PERCOLATION ON THE INFORMATION-THEORETICALLY SECURE SIGNAL TO INTERFERENCE RATIO GRAPH

Vaze, Rahul and Iyer, Srikanth (2015) PERCOLATION ON THE INFORMATION-THEORETICALLY SECURE SIGNAL TO INTERFERENCE RATIO GRAPH. In: JOURNAL OF APPLIED PROBABILITY, 51 (4). pp. 910-920.

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Abstract

We consider a continuum percolation model consisting of two types of nodes, namely legitimate and eavesdropper nodes, distributed according to independent Poisson point processes in R-2 of intensities lambda and lambda(E), respectively. A directed edge from one legitimate node A to another legitimate node B exists provided that the strength of the signal transmitted from node A that is received at node B is higher than that received at any eavesdropper node. The strength of the signal received at a node from a legitimate node depends not only on the distance between these nodes, but also on the location of the other legitimate nodes and an interference suppression parameter gamma. The graph is said to percolate when there exists an infinitely connected component. We show that for any finite intensity lambda(E) of eavesdropper nodes, there exists a critical intensity lambda(c) < infinity such that for all lambda > lambda(c) the graph percolates for sufficiently small values of the interference parameter. Furthermore, for the subcritical regime, we show that there exists a lambda(0) such that for all lambda < lambda(0) <= lambda(c) a suitable graph defined over eavesdropper node connections percolates that precludes percolation in the graphs formed by the legitimate nodes.

Item Type:	Journal Article
Publication:	JOURNAL OF APPLIED PROBABILITY
Publisher:	APPLIED PROBABILITY TRUST
Additional Information:	Copy right for this article belongs to the APPLIED PROBABILITY TRUST, THE UNIVERSITY, SCHOOL MATHEMATICS STATISTICS, SHEFFIELD S3 7RH, ENGLAND
Keywords:	Percolation; information-theoretic security; wireless communication; SINR graph
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	26 Jun 2015 05:10
Last Modified:	26 Jun 2015 05:10
URI:	http://eprints.iisc.ac.in/id/eprint/51748

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