Polarization for arbitrary discrete memoryless channels
2009 IEEE Information Theory Workshop, ITW 2009
144 - 148
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Please cite this item using this persistent URLhttp://hdl.handle.net/11693/28616
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. © 2009 IEEE.
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Channel polarization : a method for constructing capacity - achieving codes for symmetric binary-input memoryless channels Arikan, E. (IEEE, 2009)A 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 ...
Arikan, E. (2010)The notion of source polarization is introduced and investigated. This complements the earlier work on channel polarization. An application to Slepian-Wolf coding is also considered. The paper is restricted to the case of ...
Arikan, E.; Ul Hassan, N.; Lentmaier, M.; Montorsi, G.; Sayir, J. (Korean Institute of Communication Sciences, 2015)Three areas of ongoing research in channel coding are surveyed, and recent developments are presented in each area: Spatially coupled low-density parity-check (LDPC) codes, nonbinary LDPC codes, and polar coding.