On the Arikan Transformations of Binary-Input Discrete Memoryless Channels
Abstract
The polar codes introduced by Arikan in 2009 achieve the capacity of binary-input discrete memoryless channels (BIDMCs) with low complexity encoding and decoding. Identifying the unreliable synthetic channels, generated by Arikan transformation during the construction of these polar codes, is crucial. Currently, because of the large size of the output alphabets of synthetic channels, there is no efficient and practical approach to evaluate their reliability in general. To tackle this problem, by converting the generation of synthetic channels in polar code construction into algebraic operations, in this paper we develop a method to characterize the synthetic channels as random switching channels of binary symmetric channels when the underlying channels are symmetric. Moreover, a lower bound for the average number of elements that possess the same likelihood ratio within the output alphabet of any synthetic channel generated in polar codes is also derived.
Keywords
Cite
@article{arxiv.2510.22896,
title = {On the Arikan Transformations of Binary-Input Discrete Memoryless Channels},
author = {Yadong Jiao and Xiaoyan Cheng and Yuansheng Tang and Ming Xu},
journal= {arXiv preprint arXiv:2510.22896},
year = {2025}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2506.04163