On the Polarization of Rényi Entropy.

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 Renyi entropy. Our study shows that under conditional Renyi 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 (entropy, mutual information, etc.).