Abstract
This paper considers the problem of sequential binary hypothesis testing based on observations from a network of $m$ sensors where a subset of the sensors is compromised by a malicious adversary. The asymptotic average sample number required to reach a certain level of error probability is selected as the performance metric of the system. We propose an asymptotically optimal voting algorithm for the sensor network with a fusion center and generalize it to fully-distributed networks, where the algorithm stays asymptotically optimal under the weak assumption that the sensor network is connected. Moreover, we prove that both of the proposed algorithms are asymptotically optimal in the presence of Byzantine sensors, in the sense that each of them forms a Nash equilibrium with the worst-case attack (flip-attack). Compared to existing distributed detection strategies, the proposed scheme has a low message complexity, which is independent of the error probability and the sample number, by taking advantage of the sparsity of votes. The results are corroborated by numerical simulations.
Highlights
Distributed inference with sensor networks has drawn substantial research attention due to its wide application in power grids, cognitive radio [1], wireless sensor networks [2], Internet of Things, etc
3) In the presence of attack, when the number of compromised sensors is known, we prove that the detection strategy VSPRT (DVSPRT) and system disturbing strategy flip-attack form a Nash equilibrium pair, i.e., the proposed VSPRT (DVSPRT) scheme achieves the fundamental limit among all possible detection strategies
4) We further prove that the proposed distributed voting SPRT (DVSPRT) scheme has message complexity O(mM )1, which is independent of error probability and sample number
Summary
Background and Motivation: Distributed inference with sensor networks has drawn substantial research attention due to its wide application in power grids, cognitive radio [1], wireless sensor networks [2], Internet of Things, etc. The aforementioned distributed detection schemes assume the existence of a fusion center (FC) that can communicate with all the sensors in the network. Naive average consensus algorithm utilized in the previous distributed detection schemes is not resilient when there are malicious agents in the network [12]. Our work and contribution: We consider the distributed binary hypothesis testing problem where a binary state θ = {0, 1} is detected by a group of m sensors that generate observations according to a background hypothesis. This paper aims to design a distributed detection scheme to decide on the time to stop and the hypothesis to choose based on observations from the partly corrupted sensor network with minimum average sample number under error probability constraints.
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