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arXiv · 1512.08050

Large deviation, Basic Information Theory for Wireless Sensor Networks

Kwabena Doku-Amponsah
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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.

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Kwabena Doku-Amponsah. 2015-12-25. Large deviation, Basic Information Theory for Wireless Sensor Networks. https://doi.org/10.3844/jmssp.2017.325.329

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