Bayesian Detection in Bounded Height Tree Networks

We study the detection performance of large scale sensor networks, configured as trees with bounded height, in which information is progressively compressed as it moves towards the root of the tree. We show that, under a Bayesian formulation, the error probability decays exponentially fast, and we provide bounds for the error exponent. We then focus on the case where the tree has certain symmetry properties. We derive the form of the optimal exponent within a restricted class of easily implementable strategies, as well as optimal strategies within that class. We also find conditions under which (suitably defined) majority rules are optimal. Finally, we provide evidence that in designing a network it is preferable to keep the branching factor small for nodes other than the neighbors of the leaves.

[1]  T. Cover.  Hypothesis Testing with Finite Statistics , 1969 .

[2]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[3]  Nils Sandell,et al.  Detection with Distributed Sensors , 1980, IEEE Transactions on Aerospace and Electronic Systems.

[4]  P.K. Varshney,et al.  Optimal Data Fusion in Multiple Sensor Detection Systems , 1986, IEEE Transactions on Aerospace and Electronic Systems.

[5]  L.W. Nolte,et al.  Design and Performance Comparison of Distributed Detection Networks , 1987, IEEE Transactions on Aerospace and Electronic Systems.

[6]  Ramanarayanan Viswanathan,et al.  Optimal serial distributed decision fusion , 1987, 26th IEEE Conference on Decision and Control.

[7]  John N. Tsitsiklis,et al.  Decentralized detection by a large number of sensors , 1988, Math. Control. Signals Syst..

[8]  J. Tsitsiklis,et al.  Explicit Solutions for Some Simple Decentralized Detection Problems , 1990, 1989 American Control Conference.

[9]  J. Tsitsiklis,et al.  Explicit Solutions for Some Simple Decentralized Detection Problems , 1989 .

[10]  Michael. Athans,et al.  On optimal distributed decision architectures in a hypothesis testing environment , 1992 .

[11]  D. Kleinman,et al.  Optimization of detection networks. I. Tandem structures , 1990, 1990 IEEE International Conference on Systems, Man, and Cybernetics Conference Proceedings.

[12]  E. Drakopoulos,et al.  Optimum multisensor fusion of correlated local decisions , 1991 .

[13]  John N. Tsitsiklis,et al.  Some properties of optimal thresholds in decentralized detection , 1992, Other Conferences.

[14]  Peter Willett,et al.  The suboptimality of randomized tests in distributed and quantized detection systems , 1992, IEEE Trans. Inf. Theory.

[15]  W. Gray,et al.  Optimal data fusion of correlated local decisions in multiple sensor detection systems , 1992 .

[16]  M. Athans,et al.  Distributed detection by a large team of sensors in tandem , 1992 .

[17]  Rick S. Blum,et al.  Optimum distributed detection of weak signals in dependent sensors , 1992, IEEE Trans. Inf. Theory.

[18]  D. Kleinman,et al.  Optimization of Detection Networks: Part 11-Tree Structures , 1993 .

[19]  J. Tsitsiklis.  Decentralized Detection' , 1993 .

[20]  John N. Tsitsiklis,et al.  Extremal properties of likelihood-ratio quantizers , 1993, IEEE Trans. Commun..

[21]  D. Kleinman,et al.  Optimization of detection networks with multiple event structures , 1994, IEEE Trans. Autom. Control..

[22]  Pramod K. Varshney,et al.  A unified approach to the design of decentralized detection systems , 1995 .

[23]  Rick S. Blum,et al.  Distributed detection with multiple sensors I. Advanced topics , 1997, Proc. IEEE.

[24]  Pramod K. Varshney,et al.  Distributed detection with multiple sensors I. Fundamentals , 1997, Proc. IEEE.

[25]  Amir Dembo,et al.  Large Deviations Techniques and Applications , 1998 .

[26]  N. Bingham.  Probability Theory: An Analytic View , 2002 .

[27]  Venugopal V. Veeravalli,et al.  Decentralized detection in sensor networks , 2003, IEEE Trans. Signal Process..

[28]  Venugopal V. Veeravalli,et al.  Asymptotic results for decentralized detection in power constrained wireless sensor networks , 2004, IEEE Journal on Selected Areas in Communications.

[29]  P.K. Varshney,et al.  Decision fusion rules in multi-hop wireless sensor networks , 2005, IEEE Transactions on Aerospace and Electronic Systems.

[30]  Wenjun Li,et al.  Distributed Detection in Large-Scale Sensor Networks with Correlated Sensor Observations , 2005 .

[31]  Andrea E. F. Clementi,et al.  Divide and Conquer Is Almost Optimal for the Bounded-Hop MST Problem on Random Euclidean Instances , 2005, SIROCCO.

[32]  Venugopal V. Veeravalli,et al.  How Dense Should a Sensor Network Be for Detection With Correlated Observations? , 2006, IEEE Transactions on Information Theory.

[33]  Moe Z. Win,et al.  On the Subexponential Decay of Detection Error Probabilities in Long Tandems , 2008, IEEE Trans. Inf. Theory.

[34]  Moe Z. Win,et al.  Data Fusion Trees for Detection: Does Architecture Matter? , 2008, IEEE Transactions on Information Theory.

[35]  Wee Peng Tay.  Decentralized detection in resource-limited sensor network architectures , 2008 .