Super Critical and Sub Critical Regimes of Percolation with Secure Communication

TL;DR

This paper analyzes percolation thresholds in secure communication networks modeled by Poisson point processes, deriving bounds on legitimate node density needed for connectivity amid eavesdroppers, for both path-loss and fading scenarios.

Contribution

It provides universal lower bounds on the legitimate node density for secure percolation, independent of eavesdropper density, in both path-loss and fading models.

Findings

Derived bounds on legitimate node density for percolation

Universal lower bounds independent of eavesdropper density

Applicable to both path-loss and fading models

Abstract

Percolation in an information-theoretically secure graph is considered where both the legitimate and the eavesdropper nodes are distributed as Poisson point processes. For both the path-loss and the path-loss plus fading model, upper and lower bounds on the minimum density of the legitimate nodes (as a function of the density of the eavesdropper nodes) required for non-zero probability of having an unbounded cluster are derived. The lower bound is universal in nature, i.e. the constant does not depend on the density of the eavesdropper nodes.