Decentralized Detection in Undirected Network Topologies

Consider the well-studied decentralized Bayesian detection problem with the twist of an undirected network topology, each edge representing a bidirectional (and perhaps unreliable) finite-rate communication link between two distributed sensor nodes. Every node operates in parallel, processing any particular local measurement in two (discrete) decision stages: the first selects the symbols (if any) transmitted to its immediate neighbors and the second, upon receiving the symbols (or lack thereof) from the same neighbors, decides the value of its local state. We adapt the team solution already known for directed acyclic networks and establish conditions such that the iterative numerical algorithm to collectively optimize the local decision rules admits an efficient message-passing interpretation, featuring an asynchronous distributed implementation in which total computation and communication overhead scales only linearly with the number of nodes. In sharp contrast to the directed case, this message-passing algorithm retains its global correctness and convergence guarantees without restrictions on the network topology.