Computer Science > Information Theory
[Submitted on 23 Apr 2018 (v1), last revised 4 May 2020 (this version, v2)]
Title:Modular Arithmetic Erasure Channels and Their Multilevel Channel Polarization
View PDFAbstract:This study proposes \emph{modular arithmetic erasure channels} (MAECs), a novel class of erasure-like channels with an input alphabet that need not be binary. This class contains the binary erasure channel (BEC) and some other known erasure-like channels as special cases. For MAECs, we provide recursive formulas of Arıkan-like polar transform to simulate channel polarization. In other words, we show that the synthetic channels of MAECs are equivalent to other MAECs. This is a generalization of well-known recursive formulas of the polar transform for BECs. Using our recursive formulas, we also show that a recursive application of the polar transform for MAECs results in \emph{multilevel channel polarization,} which is an asymptotic phenomenon that is characteristic of non-binary polar codes. Specifically, we establish a method to calculate the limiting proportions of the partially noiseless and noisy channels that are generated as a result of multilevel channel polarization for MAECs. In the particular case of MAECs, this calculation method solves an open problem posed by Nasser (2017) in the study of non-binary polar codes.
Submission history
From: Yuta Sakai [view email][v1] Mon, 23 Apr 2018 06:27:22 UTC (145 KB)
[v2] Mon, 4 May 2020 13:14:25 UTC (144 KB)
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