Large deviation, Basic Information Theory for Wireless Sensor Networks

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.

5 pages

References in corpus (1)

• Asymptotic Equipartition Properties for simple hierarchical and networked structures