# Distributed compression through the lens of algorithmic information theory: a primer

## TL;DR

This paper introduces an accessible overview of a new approach to distributed data compression based on Algorithmic Information Theory, which applies to individual data strings without assuming a probabilistic model.

## Contribution

It presents a simplified, accessible explanation of an AIT-based analogue of the Slepian-Wolf theorem that works for individual data strings, not just stochastic models.

## Key findings

- The AIT version of the Slepian-Wolf theorem applies to individual strings.
- It requires knowledge of the complexity profile of input data.
- The approach does not rely on probabilistic assumptions.

## Abstract

Distributed compression is the task of compressing correlated data by several parties, each one possessing one piece of data and acting separately. The classical Slepian-Wolf theorem (D. Slepian, J. K. Wolf, IEEE Transactions on Inf. Theory, 1973) shows that if data is generated by independent draws from a joint distribution, that is by a memoryless stochastic process, then distributed compression can achieve the same compression rates as centralized compression when the parties act together. Recently, the author (M. Zimand, STOC 2017) has obtained an analogue version of the Slepian-Wolf theorem in the framework of Algorithmic Information Theory (also known as Kolmogorov complexity). The advantage over the classical theorem, is that the AIT version works for individual strings, without any assumption regarding the generative process. The only requirement is that the parties know the complexity profile of the input strings, which is a simple quantitative measure of the data correlation. The goal of this paper is to present in an accessible form that omits some technical details the main ideas from the reference (M. Zimand, STOC 2017).