Pedro C. Pinto

Locating the Source of Diffusion in Large-Scale Networks

How can we localize the source of diffusion in a complex network? Because of the tremendous size of many real networks-such as the internet or the human social graph-it is usually unfeasible 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(α)), where α=1 for arbitrary trees and α=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.

Secure Communication in Stochastic Wireless Networks—Part I: Connectivity

The ability to exchange secret information is critical to many commercial, governmental, and military networks. Information-theoretic security-widely accepted as the strictest notion of security-relies on channel coding techniques that exploit the inherent randomness of the propagation channels to strengthen the security of digital communications systems. Motivated by recent developments in the field, we aim to characterize the fundamental secrecy limits of wireless networks. The paper is comprised of two separate parts. In Part I, we define the intrinsically secure communications graph (iS-graph), a random graph which describes the connections that can be securely established over a large-scale network. We provide conclusive results for the local connectivity of the Poisson iS-graph, in terms of node degrees and isolation probabilities. We show how the secure connectivity of the network varies with the wireless propagation effects, the secrecy rate threshold of each link, and the noise powers of legitimate nodes and eavesdroppers. We then propose sectorized transmission and eavesdropper neutralization as viable strategies for improving the secure connectivity. Our results help clarify how the spatial density of eavesdroppers can compromise the intrinsic security of wireless networks. In Part II of the paper, we study the achievable secrecy rates and the effect of eavesdropper collusion.

Secure Communication in Stochastic Wireless Networks—Part II: Maximum Rate and Collusion

In Part I of this paper, we introduced the intrinsically secure communications graph (iS-graph)-a random graph which describes the connections that can be established with strong secrecy over a large-scale network, in the presence of eavesdroppers. We focused on the local connectivity of the iS-graph, and proposed techniques to improve it. In this second part, we characterize the maximum secrecy rate (MSR) that can be achieved between a node and its neighbors. We then consider the scenario where the eavesdroppers are allowed to collude, i.e., exchange and combine information. We quantify exactly how eavesdropper collusion degrades the secrecy properties of the network, in comparison to a noncolluding scenario. Our analysis helps clarify how the presence of eavesdroppers can jeopardize the success of wireless physical-layer security.

Position-Based Jamming for Enhanced Wireless Secrecy

Signal interference and packet collisions are typically viewed as negative factors that hinder wireless communication networks. When security is the primary concern, signal interference may actually be very helpful. Starting with a stochastic network model, we are able to show that packet collisions caused by jamming nodes can indeed be used effectively to attain new levels of secrecy in multiterminal wireless environments. To this effect, we propose a practical jamming protocol that uses the well-known request-to-send/clear-to-send (RTS/CTS) handshake of the IEEE 802.11 standard as a signaling scheme. Various jammer selection strategies are investigated depending on the position of source, destination, and jamming nodes. The goal is to cause as much interference as possible to eavesdroppers that are located in unknown positions, while limiting the interference observed by the legitimate receiver. To evaluate the performance of each strategy, we introduce and compute a measure for the secure throughput. Our results show that jamming can increase the levels of secrecy significantly albeit at a substantial cost in terms of energy efficiency.

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.

Teaching signal processing online: A report from the trenches

After years of experimentation, online teaching has gone through a phase transition with the appearance of massive open online courses (MOOCs), following the model pioneered by Salman Khan with short videos and the use of tablets. Dozens of university-level courses are now available, and followed by hundreds of thousands of online students. We report on early experiences with teaching “Fundamentals of Electrical Engineering” and “Digital Signal Processing” on an open online platform (Coursera). We address in particular: (i) suitability of online platforms for signal processing oriented topics; (ii) structuring of material for the online format; (iii) quizzes and exercises for large classes; (iv) grading methods and possible certification issues; (v) learning from teaching, forums, and data mining of students feedback.