Theoretical Bounds in Minimax Decentralized Hypothesis Testing

Minimax decentralized detection is studied under two scenarios: with and without a fusion center when the source of uncertainty is the Bayesian prior. When there is no fusion center, the constraints in the network design are determined. Both for a single decision maker and multiple decision makers, the maximum loss in detection performance due to minimax decision making is obtained. In the presence of a fusion center, the maximum loss of detection performance between with- and without fusion center networks is derived assuming that both networks are minimax robust. The results are finally generalized.Comment: Submitted to IEEE Trans. on Signal Processin

Bayesian Design of Tandem Networks for Distributed Detection With Multi-bit Sensor Decisions

We consider the problem of decentralized hypothesis testing under communication constraints in a topology where several peripheral nodes are arranged in tandem. Each node receives an observation and transmits a message to its successor, and the last node then decides which hypothesis is true. We assume that the observations at different nodes are, conditioned on the true hypothesis, independent and the channel between any two successive nodes is considered error-free but rate-constrained. We propose a cyclic numerical design algorithm for the design of nodes using a person-by-person methodology with the minimum expected error probability as a design criterion, where the number of communicated messages is not necessarily equal to the number of hypotheses. The number of peripheral nodes in the proposed method is in principle arbitrary and the information rate constraints are satisfied by quantizing the input of each node. The performance of the proposed method for different information rate constraints, in a binary hypothesis test, is compared to the optimum rate-one solution due to Swaszek and a method proposed by Cover, and it is shown numerically that increasing the channel rate can significantly enhance the performance of the tandem network. Simulation results for $M$-ary hypothesis tests also show that by increasing the channel rates the performance of the tandem network significantly improves

On optimal quantization rules for some problems in sequential decentralized detection

We consider the design of systems for sequential decentralized detection, a problem that entails several interdependent choices: the choice of a stopping rule (specifying the sample size), a global decision function (a choice between two competing hypotheses), and a set of quantization rules (the local decisions on the basis of which the global decision is made). This paper addresses an open problem of whether in the Bayesian formulation of sequential decentralized detection, optimal local decision functions can be found within the class of stationary rules. We develop an asymptotic approximation to the optimal cost of stationary quantization rules and exploit this approximation to show that stationary quantizers are not optimal in a broad class of settings. We also consider the class of blockwise stationary quantizers, and show that asymptotically optimal quantizers are likelihood-based threshold rules.Comment: Published as IEEE Transactions on Information Theory, Vol. 54(7), 3285-3295, 200

Distributed Detection in Sensor Networks with Limited Range Sensors

We consider a multi-object detection problem over a sensor network (SNET) with limited range sensors. This problem complements the widely considered decentralized detection problem where all sensors observe the same object. While the necessity for global collaboration is clear in the decentralized detection problem, the benefits of collaboration with limited range sensors is unclear and has not been widely explored. In this paper we develop a distributed detection approach based on recent development of the false discovery rate (FDR). We first extend the FDR procedure and develop a transformation that exploits complete or partial knowledge of either the observed distributions at each sensor or the ensemble (mixture) distribution across all sensors. We then show that this transformation applies to multi-dimensional observations, thus extending FDR to multi-dimensional settings. We also extend FDR theory to cases where distributions under both null and positive hypotheses are uncertain. We then propose a robust distributed algorithm to perform detection. We further demonstrate scalability to large SNETs by showing that the upper bound on the communication complexity scales linearly with the number of sensors that are in the vicinity of objects and is independent of the total number of sensors. Finally, we deal with situations where the sensing model may be uncertain and establish robustness of our techniques to such uncertainties.Comment: Submitted to IEEE Transactions on Signal Processin

Rate Allocation for Decentralized Detection in Wireless Sensor Networks

We consider the problem of decentralized detection where peripheral nodes make noisy observations of a phenomenon and send quantized information about the phenomenon towards a fusion center over a sum-rate constrained multiple access channel. The fusion center then makes a decision about the state of the phenomenon based on the aggregate received data. Using the Chernoff information as a performance metric, Chamberland and Veeravalli previously studied the structure of optimal rate allocation strategies for this scenario under the assumption of an unlimited number of sensors. Our key contribution is to extend these result to the case where there is a constraint on the maximum number of active sensors. In particular, we find sufficient conditions under which the uniform rate allocation is an optimal strategy, and then numerically verify that these conditions are satisfied for some relevant sensor design rules under a Gaussian observation model.Comment: Accepted at SPAWC 201