# On the Common Randomness Capacity of a Special Class of Two-way Channels

## TL;DR

This paper investigates the capacity for two nodes to generate shared randomness over special intertwined two-way channels, providing bounds and constructive schemes for achieving this in complex communication settings.

## Contribution

It introduces new bounds and constructive schemes for common randomness capacity in intertwined two-way channels, extending understanding of their fundamental limits.

## Key findings

- Outer bound on CR capacity for intertwined receiver-decomposable channels
- Bound on auxiliary variable cardinality
- Outer bound matches Venkatesan-Anantharam CR capacity for certain settings

## Abstract

In this paper, we would like to study the common randomness (CR) capacity of intertwined two-way channels, namely those whose marginal channel transition probabilities depends also on the signal they transmit. We bring a few special settings and provide constructive schemes with which the two nodes can agree upon a common randomness. We then provide an outer bound on the CR capacity of intertwined receiver-decomposable (RD) two-way channel and will provide a bound on the cardinality of the available auxiliary variables. We will also show this outer bound is bounded above by Venkatesan-Anantharam CR capacity which makes it tight for decomposing two-way setting.