# User Activity Detection via Group Testing and Coded Computation

## TL;DR

This paper introduces a novel user activity detection scheme in large networks using group testing and coded computation, achieving efficient detection even with noisy channels.

## Contribution

It proposes a randomized detection algorithm leveraging coding for disjunctions over MACs, with theoretical bounds on detection steps and channel uses.

## Key findings

- Detection requires $O(k \log (rac{N}{k }))$ steps with efficient MAC codes.
- A suboptimal code achieves $O (k \log (N) \max \{\log k , \log \log N
ight") channel uses in noisy environments.
- Efficient disjunction codes are crucial for activity detection in large-scale noisy networks.

## Abstract

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.