This paper proposes a massive digital over-the-air computation (MD-AirComp) scheme for communication-efficient federated edge learning (FEEL). MD-AirComp leverages an unsourced massive access protocol to enhance compatibility with current and next-generation wireless networks. It uses vector quantization to reduce uplink communication overhead and employs shared quantization and modulation codebooks. At the receiver, a near-optimal approximate message passing-based algorithm is proposed to compute the model aggregation results from the superposed sequences, which relies on estimating the number of devices transmitting each code sequence rather than decoding individual transmitters' messages. MD-AirComp is applied to FEEL, significantly accelerating convergence compared to state-of-the-art methods while using the same communication resources. The proposed scheme is compatible with both scalar and vector quantization schemes and can be deployed in existing digital communication systems. The algorithm uses majority voting to estimate the number of active devices and exploits multiple observations from multi-antenna BS to enhance detection accuracy. The convergence rate of FEEL with MD-AirComp is analyzed and found to be $ \mathcal{O}\left(\frac{1}{\sqrt{T}}\right) $, where T is the number of global training rounds. The proposed MD-AirComp scheme is shown to be communication-efficient and suitable for various edge computing tasks. The algorithm is implemented using an approximate message passing (AMP) based digital aggregation (AMP-DA) algorithm, which is efficient for detecting sparse signals and estimating the number of active devices. The computational complexity of the proposed AMP-DA algorithm is analyzed and found to be of the order $ \mathcal{O}(I_{0}LNMD) $, which scales linearly with the quantization level N. The convergence analysis of MD-AirComp-based FEEL is presented, showing that the scheme achieves a convergence rate of $ \mathcal{O}\left(\frac{1}{\sqrt{T}}\right) $, which is optimal for communication-efficient FEEL.This paper proposes a massive digital over-the-air computation (MD-AirComp) scheme for communication-efficient federated edge learning (FEEL). MD-AirComp leverages an unsourced massive access protocol to enhance compatibility with current and next-generation wireless networks. It uses vector quantization to reduce uplink communication overhead and employs shared quantization and modulation codebooks. At the receiver, a near-optimal approximate message passing-based algorithm is proposed to compute the model aggregation results from the superposed sequences, which relies on estimating the number of devices transmitting each code sequence rather than decoding individual transmitters' messages. MD-AirComp is applied to FEEL, significantly accelerating convergence compared to state-of-the-art methods while using the same communication resources. The proposed scheme is compatible with both scalar and vector quantization schemes and can be deployed in existing digital communication systems. The algorithm uses majority voting to estimate the number of active devices and exploits multiple observations from multi-antenna BS to enhance detection accuracy. The convergence rate of FEEL with MD-AirComp is analyzed and found to be $ \mathcal{O}\left(\frac{1}{\sqrt{T}}\right) $, where T is the number of global training rounds. The proposed MD-AirComp scheme is shown to be communication-efficient and suitable for various edge computing tasks. The algorithm is implemented using an approximate message passing (AMP) based digital aggregation (AMP-DA) algorithm, which is efficient for detecting sparse signals and estimating the number of active devices. The computational complexity of the proposed AMP-DA algorithm is analyzed and found to be of the order $ \mathcal{O}(I_{0}LNMD) $, which scales linearly with the quantization level N. The convergence analysis of MD-AirComp-based FEEL is presented, showing that the scheme achieves a convergence rate of $ \mathcal{O}\left(\frac{1}{\sqrt{T}}\right) $, which is optimal for communication-efficient FEEL.