Percolation and Connectivity in the Intrinsically Secure Communications Graph

The ability to exchange secret information is critical to many commercial, governmental, and military networks. The intrinsically secure communications graph (iS-graph) is a random graph which describes the connections that can be securely established over a large-scale network, by exploiting the physical properties of the wireless medium. This paper aims to characterize the global properties of the iS-graph in terms of: (i) percolation on the infinite plane, and (ii) full connectivity on a finite region. First, for the Poisson iS-graph defined on the infinite plane, the existence of a phase transition is proven, whereby an unbounded component of connected nodes suddenly arises as the density of legitimate nodes is increased. This shows that long-range secure communication is still possible in the presence of eavesdroppers. Second, full connectivity on a finite region of the Poisson iS-graph is considered. The exact asymptotic behavior of full connectivity in the limit of a large density of legitimate nodes is characterized. Then, simple, explicit expressions are derived in order to closely approximate the probability of full connectivity for a finite density of legitimate nodes. The results help clarify how the presence of eavesdroppers can compromise long-range secure communication.Comment: Submitted for journal publicatio

Continuum Percolation in the Intrinsically Secure Communications Graph

The intrinsically secure communications graph (iS-graph) is a random graph which captures the connections that can be securely established over a large-scale network, in the presence of eavesdroppers. It is based on principles of information-theoretic security, widely accepted as the strictest notion of security. In this paper, we are interested in characterizing the global properties of the iS-graph in terms of percolation on the infinite plane. We prove the existence of a phase transition in the Poisson iS-graph, whereby an unbounded component of securely connected nodes suddenly arises as we increase the density of legitimate nodes. Our work shows that long-range communication in a wireless network is still possible when a secrecy constraint is present.Comment: Accepted in the IEEE International Symposium on Information Theory and its Applications (ISITA'10), Taichung, Taiwan, Oct. 201

A Unifying Framework for Local Throughput in Wireless Networks

With the increased competition for the electromagnetic spectrum, it is important to characterize the impact of interference in the performance of a wireless network, which is traditionally measured by its throughput. This paper presents a unifying framework for characterizing the local throughput in wireless networks. We first analyze the throughput of a probe link from a connectivity perspective, in which a packet is successfully received if it does not collide with other packets from nodes within its reach (called the audible interferers). We then characterize the throughput from a signal-to-interference-plus-noise ratio (SINR) perspective, in which a packet is successfully received if the SINR exceeds some threshold, considering the interference from all emitting nodes in the network. Our main contribution is to generalize and unify various results scattered throughout the literature. In particular, the proposed framework encompasses arbitrary wireless propagation effects (e.g, Nakagami-m fading, Rician fading, or log-normal shadowing), as well as arbitrary traffic patterns (e.g., slotted-synchronous, slotted-asynchronous, or exponential-interarrivals traffic), allowing us to draw more general conclusions about network performance than previously available in the literature.Comment: Submitted for journal publicatio

Communication in a Poisson Field of Interferers -- Part II: Channel Capacity and Interference Spectrum

In Part I of this paper, we presented a mathematical model for communication subject to both network interference and noise, where the interferers are scattered according to a spatial Poisson process, and are operating asynchronously in a wireless environment subject to path loss, shadowing, and multipath fading. We determined the distribution of the aggregate interference and the error performance of the link. In this second part, we characterize the capacity of the link subject to both network interference and noise. Then, we put forth the concept of spectral outage probability (SOP), a new characterization of the aggregate radio-frequency emission generated by communicating nodes in a wireless network. We present some applications of the SOP, namely the establishment of spectral regulations and the design of covert military networks. The proposed framework captures all the essential physical parameters that affect the aggregate network emission, yet is simple enough to provide insights that may be of value in the design and deployment of wireless networks.Comment: To appear in IEEE Transactions on Wireless Communication

Wireless Secrecy in Large-Scale Networks

The ability to exchange secret information is critical to many commercial, governmental, and military networks. The intrinsically secure communications graph (iS-graph) is a random graph which describes the connections that can be securely established over a large-scale network, by exploiting the physical properties of the wireless medium. This paper provides an overview of the main properties of this new class of random graphs. We first analyze the local properties of the iS-graph, namely the degree distributions and their dependence on fading, target secrecy rate, and eavesdropper collusion. To mitigate the effect of the eavesdroppers, we propose two techniques that improve secure connectivity. Then, we analyze the global properties of the iS-graph, namely percolation on the infinite plane, and full connectivity on a finite region. These results help clarify how the presence of eavesdroppers can compromise secure communication in a large-scale network.Comment: To appear: Proc. IEEE Information Theory and Applications Workshop (ITA'11), San Diego, CA, Feb. 2011, pp. 1-10, Invited Pape

