Differential entropy of the conditional expectation under additive gaussian voise

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buir.contributor.authorAtalik, Arda
buir.contributor.orcidAtalik, Arda | 0000-0003-3439-7838
dc.citation.epage4866en_US
dc.citation.spage4851en_US
dc.citation.volumeNumber70en_US
dc.contributor.authorAtalik, Arda
dc.contributor.authorKöse, Alper
dc.contributor.authorGastpar, Michael
dc.date.accessioned2023-03-02T15:02:21Z
dc.date.available2023-03-02T15:02:21Z
dc.date.issued2022
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.description.abstractThe conditional mean is a fundamental and important quantity whose applications include the theories of estimation and rate-distortion. It is also notoriously difficult to work with. This paper establishes novel bounds on the differential entropy of the conditional mean in the case of finite-variance input signals and additive Gaussian noise. The main result is a new lower bound in terms of the differential entropies of the input signal and the noisy observation. The main results are also extended to the vector Gaussian channel and to the natural exponential family. Various other properties such as upper bounds, asymptotics, Taylor series expansion, and connection to Fisher Information are obtained. Two applications of the lower bound in the remote-source coding and CEO problem are discussed.en_US
dc.identifier.doi10.1109/TSP.2022.3211403
dc.identifier.urihttp://hdl.handle.net/11693/112036
dc.language.isoEnglishen_US
dc.publisherInstitute of Electrical and Electronics Engineersen_US
dc.relation.isversionofhttps://www.doi.org/10.1109/TSP.2022.3211403
dc.source.titleIEEE Transactions on Signal Processingen_US
dc.subjectDifferential entropyen_US
dc.subjectConditional mean estimatoren_US
dc.subjectGaussian noiseen_US
dc.subjectExponential familyen_US
dc.subjectRemote source coding problemen_US
dc.subjectCEO problemen_US
dc.titleDifferential entropy of the conditional expectation under additive gaussian voiseen_US
dc.typeArticleen_US

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