Polarization for arbitrary discrete memoryless channels

Date
2009
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Source Title
Proceedings of the 2009 IEEE Information Theory Workshop, ITW 2009
Print ISSN
Electronic ISSN
Publisher
IEEE
Volume
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Pages
144 - 148
Language
English
Type
Conference Paper
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Abstract

Channel polarization, originally proposed for binary-input channels, is generalized to arbitrary discrete memoryless channels. Specifically, it is shown that when the input alphabet size is a prime number, a similar construction to that for the binary case leads to polarization. This method can be extended to channels of composite input alphabet sizes by decomposing such channels into a set of channels with prime input alphabet sizes. It is also shown that all discrete memoryless channels can be polarized by randomized constructions. The introduction of randomness does not change the order of complexity of polar code construction, encoding, and decoding. A previous result on the error probability behavior of polar codes is also extended to the case of arbitrary discrete memoryless channels. The generalization of polarization to channels with arbitrary finite input alphabet sizes leads to polar-coding methods for approaching the true (as opposed to symmetric) channel capacity of arbitrary channels with discrete or continuous input alphabets.

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Keywords
Capacity-achieving codes, Channel polarization, Polar codes, Discrete memoryless channels, Error probabilities, Prime number, Communication channels (information theory)
Citation
Published Version (Please cite this version)