unambiguous symbol, and we give necessary and sufficient conditions for analyticity of the entropy rate for this case. Finally, we show that under the positivity assumptions, the hidden Markov chain itself varies analytically, in a strong sense, as a function of the underlying Markov chain parameters. © 2006 IEEE.
Persistent Identifierhttp://hdl.handle.net/10722/156183
ISSN
2015 Impact Factor: 1.737
2015 SCImago Journal Rankings: 1.433
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorHan, Gen_US
dc.contributor.authorMarcus, Ben_US
dc.date.accessioned2012-08-08T08:40:45Z-
dc.date.available2012-08-08T08:40:45Z-
dc.date.issued2006en_US
dc.identifier.citationIEEE Transactions On Information Theory, 2006, v. 52 n. 12, p. 5251-5266en_US
dc.identifier.issn0018-9448en_US
dc.identifier.urihttp://hdl.handle.net/10722/156183-
dc.description.abstractWe prove that under mild positivity assumptions the entropy rate of a hidden Markov chain varies analytically as a function of the underlying Markov chain parameters. A general principle to determine the domain of analyticity is stated. An example is given to estimate the radius of convergence for the entropy rate. We then show that the positivity assumptions can be relaxed, and examples are given for the relaxed conditions. We study a special class of hidden Markov chains in more detail: binary hidden Markov chains with an unambiguous symbol, and we give necessary and sufficient conditions for analyticity of the entropy rate for this case. Finally, we show that under the positivity assumptions, the hidden Markov chain itself varies analytically, in a strong sense, as a function of the underlying Markov chain parameters. © 2006 IEEE.en_US
dc.languageengen_US
dc.publisherIEEE. The Journal's web site is located at http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?puNumber=18en_US
dc.relation.ispartofIEEE Transactions on Information Theoryen_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.rights©2006 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.-
dc.subjectAnalyticityen_US
dc.subjectEntropyen_US
dc.subjectEntropy Rateen_US
dc.subjectHidden Markov Chainen_US
dc.subjectHidden Markov Processen_US
dc.titleAnalyticity of entropy rate of hidden Markov chainsen_US
dc.typeArticleen_US
dc.identifier.emailHan, G:ghan@hku.hken_US
dc.identifier.authorityHan, G=rp00702en_US
dc.description.naturepublished_or_final_versionen_US
dc.identifier.doi10.1109/TIT.2006.885481en_US
dc.identifier.scopuseid_2-s2.0-33947364296en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-33947364296&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume52en_US
dc.identifier.issue12en_US
dc.identifier.spage5251en_US
dc.identifier.epage5266en_US
dc.identifier.isiWOS:000242503300005-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridHan, G=8640067800en_US
dc.identifier.scopusauthoridMarcus, B=7102086378en_US

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