  Inspired by group testing algorithms and the coded computation paradigm, we
propose and analyze a novel multiple access scheme for detecting active users
in large-scale networks. The scheme consists of a simple randomized detection
algorithm that uses computation coding as intermediate steps for computing
logical disjunction functions over the multiple access channel (MAC). First we
show that given an efficient MAC code for disjunction computation the algorithm
requires $O(k \log (\frac{N}{k }))$ decision steps for detecting $k$ active
users out of $N+k$ users. Subsequently we present a simple suboptimal code for
a class of MACs with arbitrarily varying sub-gaussian noise that uniformly
requires $O (k \log (N) \max \{ \log k , \log \log N \} )$ channel uses for
solving the activity detection problem. This shows that even in the presence of
noise an efficient detection of active users is possible. Our approach reveals
that the true crux of the matter lies in constructing efficient codes for
computing disjunctions over a MAC.
