# Communication for Generating Correlation: A Unifying Survey

## TL;DR

This survey reviews recent progress on using minimal communication to manipulate and generate correlated random variables in distributed systems, highlighting theoretical limits and practical implications.

## Contribution

It provides a comprehensive overview of measures, achievability results, and performance limits in the manipulation of correlated randomness through communication.

## Key findings

- Shared correlations can be converted into perfect shared randomness with minimal communication.
- Perfect shared randomness enables solutions to various distributed tasks.
- The survey identifies key open problems and future research directions.

## Abstract

The task of manipulating correlated random variables in a distributed setting has received attention in the fields of both Information Theory and Computer Science. Often shared correlations can be converted, using a little amount of communication, into perfectly shared uniform random variables. Such perfect shared randomness, in turn, enables the solutions of many tasks. Even the reverse conversion of perfectly shared uniform randomness into variables with a desired form of correlation turns out to be insightful and technically useful. In this survey article, we describe progress-to-date on such problems and lay out pertinent measures, achievability results, limits of performance, and point to new directions.