# On the Polarization of R\'{e}nyi Entropy

## TL;DR

This paper extends polarization theory to Rényi entropy, revealing that sub-channel extremal states can differ under various orders, providing deeper micro-scale insights into polarization phenomena.

## Contribution

It introduces polarization analysis based on Rényi entropy, showing that sub-channel extremal states can vary with entropy order, unlike traditional Shannon-based theories.

## Key findings

- Sub-channels can have opposite extremal states under different Rényi entropy orders.
- Polarization phenomena can be analyzed at the micro scale, focusing on probability pairs.
- The theory broadens understanding of information measures beyond Shannon entropy.

## Abstract

Existing polarization theories have mostly been concerned with Shannon's information measures, such as Shannon entropy and mutual information, and some related measures such as the Bhattacharyya parameter. In this work, we extend polarization theories to a more general information measure, namely, the R\'{e}nyi entropy. Our study shows that under conditional R\'{e}nyi entropies of different orders, the same synthetic sub-channel may exhibit opposite extremal states. This result reveals more insights into the polarization phenomenon on the micro scale (probability pairs) rather than on the average scale.