{"@context":{"@vocab":"https://cir.nii.ac.jp/schema/1.0/","rdfs":"http://www.w3.org/2000/01/rdf-schema#","dc":"http://purl.org/dc/elements/1.1/","dcterms":"http://purl.org/dc/terms/","foaf":"http://xmlns.com/foaf/0.1/","prism":"http://prismstandard.org/namespaces/basic/2.0/","cinii":"http://ci.nii.ac.jp/ns/1.0/","datacite":"https://schema.datacite.org/meta/kernel-4/","ndl":"http://ndl.go.jp/dcndl/terms/","jpcoar":"https://github.com/JPCOAR/schema/blob/master/2.0/"},"@id":"https://cir.nii.ac.jp/crid/1570009752661495552.json","@type":"Article","productIdentifier":[{"identifier":{"@type":"NAID","@value":"110007537878"}}],"dc:title":[{"@language":"en","@value":"Properties of a Wore-Valued Source with a Non-prefix-free Word Set"}],"dc:language":"en","description":[{"type":"abstract","notation":[{"@language":"en","@value":"Recently, a word-valued source has been proposed as a new class of information source models. A word-valued source is regarded as a source with a probability distribution over a word set. Although a word-valued source is a nonstationary source in general, it has been proved that an entropy rate of the source exists and the Asymptotic Equipartition Property (AEP) holds when the word set of the source is prefix-free. However, when the word set is not prefix-free (non-prefix-free), only an upper bound on the entropy density rate for an i.i.d. word-valued source has been derived so far. In this paper, we newly derive a lower bound on the entropy density rate for an i.i.d. word-valued source with a finite non-prefix-free word set. Then some numerical examples are given in order to investigate the behavior of the bounds."}]}],"creator":[{"@id":"https://cir.nii.ac.jp/crid/1580009752661495553","@type":"Researcher","personIdentifier":[{"@type":"NRID","@value":"9000016489303"}],"foaf:name":[{"@language":"en","@value":"ISHIDA Takashi"}],"jpcoar:affiliationName":[{"@language":"en","@value":"Department of the Industrial and Management Systems Engineering, School of Science and Engineering, Waseda University"}]},{"@id":"https://cir.nii.ac.jp/crid/1580009752661495552","@type":"Researcher","personIdentifier":[{"@type":"NRID","@value":"9000004826843"}],"foaf:name":[{"@language":"en","@value":"GOTO Masayuki"}],"jpcoar:affiliationName":[{"@language":"en","@value":"Faculty of Environmental and Information Studies, Musashi Institute of 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Shigeichi"}],"jpcoar:affiliationName":[{"@language":"en","@value":"Department of the Industrial and Management Systems Engineering, School of Science and Engineering, Waseda University"}]}],"publication":{"publicationIdentifier":[{"@type":"ISSN","@value":"09168508"},{"@type":"NCID","@value":"AA10826239"}],"prism:publicationName":[{"@value":"IEICE transactions on fundamentals of electronics, communications and computer sciences"},{"@language":"en","@value":"IEICE Trans. on Fundamentals"}],"dc:publisher":[{"@value":"一般社団法人電子情報通信学会"},{"@language":"en","@value":"The Institute of Electronics, Information and Communication Engineers"}],"prism:publicationDate":"2006-12-01","prism:volume":"89","prism:number":"12","prism:startingPage":"3710","prism:endingPage":"3723"},"foaf:topic":[{"@id":"https://cir.nii.ac.jp/all?q=word-valued%20source","dc:title":"word-valued source"},{"@id":"https://cir.nii.ac.jp/all?q=word%20set","dc:title":"word set"},{"@id":"https://cir.nii.ac.jp/all?q=non-prefix-free","dc:title":"non-prefix-free"},{"@id":"https://cir.nii.ac.jp/all?q=entropy%20rate","dc:title":"entropy rate"},{"@id":"https://cir.nii.ac.jp/all?q=entropy%20density%20rate","dc:title":"entropy density rate"},{"@id":"https://cir.nii.ac.jp/all?q=Asymptotic%20Equipartition%20Property%20(AEP)","dc:title":"Asymptotic Equipartition Property (AEP)"},{"@id":"https://cir.nii.ac.jp/all?q=word-valued%20source","dc:title":"word-valued source"},{"@id":"https://cir.nii.ac.jp/all?q=word%20set","dc:title":"word set"},{"@id":"https://cir.nii.ac.jp/all?q=non-prefix-free","dc:title":"non-prefix-free"},{"@id":"https://cir.nii.ac.jp/all?q=entropy%20rate","dc:title":"entropy rate"},{"@id":"https://cir.nii.ac.jp/all?q=entropy%20density%20rate","dc:title":"entropy density rate"},{"@id":"https://cir.nii.ac.jp/all?q=Asymptotic%20Equipartition%20Property%20(AEP)","dc:title":"Asymptotic Equipartition Property (AEP)"}],"relatedProduct":[{"@id":"https://cir.nii.ac.jp/crid/1360855568899639808","@type":"Article","relationType":["cites"],"jpcoar:relatedTitle":[{"@value":"A class of distortionless codes designed by Bayes decision theory"}]},{"@id":"https://cir.nii.ac.jp/crid/1361137044589786624","@type":"Article","relationType":["cites"],"jpcoar:relatedTitle":[{"@value":"The Basic Theorems of Information Theory"}]},{"@id":"https://cir.nii.ac.jp/crid/1361418519963083648","@type":"Article","relationType":["cites"],"jpcoar:relatedTitle":[{"@value":"The Individual Ergodic Theorem of Information Theory"}]},{"@id":"https://cir.nii.ac.jp/crid/1362262944576221184","@type":"Article","relationType":["cites"],"jpcoar:relatedTitle":[{"@value":"Compression of individual sequences via variable-rate coding"}]},{"@id":"https://cir.nii.ac.jp/crid/1362825895528878720","@type":"Article","relationType":["cites"],"jpcoar:relatedTitle":[{"@value":"A universal algorithm for sequential data 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communication"}]},{"@id":"https://cir.nii.ac.jp/crid/1570572701765248384","@type":"Article","relationType":["cites"],"jpcoar:relatedTitle":[{"@language":"en","@value":"On the AEP of wordvalued sources"}]},{"@id":"https://cir.nii.ac.jp/crid/1571135652465560704","@type":"Article","relationType":["cites"],"jpcoar:relatedTitle":[{"@language":"en","@value":"A Source Model With Probability Distribution over Word Set and Recurrence Time Theorem"}]},{"@id":"https://cir.nii.ac.jp/crid/1571417125349495936","@type":"Article","relationType":["cites"]},{"@id":"https://cir.nii.ac.jp/crid/1572543025256338688","@type":"Article","relationType":["cites"],"jpcoar:relatedTitle":[{"@language":"en","@value":"Properties of a word-valued source with a non-prefix-free word 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