  Group testing has recently attracted significant attention from the research
community due to its applications in diagnostic virology. An instance of the
group testing problem includes a ground set of individuals which includes a
small subset of infected individuals. The group testing procedure consists of a
number of tests, such that each test indicates whether or not a given subset of
individuals includes one or more infected individuals. The goal of the group
testing procedure is to identify the subset of infected individuals with the
minimum number of tests. Motivated by practical scenarios, such as testing for
viral diseases, this paper focuses on the following group testing settings: (i)
the group testing procedure is noisy, i.e., the outcome of the group testing
procedure can be flipped with a certain probability; (ii) there is a certain
amount of side information on the distribution of the infected individuals
available to the group testing algorithm. The paper makes the following
contributions. First, we propose a probabilistic model, referred to as an
interaction model, that captures the side information about the probability
distribution of the infected individuals. Next, we present a decoding scheme,
based on the belief propagation, that leverages the interaction model to
improve the decoding accuracy. Our results indicate that the proposed algorithm
achieves higher success probability and lower false-negative and false-positive
rates when compared to the traditional belief propagation especially in the
high noise regime.
