Complex Analysis of Channel Polarization on Discrete BMS Channels
Abstract
We develop component evolution (CE), a framework based on complex function theory for finite-blocklength channel polarization on discrete binary-input memoryless output-symmetric (BMS) channels. In this view, the Bhattacharyya parameter is treated as a real-valued instance of a broader class of complex-valued channel functionals. CE systematically derives analytic expressions for the Bhattacharyya parameters of the bit-channels of a given discrete BMS channel at arbitrary polarization levels. CE also enables structural analysis, providing new evidence of extremality of the binary erasure channel (BEC) and binary symmetric channel (BSC), and revealing new channel-dependent recursions for a class of BSC bit-channels.
Keywords
Cite
@article{arxiv.2605.03805,
title = {Complex Analysis of Channel Polarization on Discrete BMS Channels},
author = {Dongxiao Xu and Moritz Wiese and Holger Boche},
journal= {arXiv preprint arXiv:2605.03805},
year = {2026}
}
Comments
Submitted to IEEE Information Theory Workshop 2026