Polar Coding Without Alphabet Extension for Asymmetric Models
This paper considers polar coding for asymmetric settings, that is, channel coding for asymmetric channels and lossy source coding for nonuniform sources and/or asymmetric distortion measures. The difficulty for asymmetric settings comes from the fact that the optimal symbol distributions of codewor...
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| Veröffentlicht in: | IEEE transactions on information theory Jg. 59; H. 12; S. 7829 - 7838 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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New York, NY
IEEE
01.12.2013
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 0018-9448, 1557-9654 |
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| Abstract | This paper considers polar coding for asymmetric settings, that is, channel coding for asymmetric channels and lossy source coding for nonuniform sources and/or asymmetric distortion measures. The difficulty for asymmetric settings comes from the fact that the optimal symbol distributions of codewords are not always uniform. It is known that such nonuniform distributions can be realized by Gallager's scheme which maps multiple auxiliary symbols distributed uniformly to an actual symbol. However, the complexity of Gallager's scheme increases considerably for the case that the optimal distribution cannot be approximated by simple rational numbers. To overcome this problem for the asymmetric settings, a new polar coding scheme is proposed, which can attain the channel capacity without any alphabet extension by invoking results on polar coding for lossless compression. It is also shown that the proposed scheme achieves a better tradeoff between complexity and decoding error probability in many cases. |
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| AbstractList | This paper considers polar coding for asymmetric settings, that is, channel coding for asymmetric channels and lossy source coding for nonuniform sources and/or asymmetric distortion measures. The difficulty for asymmetric settings comes from the fact that the optimal symbol distributions of codewords are not always uniform. It is known that such nonuniform distributions can be realized by Gallager's scheme which maps multiple auxiliary symbols distributed uniformly to an actual symbol. However, the complexity of Gallager's scheme increases considerably for the case that the optimal distribution cannot be approximated by simple rational numbers. To overcome this problem for the asymmetric settings, a new polar coding scheme is proposed, which can attain the channel capacity without any alphabet extension by invoking results on polar coding for lossless compression. It is also shown that the proposed scheme achieves a better tradeoff between complexity and decoding error probability in many cases. This paper considers polar coding for asymmetric settings, that is, channel coding for asymmetric channels and lossy source coding for nonuniform sources and/or asymmetric distortion measures. The difficulty for asymmetric settings comes from the fact that the optimal symbol distributions of codewords are not always uniform. It is known that such nonuniform distributions can be realized by Gallager's scheme which maps multiple auxiliary symbols distributed uniformly to an actual symbol. However, the complexity of Gallager's scheme increases considerably for the case that the optimal distribution cannot be approximated by simple rational numbers. To overcome this problem for the asymmetric settings, a new polar coding scheme is proposed, which can attain the channel capacity without any alphabet extension by invoking results on polar coding for lossless compression. It is also shown that the proposed scheme achieves a better tradeoff between complexity and decoding error probability in many cases. [PUBLICATION ABSTRACT] |
| Author | Honda, Junya Yamamoto, Hirosuke |
| Author_xml | – sequence: 1 givenname: Junya surname: Honda fullname: Honda, Junya email: honda@it.k.u-tokyo.ac.jp organization: Dept. of Complexity Sci. & Eng., Univ. of Tokyo, Kashiwa, Japan – sequence: 2 givenname: Hirosuke surname: Yamamoto fullname: Yamamoto, Hirosuke email: Hirosuke@ieee.org organization: Dept. of Complexity Sci. & Eng., Univ. of Tokyo, Kashiwa, Japan |
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| Keywords | Alphabet Channel capacity Error probability Source coding Asymmetric channels lossy source coding Lossless compression Lossy medium Decoding Polar code polar codes Channel coding |
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| References | ref13 ref12 ref15 ref14 arikan (ref1) 2009; 55 arikan (ref11) 2009 korada (ref6) 2009 ref22 ref21 ref17 ref16 ref19 mori (ref20) 0 ref18 ref8 gallager (ref7) 1968 mori (ref2) 2010 ref9 ref4 cover (ref23) 2006 ref3 ref5 tal (ref10) 2011 |
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| SubjectTerms | Applied sciences Approximation Asymmetric channels Channel coding Codes Coding, codes Complexity theory Decoding Error probability Exact sciences and technology Information theory Information, signal and communications theory Integrated circuits lossy source coding polar codes Probability distribution Signal and communications theory Source coding Systems, networks and services of telecommunications Telecommunications Telecommunications and information theory Transmission and modulation (techniques and equipments) |
| Title | Polar Coding Without Alphabet Extension for Asymmetric Models |
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