Asymptotic Distribution of Multilevel Channel Polarization for a Certain Class of Erasure Channels
Information Theory
2020-08-24 v1 math.IT
Abstract
This study examines multilevel channel polarization for a certain class of erasure channels that the input alphabet size is an arbitrary composite number. We derive limiting proportions of partially noiseless channels for such a class. The results of this study are proved by an argument of convergent sequences, inspired by Alsan and Telatar's simple proof of polarization, and without martingale convergence theorems for polarization process.
Keywords
Cite
@article{arxiv.1801.04422,
title = {Asymptotic Distribution of Multilevel Channel Polarization for a Certain Class of Erasure Channels},
author = {Yuta Sakai and Ken-ichi Iwata and Hiroshi Fujisaki},
journal= {arXiv preprint arXiv:1801.04422},
year = {2020}
}
Comments
31 pages; 1 figure; 1 table; a short version of this paper has been submitted to the 2018 IEEE International Symposium on Information Theory (ISIT2018)