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On the information dimension rate of stochastic processes

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dc.affiliation.dptoUC3M. Departamento de Teoría de la Señal y Comunicacioneses
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Tratamiento de la Señal y Aprendizaje (GTSA)es
dc.contributor.authorGeiger, Bernhard C.
dc.contributor.authorKoch, Tobias Mirco
dc.date.accessioned2018-02-13T09:23:56Z
dc.date.available2018-02-13T09:23:56Z
dc.date.issued2017-08-15
dc.descriptionProceeding of: 2017 IEEE International Symposium on Information Theory, Aachen, Germany, 25-30 June 2017en
dc.description.abstractJalali and Poor ("Universal compressed sensing," arXiv:1406.7807v3, Jan. 2016) have recently proposed a generalization of Rényi's information dimension to stationary stochastic processes by defining the information dimension of the stochastic process as the information dimension of k samples divided by k in the limit as k →∞ to. This paper proposes an alternative definition of information dimension as the entropy rate of the uniformly-quantized stochastic process divided by minus the logarithm of the quantizer step size 1/m in the limit as m →∞ ; to. It is demonstrated that both definitions are equivalent for stochastic processes that are ψ*-mixing, but that they may differ in general. In particular, it is shown that for Gaussian processes with essentially-bounded power spectral density (PSD), the proposed information dimension equals the Lebesgue measure of the PSD's support. This is in stark contrast to the information dimension proposed by Jalali and Poor, which is 1 if the process's PSD is positive on a set of positive Lebesgue measure, irrespective of its support size.es
dc.description.sponsorshipThe work of Bernhard C. Geiger has been funded by the Erwin Schrödinger Fellowship J 3765 of the Austrian Science Fund and by the German Ministry of Education and Research in the framework of an Alexander von Humboldt Professorship. The work of Tobias Koch has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement number 714161), from the 7th European Union Framework Programme under Grant 333680, from the Spanish Ministerio de Economía y Competitividad under Grants TEC2013- 41718-R, RYC-2014-16332 and TEC2016-78434-C3-3-R (AEI/FEDER, EU), and from the Comunidad de Madrid under Grant S2103/ICE-2845.es
dc.format.extent5es
dc.format.mimetypeapplication/pdf
dc.identifier.bibliographicCitation2017 IEEE International Symposium on Information Theory [Proceedings], pp. 888-892es
dc.identifier.doihttps://doi.org/10.1109/ISIT.2017.8006656
dc.identifier.isbn978-1-5090-4096-4
dc.identifier.publicationfirstpage888es
dc.identifier.publicationlastpage892es
dc.identifier.publicationtitle2017 IEEE International Symposium on Information Theory [Proceedings]es
dc.identifier.urihttps://hdl.handle.net/10016/26234
dc.identifier.uxxiCC/0000027313
dc.language.isoenges
dc.publisherIEEEes
dc.relation.eventdate2017-06-25es
dc.relation.eventplaceAachen, Alemaniaes
dc.relation.eventtitle2017 IEEE International Symposium on Information Theoryes
dc.relation.ispartofhttp://hdl.handle.net/10016/28825
dc.relation.projectIDinfo:eu-repo/grantAgreement/EC/H2020/714161es
dc.relation.projectIDinfo:eu-repo/grantAgreement/EC/FP7/333680es
dc.relation.projectIDGobierno de España. TEC2013-41718-Res
dc.relation.projectIDGobierno de España. RYC-2014-16332es
dc.relation.projectIDGobierno de España. TEC2016-78434-C3-3-R (AEI/FEDER, EU)es
dc.relation.projectIDComunidad de Madrid. S2103/ICE-2845/CASI-CAMes
dc.rights© 2017 IEEEes
dc.rights.accessRightsopen accesses
dc.subject.ecienciaElectrónicaes
dc.subject.ecienciaTelecomunicacioneses
dc.subject.otherEntropyes
dc.subject.otherRate-distortiones
dc.subject.otherGaussian processeses
dc.subject.otherCompressed sensinges
dc.subject.otherEncodinges
dc.titleOn the information dimension rate of stochastic processeses
dc.typeconference paper*
dc.type.hasVersionAM*
dspace.entity.typePublication
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