Before revision:  Thereby, we generalize prior work on the recovery of hierarchically sparse signals from Kronecker-structured linear measurements. This structure arises in a variety of communication scenariosin the context of massive internet of things. We numerical demonstrate that the fast and scalable HiHTP algorithm is  suitable for solving these types of problems and evaluate its performance in terms of sparse signal recovery and block detection capability.
After revision:  Thereby, we generalize prior work on Kronecker-product measurements. As an exemplary application, we apply the theory to two communication scenarios. The fast and scalable HiHTP algorithm is suitable for solving these types of problems and evaluate its performance in terms of sparse signal recovery and block detection capability.