A General Method for the Design of Tree Networks Under Communication Constraints

TL;DR

This paper introduces a general, cyclic design method for tree-structured distributed detection systems with communication constraints, optimizing node and fusion center design to minimize error probability.

Contribution

It presents a novel person-by-person design approach for nodes in arbitrary tree networks, enabling efficient optimization under communication constraints.

Findings

Design method applicable to arbitrary tree topologies

Efficient computation of node parameters in the restricted model

Applicable to general M-ary hypothesis testing

Abstract

We consider a distributed detection system with communication constraints, where several nodes are arranged in an arbitrary tree topology, under the assumption of conditionally independent observations. We propose a cyclic design procedure using the minimum expected error probability as a design criterion while adopting a person-by-person methodology. We design each node jointly together with the fusion center, while other nodes are kept fixed, and show that the design of each node using the person-by-person methodology is analogous to the design of a network with two nodes, a network which we refer to as the restricted model. We further show how the parameters in the restricted model for the design of a node in the tree network can be found in a computationally efficient manner. The proposed numerical methodology can be applied for the design of nodes arranged in arbitrary tree topologies with arbitrary channel rates for the links between nodes and for a general M-ary hypothesis testing problem.