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ISSN: 1549-3644 (Print)
ISSN: 1558-6359 (Online)
Research Article Open Access

Large Deviation, Basic Information Theory for Wireless Sensor Networks

Kwabena Doku-Amponsah1
  • 1 School of Physical and Mathematical Sciences, Ghana

Abstract

In this research paper, we establish Shannon-McMillan-Breiman Theorem for Wireless Sensor Networks modelled as Coloured Geometric Random Networks. For, large n we show that a Wireless Sensor Network consisting of n sensors in [0; 1]d linked by an expected number of edges of order n log n can be transmitted by approximately [n(log n)2 πd/2/(d/2)!] H bits, where H is an entropy defined explicitly from the parameters of the Coloured Geometric Random Network. In the process, we derive a joint Large Deviation Principle (LDP) for the empirical sensor measure and the empirical link measure of coloured random geometric network models.

Journal of Mathematics and Statistics
Volume 13 No. 4, 2017, 325-329

DOI: https://doi.org/10.3844/jmssp.2017.325.329

Submitted On: 19 February 2017 Published On: 20 October 2017

How to Cite: Doku-Amponsah, K. (2017). Large Deviation, Basic Information Theory for Wireless Sensor Networks. Journal of Mathematics and Statistics, 13(4), 325-329. https://doi.org/10.3844/jmssp.2017.325.329

Open AccessCopyright: © 2017 Kwabena Doku-Amponsah. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • Shannon-McMillian-Breiman Theorem
  • Joint Large Deviation Principle
  • Coloured Geometric Random Graph
  • Empirical Sensor Measure
  • Empirical Link Measure
  • Wireless Sensor Networks
  • Sensor Law
  • Near Entropy
  • Relative Entropy Sensor Graph
  • Mathematics Subject Classification: 94A15, 94A24, 60F10, 05C80