Error probability bounds for binary relay trees with unreliable communication links

We study the decentralized detection problem in the context of balanced binary relay trees. We assume that the communication links in the tree network fail with certain probabilities. Not surprisingly, the step-wise reduction of the total detection error probability is slower than the case where the network has no communication link failures. We show that, under the assumption of identical communication link failure probability in the tree, the exponent of the total error probability at the fusion center is o(√N) in the asymptotic regime. In addition, if the given communication link failure probabilities decrease to 0 as communications get closer to the fusion center, then the decay exponent of the total error probability is Θ(√N), provided that the decay of the failure probabilities is sufficiently fast.

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