Group Testing for Binary Markov Sources: Data-Driven Group Queries for Cooperative Sensor Networks

Abstract

Group testing has been used in many applications to efficiently identify rare events in a large population. In this paper, the concept of group testing is generalized to applications with correlated source models to derive scheduling policies for sensors' adopting cooperative transmissions. The tenet of our work is that in a wireless sensor network it is advantageous to allocate the same channel dimensions to all sensor sources that have the same response to a sequence of queries or tests. That is, nodes that have the same data attributes should transmit as a cooperative super-source. Specifically, we consider the case where sensors' data are modeled spatially as a one-dimensional Markov chain. Two strategies are considered: the recursive algorithm and the tree-based algorithm. The recursive scheme allows us to illustrate the performance of group testing for finite populations while the tree-based algorithm is used to derive the achievable scaling performances of the class of group testing strategies as the number of sensors increases. We show that the total number of queries required to gather all sensors' data scales in the order of the joint entropy. A further generalization of this concept provides the basis of deriving efficient data-gathering algorithms for correlated sources.