# Strong Coordination over Noisy Channels: Is Separation Sufficient?

## TL;DR

This paper investigates how two agents can achieve strong coordination over noisy channels, proposing two novel coding schemes and analyzing their effectiveness in terms of coordination capacity.

## Contribution

It introduces two new schemes for noisy strong coordination and derives inner bounds for the coordination capacity region, comparing their performance.

## Key findings

- Joint scheme reduces local randomness needed at agent Y.
- Separate scheme extracts randomness after decoding.
- Joint scheme can outperform separate scheme in certain scenarios.

## Abstract

We study the problem of strong coordination of actions of two agents $X$ and $Y$ that communicate over a noisy communication channel such that the actions follow a given joint probability distribution. We propose two novel schemes for this noisy strong coordination problem, and derive inner bounds for the underlying strong coordination capacity region. The first scheme is a joint coordination-channel coding scheme that utilizes the randomness provided by the communication channel to reduce the local randomness required in generating the action sequence at agent $Y$. The second scheme exploits separate coordination and channel coding where local randomness is extracted from the channel after decoding. Finally, we present an example in which the joint scheme is able to outperform the separate scheme in terms of coordination rate.