NDLI: Multilevel Channel Polarization for Arbitrary Discrete Memoryless Channels

Content Provider	IEEE Xplore Digital Library
Author	Sahebi, A.G. Pradhan, S.S.
Copyright Year	1963
Abstract	It is shown that polar codes, with their original (u,u+v) kernel, achieve the symmetric capacity of discrete memoryless channels with arbitrary input alphabet sizes. It is shown that in general, channel polarization happens in several, rather than only two levels so that the synthesized channels are either useless, perfect or “partially perfect.” Any subset of the channel input alphabet which is closed under addition induces a coset partition of the alphabet through its shifts. For any such partition of the input alphabet, there exists a corresponding partially perfect channel whose outputs uniquely determine the coset to which the channel input belongs. By a slight modification of the encoding and decoding rules, it is shown that perfect transmission of certain information symbols over partially perfect channels is possible. Our result is general regarding both the cardinality and the algebraic structure of the channel input alphabet; i.e., we show that for any channel input alphabet size and any Abelian group structure on the alphabet, polar codes are optimal. Due to the modifications, we make to the encoding rule of polar codes, the constructed codes fall into a larger class of structured codes called nested group codes.
Sponsorship	IEEE Information Theory Society
Starting Page	7839
Ending Page	7857
Page Count	19
File Size	7570481
File Format	PDF
ISSN	00189448
Volume Number	59
Issue Number	12
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2013-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Channel capacity Encoding Memoryless systems Decoding Indexes Kernel Standards polar codes Channel polarization discrete memoryless channels group codes
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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