Varentropy decreases under the polar transform

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dc.citation.epage3400en_US
dc.citation.issueNumber6en_US
dc.citation.spage3390en_US
dc.citation.volumeNumber62en_US
dc.contributor.authorArıkan, E.en_US
dc.date.accessioned2018-04-12T10:42:29Z
dc.date.available2018-04-12T10:42:29Z
dc.date.issued2016en_US
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.description.abstractWe consider the evolution of variance of entropy (varentropy) in the course of a polar transform operation on binary data elements (BDEs). A BDE is a pair (X,Y) consisting of a binary random variable X and an arbitrary side information random variable Y. The varentropy of (X,Y) is defined as the variance of the random variable-log pX|Y(X|Y). A polar transform of order two is a certain mapping that takes two independent BDEs and produces two new BDEs that are correlated with each other. It is shown that the sum of the varentropies at the output of the polar transform is less than or equal to the sum of the varentropies at the input, with equality if and only if at least one of the inputs has zero varentropy. This result is extended to polar transforms of higher orders and it is shown that the varentropy asymptotically decreases to zero when the BDEs at the input are independent and identically distributed.en_US
dc.identifier.doi10.1109/TIT.2016.2555841en_US
dc.identifier.issn0018-9448
dc.identifier.urihttp://hdl.handle.net/11693/36501
dc.language.isoEnglishen_US
dc.publisherInstitute of Electrical and Electronics Engineers Inc.en_US
dc.relation.isversionofhttp://dx.doi.org/10.1109/TIT.2016.2555841en_US
dc.source.titleIEEE Transactions on Information Theoryen_US
dc.subjectDispersionen_US
dc.subjectPolar codingen_US
dc.subjectVarentropyen_US
dc.titleVarentropy decreases under the polar transformen_US
dc.typeArticleen_US
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