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The group testing problem is concerned with identifying a small set of $k$infected individuals in a large population of $n$ people. At our disposal is atesting scheme that can test groups of individuals. A test comes back positiveif and only if at least one individual is infected. In this note, we laygroundwork for analysing belief propagation for group testing when $k$ scaleslinearly in $n$. To this end, we derive the offspring distribution fordifferent types of individuals. With these distributions at hand, one canemploy the population dynamics algorithm to simulate the posterior marginaldistribution resulting from belief propagation.

Note on the offspring distribution for group testing in the linear regime