  This paper presents the first broadband digital over-the-air computation
(AirComp) system for phase asynchronous OFDM-based federated edge learning
systems. Existing analog AirComp systems often assume perfect phase alignment
via channel precoding and utilize uncoded analog modulation for model
aggregation. In contrast, our digital AirComp system leverages digital
modulation and channel codes to overcome phase asynchrony, thereby achieving
accurate model aggregation in the asynchronous multi-user OFDM systems. To
realize a digital AirComp system, we propose a non-orthogonal multiple access
protocol that allows simultaneous transmissions from multiple edge devices, and
present a joint channel decoding and aggregation (Jt-CDA) decoder (i.e.,
full-state joint decoder). To reduce the computation complexity, we further
present a reduced-complexity Jt-CDA decoder (i.e., reduced-state joint
decoder), and its arithmetic sum bit error rate performance is similar to that
of the full-state joint decoder for most signal-to-noise ratio (SNR) regimes.
Simulation results on test accuracy (of CIFAR10 dataset) versus SNR show that:
1) analog AirComp systems are sensitive to phase asynchrony under practical
setup, and the test accuracy performance exhibits an error floor even at high
SNR regime; 2) our digital AirComp system outperforms an analog AirComp system
by at least 1.5 times when SNR 9dB, demonstrating the advantage of digital
AirComp in asynchronous multi-user OFDM systems.
