Universal Polarization

TL;DR

This paper introduces a universal channel polarization method that combines distinct channels to create polarized channels, ensuring universality and enabling the construction of codes with arbitrary rates.

Contribution

A novel universal polarization technique that differs from Arikan's method by combining distinct channels, preserving channel ordering, and allowing arbitrary rate code construction.

Findings

Creates polarized channels with locations independent of the underlying channel.

Ensures good polar codes perform well over less noisy channels.

Generalizes to construct codes of any rate.

Abstract

A method to polarize channels universally is introduced. The method is based on combining two distinct channels in each polarization step, as opposed to Arikan's original method of combining identical channels. This creates an equal number of only two types of channels, one of which becomes progressively better as the other becomes worse. The locations of the good polarized channels are independent of the underlying channel, guaranteeing universality. Polarizing the good channels further with Arikan's method results in universal polar codes of rate 1/2. The method is generalized to construct codes of arbitrary rates. It is also shown that the less noisy ordering of channels is preserved under polarization, and thus a good polar code for a given channel will perform well over a less noisy one.