An information theoretic approach to DSN evaluation

Evaluation of Distributed Sensor Networks (DSN\u27s) for optimal detection using Bayesian cost formulation methods has been the objective of several studies. There have been a few studies on DSN evaluation using an information theoretic approach, wherein an assymetric channel models a detector. We look at the multi-sensor system at the receiver as a black-box and model it as an assymetric channel whose cross over probabilities depend on the probabilties of detection and of false alarm. These probabilities in turn depend on the thresholds of the local detectors and on the fusion rule used. We consider the case wherein the receiver has control over the value of the probability of the signal being present, by influencing trans?mitter coding. The probability to be used at the receiver is the one that solves the MED (Minimum Equivocation Detetion) problem. Minimizing the equivocation between the input and output is the same as maximizing the mutual information. The input probability, P0, at the receiver that maximizes the mutual information is then achieved by having an encoder between the transmitter and the multi-sensor system at the receiver. The only factor in encoding is the proportion of 0\u27s to 1\u27s. Variable length codes with different ordering of 0\u27s and 1\u27s are possible to get the same performance. Results show that as we move towards an optimum ROC (Receiver Operating Characteristic) curve, the mutual information attains a higher value. The value of P0 that helps attain this value is then derived by encoding the transmitter output

A Game-Theoretic Framework for Optimum Decision Fusion in the Presence of Byzantines

Optimum decision fusion in the presence of malicious nodes - often referred to as Byzantines - is hindered by the necessity of exactly knowing the statistical behavior of Byzantines. By focusing on a simple, yet widely studied, set-up in which a Fusion Center (FC) is asked to make a binary decision about a sequence of system states by relying on the possibly corrupted decisions provided by local nodes, we propose a game-theoretic framework which permits to exploit the superior performance provided by optimum decision fusion, while limiting the amount of a-priori knowledge required. We first derive the optimum decision strategy by assuming that the statistical behavior of the Byzantines is known. Then we relax such an assumption by casting the problem into a game-theoretic framework in which the FC tries to guess the behavior of the Byzantines, which, in turn, must fix their corruption strategy without knowing the guess made by the FC. We use numerical simulations to derive the equilibrium of the game, thus identifying the optimum behavior for both the FC and the Byzantines, and to evaluate the achievable performance at the equilibrium. We analyze several different setups, showing that in all cases the proposed solution permits to improve the accuracy of data fusion. We also show that, in some instances, it is preferable for the Byzantines to minimize the mutual information between the status of the observed system and the reports submitted to the FC, rather than always flipping the decision made by the local nodes as it is customarily assumed in previous works

Byzantine Modification Detection in Multicast Networks With Random Network Coding

An information-theoretic approach for detecting Byzantine or adversarial modifications in networks employing random linear network coding is described. Each exogenous source packet is augmented with a flexible number of hash symbols that are obtained as a polynomial function of the data symbols. This approach depends only on the adversary not knowing the random coding coefficients of all other packets received by the sink nodes when designing its adversarial packets. We show how the detection probability varies with the overhead (ratio of hash to data symbols), coding field size, and the amount of information unknown to the adversary about the random code

Information theoretic novelty detection

We present a novel approach to online change detection problems when the training sample size is small. The proposed approach is based on estimating the expected information content of a new data point and allows an accurate control of the false positive rate even for small data sets. In the case of the Gaussian distribution, our approach is analytically tractable and closely related to classical statistical tests. We then propose an approximation scheme to extend our approach to the case of the mixture of Gaussians. We evaluate extensively our approach on synthetic data and on three real benchmark data sets. The experimental validation shows that our method maintains a good overall accuracy, but significantly improves the control over the false positive rate

Multi-Layer Cyber-Physical Security and Resilience for Smart Grid

The smart grid is a large-scale complex system that integrates communication technologies with the physical layer operation of the energy systems. Security and resilience mechanisms by design are important to provide guarantee operations for the system. This chapter provides a layered perspective of the smart grid security and discusses game and decision theory as a tool to model the interactions among system components and the interaction between attackers and the system. We discuss game-theoretic applications and challenges in the design of cross-layer robust and resilient controller, secure network routing protocol at the data communication and networking layers, and the challenges of the information security at the management layer of the grid. The chapter will discuss the future directions of using game-theoretic tools in addressing multi-layer security issues in the smart grid.Comment: 16 page