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 full-state joint channel decoding and aggregation (Jt-CDA) decoder. To reduce the computation complexity, we further present a reduced-complexity Jt-CDA 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.