# Renyi partial orders for BISO channels

## TL;DR

This paper extends the understanding of partial orders in information theory by analyzing Renyi mutual information for BISO channels, establishing extremality of BSC and BEC with respect to generalized Renyi capacity.

## Contribution

It introduces Renyi partial orders for BISO channels and proves the extremality of BSC and BEC in this new setting, generalizing previous results.

## Key findings

- BSC and BEC are extremal in Renyi partial orders for BISO channels.
- Introduction of $\\alpha$-Lorenz curves as a new analytical tool.
- Generalization of capacity comparison tools to Renyi mutual information.

## Abstract

A fundamental question in information theory is to quantify the loss of information under a noisy channel. Partial orders are typical tools to that end, however, they are often also challenging to evaluate. For the special class of binary input symmetric output (BISO) channels, Geng et al. showed that among channels with the same capacity, the binary symmetric channel (BSC) and binary erasure channel (BEC) are extremal with respect to the more capable order. Here we extend on this result by considering partial orders based on Renyi mutual information. We establish the extremality of the BSC and BEC in this setting with respect to the generalized Renyi capacity. In the process, we also generalize the needed tools and introduce $\alpha$-Lorenz curves.