Polarization for arbitrary discrete memoryless channels

By Eren Sasoglu, Emre Telatar, E. Arıkan. 2009 IEEE Information Theory Workshop, 2009

343 citations recorded by the source corpus.

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.

Subfields: Computer Networks and Communications, Electrical and Electronic Engineering, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/fbdc62edeec99dee304713671fb66633d6484769

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Citations in the corpus

Source polarization (2010, background): “Pick the patternUEX|Y at random from the uniform distribution and make it available to the decoder ahead of the session.”
A Simplified Successive-Cancellation Decoder for Polar Codes (2011, methodology): “Let A ⊂ [2] be the information set of a given polar code.”
A Semi-Parallel Successive-Cancellation Decoder for Polar Codes (2013, positive): “Later works proved that polar codes achieve the channel capacity for any discrete memoryless channel and, by extension, for any continuous memoryless channel [5].”