# Empirical Coordination Subject to a Fidelity Criterion

## TL;DR

This paper investigates empirical coordination under a fidelity constraint, establishing a connection with existing frameworks and showing that near-desired distributions can be achieved with codes producing actions of similar joint types.

## Contribution

It introduces a new approach linking empirical coordination with fidelity criteria, simplifying code design by focusing on actions with similar joint types.

## Key findings

- Codes achieving empirical coordination can be designed using joint types close to the target distribution.
- A strong connection between the new framework and previous empirical coordination models is established.
- Achieving the desired distribution within a fidelity criterion is feasible with type-based coding strategies.

## Abstract

We study the problem of empirical coordination subject to a fidelity criterion for a general set-up. We prove a result which indicates a strong connection between our framework and the framework of empirical coordination developed in [1]. It turns out that when we design codes that achieve empirical coordination according to a given distribution and subject to the fidelity criterion, it is sufficient to consider codes that produce actions of the same joint type for a class of types which is close enough to our desired distribution is some sense.