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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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 59; no. 12; pp. 7829 - 7838
Main Authors: Honda, Junya, Yamamoto, Hirosuke
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.12.2013
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
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)
Alphabet
Channel capacity
Error probability
Source coding
Asymmetric channels
lossy source coding
Lossless compression
Lossy medium
Decoding
Polar code
polar codes
Channel coding
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary: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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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2013.2282305