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This paper presents the first orthogonal frequency-divisionmultiplexing(OFDM)-based digital over-the-air computation (AirComp) system forwireless federated edge learning, where multiple edge devices transmit modeldata simultaneously using non-orthogonal OFDM subcarriers, and the edge serveraggregates data directly from the superimposed signal. Existing analog AirCompsystems often assume perfect phase alignment via channel precoding and utilizeuncoded analog transmission for model aggregation. In contrast, our digitalAirComp system leverages digital modulation and channel codes to overcome phaseasynchrony, thereby achieving accurate model aggregation for phase-asynchronousmulti-user OFDM systems. To realize a digital AirComp system, we develop amedium access control (MAC) protocol that allows simultaneous transmissionsfrom different users using non-orthogonal OFDM subcarriers, and put forth jointchannel decoding and aggregation decoders tailored for convolutional and LDPCcodes. To verify the proposed system design, we build a digital AirCompprototype on the USRP software-defined radio platform, and demonstrate areal-time LDPC-coded AirComp system with up to four users. Trace-drivensimulation results on test accuracy versus SNR show that: 1) analog AirComp issensitive to phase asynchrony in practical multi-user OFDM systems, and thetest accuracy performance fails to improve even at high SNRs; 2) our digitalAirComp system outperforms two analog AirComp systems at all SNRs, andapproaches the optimal performance when SNR $\geq$ 6 dB for two-user LDPC-codedAirComp, demonstrating the advantage of digital AirComp in phase-asynchronousmulti-user OFDM systems.

Broadband Digital Over-the-Air Computation for Wireless Federated Edge Learning