  This paper presents the first orthogonal frequency-division
multiplexing(OFDM)-based digital over-the-air computation (AirComp) system for
wireless federated edge learning, where multiple edge devices transmit model
data simultaneously using non-orthogonal OFDM subcarriers, and the edge server
aggregates data directly from the superimposed signal. Existing analog AirComp
systems often assume perfect phase alignment via channel precoding and utilize
uncoded analog transmission for model aggregation. In contrast, our digital
AirComp system leverages digital modulation and channel codes to overcome phase
asynchrony, thereby achieving accurate model aggregation for phase-asynchronous
multi-user OFDM systems. To realize a digital AirComp system, we develop a
medium access control (MAC) protocol that allows simultaneous transmissions
from different users using non-orthogonal OFDM subcarriers, and put forth joint
channel decoding and aggregation decoders tailored for convolutional and LDPC
codes. To verify the proposed system design, we build a digital AirComp
prototype on the USRP software-defined radio platform, and demonstrate a
real-time LDPC-coded AirComp system with up to four users. Trace-driven
simulation results on test accuracy versus SNR show that: 1) analog AirComp is
sensitive to phase asynchrony in practical multi-user OFDM systems, and the
test accuracy performance fails to improve even at high SNRs; 2) our digital
AirComp system outperforms two analog AirComp systems at all SNRs, and
approaches the optimal performance when SNR $\geq$ 6 dB for two-user LDPC-coded
AirComp, demonstrating the advantage of digital AirComp in phase-asynchronous
multi-user OFDM systems.
