# Coding Theorems for Asynchronous Slepian-Wolf Coding Systems

## TL;DR

This paper extends the Slepian-Wolf coding framework to asynchronous systems with unknown delays, characterizing the achievable rate region under these conditions and highlighting differences from the synchronous case.

## Contribution

It introduces a new achievable rate region for asynchronous Slepian-Wolf coding with unknown delays and unknown source distributions within a known set.

## Key findings

- Achievable rate region differs from the synchronous case.
- Delays impact the coding rate requirements.
- System can handle unknown source distributions within a specified set.

## Abstract

The Slepian-Wolf (SW) coding system is a source coding system with two encoders and a decoder, where these encoders independently encode source sequences from two correlated sources into codewords, and the decoder reconstructs both source sequences from the codewords. In this paper, we consider the situation in which the SW coding system is asynchronous, i.e., each encoder samples a source sequence with some unknown delay. We assume that delays are unknown but maximum and minimum values of possible delays are known to encoders and the decoder. We also assume that sources are discrete stationary memoryless and the probability mass function (PMF) of the sources is unknown but the system knows that it belongs to a certain set of PMFs. For this asynchronous SW coding system, we clarify the achievable rate region which is the set of rate pairs of encoders such that the decoding error probability vanishes as the blocklength tends to infinity. We show that this region does not always coincide with that of the synchronous SW coding system in which each encoder samples a source sequence without any delay.

---
Source: https://tomesphere.com/paper/1906.02929