  Orbital angular momentum (OAM)-encoding has recently emerged as an effective
approach for increasing the channel capacity of free-space optical
communications. In this paper, OAM-based decoding is formulated as a supervised
classification problem. To maintain lower error rate in presence of severe
atmospheric turbulence, a new approach that combines effective machine learning
tools from persistent homology and convolutional neural networks (CNNs) is
proposed to decode the OAM modes. A Gaussian kernel with learnable parameters
is proposed in order to connect persistent homology to CNN, allowing the system
to extract and distinguish robust and unique topological features for the OAM
modes. Simulation results show that the proposed approach achieves up to 20%
gains in classification accuracy rate over state-of-the-art of method based on
only CNNs. These results essentially show that geometric and topological
features play a pivotal role in the OAM mode classification problem.
