|Stochastic Systems Group|
Bayesian Decentralized Detection in Unreliable Networks of Arbitrary Topology
O. Patrick Kreidl
Consider any finite-node network of spatially-distributed Bayesian detectors, assuming each node receives a noisy measurement of its local (discrete-valued) state and is explicitly constrained to make just two distinct decisions: the first determines which discrete-valued 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 multipoint-to-point channel that delivers each node's received symbols is not necessarily reliable (due to e.g., uncoded inter-symbol interference, positive erasure probabilities).
We formulate the collective design of all local processing rules as a dual-objective constrained optimization problem, minimizing a weighted sum of the global link-use-rate and global node-error-rate over the feasible subset of all measurement processing strategies. We show that its team-theoretic 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 in-network 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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