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dc.contributor.author
Renes, Joseph M.
dc.date.accessioned
2021-01-11T08:44:38Z
dc.date.available
2018-09-24T11:54:25Z
dc.date.available
2020-10-02T09:42:20Z
dc.date.available
2021-01-11T08:44:38Z
dc.date.issued
2017
dc.identifier.isbn
978-1-5090-4096-4
en_US
dc.identifier.isbn
978-1-5090-4097-1
en_US
dc.identifier.other
10.1109/ISIT.2017.8006598
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/291287
dc.description.abstract
For any given channel W with classical inputs and possibly quantum outputs, a dual classical-input channel W ⊥ can be defined by embedding the original into a channel N with quantum inputs and outputs. Here we give new uncertainty relations for a general class of entropies that lead to very close relationships between the original channel and its dual. Moreover, we show that channel duality can be combined with duality of linear codes, whereupon the uncertainty relations imply that the performance of a given code over a given channel is entirely characterized by the performance of the dual code on the dual channel. This has several applications. In the context of polar codes, it implies that the rates of polarization to ideal and useless channels must be identical. Duality also relates the tasks of channel coding and privacy amplification, implying that the finite blocklength performance of extractors and codes is precisely linked, and that optimal rate extractors can be transformed into capacity-achieving codes, and vice versa. Finally, duality also extends to the EXIT function of any channel and code. Here it implies that for any channel family, if the EXIT function for a fixed code has a sharp transition, then it must be such that the rate of the code equals the capacity at the transition. This may give a different route to proving a code family achieves capacity by establishing EXIT function transitions.
en_US
dc.language.iso
en
en_US
dc.publisher
IEEE
en_US
dc.title
Duality of channels and codes
en_US
dc.type
Conference Paper
dc.date.published
2017-08-15
ethz.book.title
2017 IEEE International Symposium on Information Theory (ISIT)
en_US
ethz.pages.start
599
en_US
ethz.pages.end
603
en_US
ethz.event
2017 IEEE International Symposium on Information Theory (ISIT 2017)
en_US
ethz.event.location
Aachen, Germany
en_US
ethz.event.date
June 25-30, 2017
en_US
ethz.identifier.wos
ethz.identifier.scopus
ethz.publication.place
Piscataway, NJ
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02010 - Dep. Physik / Dep. of Physics::02511 - Institut für Theoretische Physik / Institute for Theoretical Physics::03781 - Renner, Renato / Renner, Renato
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02010 - Dep. Physik / Dep. of Physics::02511 - Institut für Theoretische Physik / Institute for Theoretical Physics::03781 - Renner, Renato / Renner, Renato
ethz.date.deposited
2017-12-05T05:27:40Z
ethz.source
SCOPUS
ethz.source
WOS
ethz.eth
yes
en_US
ethz.availability
Metadata only
en_US
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ethz.rosetta.installDate
2018-09-24T11:54:28Z
ethz.rosetta.lastUpdated
2021-02-15T23:04:37Z
ethz.rosetta.exportRequired
true
ethz.rosetta.versionExported
true
dc.identifier.olduri
http://hdl.handle.net/20.500.11850/216996
dc.identifier.olduri
http://hdl.handle.net/20.500.11850/263480
ethz.COinS
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