Techniques for Enhanced Physical-Layer Security

Information-theoretic security--widely accepted as the strictest notion of security--relies on channel coding techniques that exploit the inherent randomness of propagation channels to strengthen the security of communications systems. Within this paradigm, we explore strategies to improve secure connectivity in a wireless network. We first consider the intrinsically secure communications graph (iS-graph), a convenient representation of the links that can be established with information-theoretic security on a large-scale network. We then propose and characterize two techniques--sectorized transmission and eavesdropper neutralization--which are shown to dramatically enhance the connectivity of the iS-graph.Comment: Pre-print, IEEE Global Telecommunications Conference (GLOBECOM'10), Miami, FL, Dec. 201

Communication in a Poisson Field of Interferers -- Part I: Interference Distribution and Error Probability

We present a mathematical model for communication subject to both network interference and noise. We introduce a framework where the interferers are scattered according to a spatial Poisson process, and are operating asynchronously in a wireless environment subject to path loss, shadowing, and multipath fading. We consider both cases of slow and fast-varying interferer positions. The paper is comprised of two separate parts. In Part I, we determine the distribution of the aggregate network interference at the output of a linear receiver. We characterize the error performance of the link, in terms of average and outage probabilities. The proposed model is valid for any linear modulation scheme (e.g., M-ary phase shift keying or M-ary quadrature amplitude modulation), and captures all the essential physical parameters that affect network interference. Our work generalizes the conventional analysis of communication in the presence of additive white Gaussian noise and fast fading, allowing the traditional results to be extended to include the effect of network interference. In Part II of the paper, we derive the capacity of the link when subject to network interference and noise, and characterize the spectrum of the aggregate interference.Comment: To appear in IEEE Transactions on Wireless Communication

Locating the Source of Diffusion in Large-Scale Networks

How can we localize the source of diffusion in a complex network? Due to the tremendous size of many real networks--such as the Internet or the human social graph--it is usually infeasible to observe the state of all nodes in a network. We show that it is fundamentally possible to estimate the location of the source from measurements collected by sparsely-placed observers. We present a strategy that is optimal for arbitrary trees, achieving maximum probability of correct localization. We describe efficient implementations with complexity O(N^{\alpha}), where \alpha=1 for arbitrary trees, and \alpha=3 for arbitrary graphs. In the context of several case studies, we determine how localization accuracy is affected by various system parameters, including the structure of the network, the density of observers, and the number of observed cascades.Comment: To appear in Physical Review Letters. Includes pre-print of main paper, and supplementary materia

Natural variability of lotic Mediterranean ecosystems or wildfire perturbations: who will win?

This study evaluates the impacts of wildfires in lotic Mediterranean ecosystems. It was carried out at Monchique ridge after big wildfires occurred during 2002 and 2003. Deferential impacts were evaluated comparing historical results obtained before the wildfires (1999 and 2001), with the post fire ones (2006 and 2007). Physical and chemical parameters of the water, habitat morphology, diatoms, macrophytes, macroinvertebrates and fishes were evaluated at 10 collecting places, before and after wildfires. High recovering rates were observed to the vegetation, but it is still possible to found fire impacts over macrophytes and river morphology. Wildfires, contributed to canopy decrease and, consequently to the growth of plants that usually are controlled by shadow. As a result, vegetation biodiversity tend to increase. River banks tend also to be invaded by terrestrial plants. Higher post fires recover rates were observed to the more aquatic communities (diatoms, macroinvertebrates and fishes). For those communities, comparing spring situations before and after the fires no substantial differences were observed. Sometimes differences between consecutive years are even higher. So it can be concluded that magnitude of wildfire impacts is less than the natural inter-annual variability of Mediterranean rivers. Long-term effects of forest fires, resulting from large woody debries, were also detected by morphological alterations, like debries dams. Habitat diversity increase and impacts on aquatic communities are expected