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

User Activity Detection via Group Testing and Coded Computation