2 research outputs found
Error Probability Bounds for Binary Relay Trees with Crummy Sensors
We study the detection error probability associated with balanced binary
relay trees, in which sensor nodes fail with some probability. We consider N
identical and independent crummy sensors, represented by leaf nodes of the
tree. The root of the tree represents the fusion center, which makes the final
decision between two hypotheses. Every other node is a relay node, which fuses
at most two binary messages into one binary message and forwards the new
message to its parent node. We derive tight upper and lower bounds for the
total error probability at the fusion center as functions of N and characterize
how fast the total error probability converges to 0 with respect to N. We show
that the convergence of the total error probability is sub-linear, with the
same decay exponent as that in a balanced binary relay tree without sensor
failures. We also show that the total error probability converges to 0, even if
the individual sensors have total error probabilities that converge to 1/2 and
the failure probabilities that converge to 1, provided that the convergence
rates are sufficiently slow
Bowdoin Orient v.132, no.1-24 (2002-2003)
https://digitalcommons.bowdoin.edu/bowdoinorient-2000s/1003/thumbnail.jp