Asymptotic Distribution of Multilevel Channel Polarization for a Certain Class of Erasure Channels

TL;DR

This paper analyzes the asymptotic behavior of multilevel channel polarization in erasure channels with composite input alphabet sizes, deriving limiting proportions of noiseless channels through a sequence convergence approach.

Contribution

It introduces a new proof technique for polarization limits in channels with composite alphabet sizes, avoiding martingale convergence theorems.

Findings

Derived limiting proportions of partially noiseless channels

Extended polarization analysis to channels with arbitrary composite input sizes

Provided a convergent sequence-based proof method

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.