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

摘要

This study examines multilevel channel polarization for a certain class oferasure channels that the input alphabet size is an arbitrary composite number.We derive limiting proportions of partially noiseless channels for such aclass. The results of this study are proved by an argument of convergentsequences, inspired by Alsan and Telatar's simple proof of polarization, andwithout martingale convergence theorems for polarization process.