Large deviation, Basic Information Theory for Wireless Sensor Networks

TL;DR

This paper establishes a large deviation principle and Shannon-MacMillan-Breiman theorem for wireless sensor networks modeled as coloured geometric random graphs, providing explicit entropy-based coding limits.

Contribution

It introduces a large deviation principle and entropy-based coding bounds for wireless sensor networks modeled as coloured geometric random graphs.

Findings

Derived a joint large deviation principle for empirical measures.

Established a coding theorem with explicit entropy bounds.

Connected geometric graph models with information theory concepts.

Abstract

In this article, we prove Shannon-MacMillan-Breiman Theorem for Wireless Sensor Networks modelled as coloured geometric random graphs. For large $n,$ we show that a Wireless Sensor Network consisting of $n$ sensors in $[0,1]^d$ connected by an average number of links of order $n\log n $ can be coded by about $[n(\log n )^2\pi^{d/2}/(d/2)!]\,\mathcal{H}$ bits, where $\mathcal{H}$ is an explicitly defined entropy. In the process, we derive a joint large deviation principle (LDP) for the \emph{empirical sensor measure} and \emph{the empirical link measure} of coloured random geometric graph models.