Stochastic Systems Group  

Bayesian Decentralized Detection in Unreliable Networks of Arbitrary Topology
O. Patrick Kreidl
SSG, MIT
Consider any finitenode network of spatiallydistributed Bayesian detectors, assuming each node receives a noisy measurement of its local (discretevalued) state and is explicitly constrained to make just two distinct decisions: the first determines which discretevalued symbol (if any) is transmitted to each of its immediate neighbors and the second, upon receiving the symbols (or lack thereof) from its neighbors, determines an estimate of its local state. Moreover, the multipointtopoint channel that delivers each node's received symbols is not necessarily reliable (due to e.g., uncoded intersymbol interference, positive erasure probabilities).
We formulate the collective design of all local processing rules as a dualobjective constrained optimization problem, minimizing a weighted sum of the global linkuserate and global nodeerrorrate over the feasible subset of all measurement processing strategies. We show that its teamtheoretic approximation leads to an efficient distributed algorithm to be executed "offline" (i.e., before measurements are processed), which strives to iteratively couple the "online" rules such that there is minimal performance loss from the innetwork processing constraints. These results generalize the existing theory of Bayesian decentralized detection for directed network topologies, and provide the first development of the theory for undirected network topologies.
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