Error Probability Bounds for M-ary Relay Trees

We study the detection error probabilities associated with an M-ary relay tree, where the leaves of the tree correspond to identical and independent sensors. Only these leaves are sensors. The root of the tree represents a fusion center that makes the overall detection decision. Each of the other nodes in the tree is a relay node that combines M summarized messages from its immediate child nodes to form a single output message using the majority dominance rule. We derive tight upper and lower bounds for the Type I and II error probabilities at the fusion center as explicit functions of the number of sensors in the case of binary message alphabets. These bounds characterize how fast the error probabilities converge to 0 with respect to the number of sensors.

[1]  Edwin K. P. Chong,et al.  Error Probability Bounds for Binary Relay Trees with Crummy Sensors , 2011, ArXiv.

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

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

[4]  Yashodhan Kanoria,et al.  Subexponential convergence for information aggregation on regular trees , 2011, IEEE Conference on Decision and Control and European Control Conference.

[5]  Venugopal V. Veeravalli,et al.  Topics in Decentralized Detection , 1992 .

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

[7]  Edwin K. P. Chong,et al.  Error Probability Bounds for Balanced Binary Relay Trees , 2012, IEEE Transactions on Information Theory.

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

[9]  Edwin K. P. Chong,et al.  Aggregation and compression of distributed binary decisions in a wireless sensor network , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[10]  Edwin K. P. Chong,et al.  Error probability bounds for binary relay trees with unreliable communication links , 2011, 2011 Conference Record of the Forty Fifth Asilomar Conference on Signals, Systems and Computers (ASILOMAR).

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

[12]  Moe Z. Win,et al.  Bayesian Detection in Bounded Height Tree Networks , 2007, IEEE Transactions on Signal Processing.

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