Channel polarization: a method for constructing capacity-achieving codes for symmetric binary-input memoryless channels

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dc.citation.epage3073en_US
dc.citation.issueNumber7en_US
dc.citation.spage3051en_US
dc.citation.volumeNumber55en_US
dc.contributor.authorArikan, E.en_US
dc.date.accessioned2016-02-08T10:03:32Z
dc.date.available2016-02-08T10:03:32Z
dc.date.issued2009en_US
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.description.abstractA method is proposed, called channel polarization, to construct code sequences that achieve the symmetric capacity I(W) of any given binary-input discrete memoryless channel (B-DMC) W. The symmetric capacity is the highest rate achievable subject to using the input letters of the channel with equal probability. Channel polarization refers to the fact that it is possible to synthesize, out of N independent copies of a given B-DMC W, a second set of N binary-input channels {WN (i): 1 ≤ i ≤ N} becomes large, the fraction of indices i for which I(WN (i) is near 1 approaches I(W) and the fraction for which I(WN (i) is near 0 approaches 1 - I(W). The polarized channels WN (i) are well-conditioned for channel coding: one need only send data at rate 1 through those with capacity near 1 and at rate 0 through the remaining. Codes constructed on the basis of this idea are called polar codes. The paper proves that, given any B-DMC W with I(W) and any target rate R < I(W), there exists a sequence of polar codes {Cn;n ≥ 1 such that Cn has block-length N = 2n, rate ≥ R, and probability of block error under successive cancellation decoding bounded as Pe (N, R) ≤ O(N-1/4 independently of the code rate. This performance is achievable by encoders and decoders with complexity O(N\log N) for each.en_US
dc.description.sponsorshipThe Scientific and Technological Research Council of Turkey (TÜBİTAK)en_US
dc.identifier.doi10.1109/TIT.2009.2021379en_US
dc.identifier.issn0018-9448
dc.identifier.urihttp://hdl.handle.net/11693/22693
dc.language.isoEnglishen_US
dc.publisherIEEEen_US
dc.relation.isversionofhttp://dx.doi.org/10.1109/TIT.2009.2021379en_US
dc.source.titleIEEE Transactions on Information Theoryen_US
dc.subjectCapacity-achieving codesen_US
dc.subjectChannel capacityen_US
dc.subjectChannel polarizationen_US
dc.subjectPlotkin constructionen_US
dc.subjectPolar codesen_US
dc.subjectReed-Muller (RM) codesen_US
dc.subjectSuccessive cancellation decodingen_US
dc.subjectCapacity-achieving codesen_US
dc.subjectChannel polarizationen_US
dc.subjectPlotkin constructionen_US
dc.subjectPolar codesen_US
dc.subjectReed-Muller (RM) codesen_US
dc.subjectSuccessive cancellation decodingen_US
dc.subjectBinary sequencesen_US
dc.subjectChannel codingen_US
dc.subjectDecodingen_US
dc.subjectPolarizationen_US
dc.subjectChannel capacityen_US
dc.titleChannel polarization: a method for constructing capacity-achieving codes for symmetric binary-input memoryless channelsen_US
dc.typeArticleen_US

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