期刊
IEEE TRANSACTIONS ON SIGNAL PROCESSING
卷 61, 期 9, 页码 2165-2177出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2013.2246156
关键词
Data fusion; decentralized detection; distributed detection; erasure channel; link failure; node failure; tree network
资金
- AFOSR [FA9550-09-1-0518]
- NSF [CCF-0916314, CCF-1018472]
- Direct For Computer & Info Scie & Enginr
- Division of Computing and Communication Foundations [0916314] Funding Source: National Science Foundation
- Division of Computing and Communication Foundations
- Direct For Computer & Info Scie & Enginr [1018472] Funding Source: National Science Foundation
We study the distributed detection problem in the context of a balanced binary relay tree, where the leaves of the tree correspond to N identical and independent sensors generating binary messages. The root of the tree is a fusion center making an overall decision. Every other node is a relay node that aggregates the messages received from its child nodes into a new message and sends it up toward the fusion center. We derive upper and lower bounds for the total error probability P-N as explicit functions of N in the case where nodes and links fail with certain probabilities. These characterize the asymptotic decay rate of the total error probability as N goes to infinity. Naturally, this decay rate is not larger than that in the non-failure case, which is root N. However, we derive an explicit necessary and sufficient condition on the decay rate of the local failure probabilities p(k) (combination of node and link failure probabilities at each level) such that the decay rate of the total error probability in the failure case is the same as that of the non-failure case. More precisely, we show that log P-N(-1) = Theta(root N) if and only if log p(k)(-1) = Omega(2(k/2)).
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