Entropy and Distributed Source Coding of Connected Soft Random Geometric Graphs

TL;DR

This paper characterizes the distributed compression limits of Soft Random Geometric Graphs (SRGGs) using new theoretical results on their entropy and limit theorems.

Contribution

It establishes the Slepian-Wolf rate region for SRGGs and introduces novel limit theorems and asymptotic properties for these graphs.

Findings

Derived the Slepian-Wolf rate region for SRGGs.

Proved new limit theorems and asymptotic equipartition properties.

Enabled distributed compression of SRGGs using random binning.

Abstract

We consider the distributed compression of Soft Random Geometric Graphs (SRGGs) above the connectivity threshold. We establish the Slepian-Wolf rate region for the SRGG in the setting where there are a finite number of encoders compressing sections of the graph independently. To do so, we prove novel limit theorems and asymptotic equipartition properties for the SRGG and its entropy, which allow us to use random binning techniques for distributed compression.