# Massive Digital Over-the-Air Computation for Communication-Efficient Federated Edge Learning

arXiv: https://arxiv.org/abs/2405.15969 · HTML: https://mlsanity.com/paper/2405.15969/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2024.

## Built on by (most cited first, 13 of 13)

- [ToDMA: Large Model-Driven Massive Token Communications for Semantic Multiple Access](https://mlsanity.com/paper/2505.10946/) (2025)
- [CSI-GPT: Integrating Generative Pre-Trained Transformer with Federated-Tuning to Acquire Downlink Massive MIMO Channels](https://mlsanity.com/paper/2406.03438/) (2024)
- [Private Collaborative Edge Inference via Over-the-Air Computation](https://mlsanity.com/paper/2407.21151/) (2024)
- [Dynamic Scheduling for Vehicle-to-Vehicle Communications Enhanced Federated Learning](https://mlsanity.com/paper/2406.17470/) (2024)
- [Scalable and Reliable Over-the-Air Federated Edge Learning](https://mlsanity.com/paper/2407.11807/) (2024)
- [Learned Digital Over-the-Air Computing for Federated Edge Learning](https://mlsanity.com/paper/2509.16577/) (2025)
- [Federated Self-Supervised Modulation Classification under Non-IID and Imbalanced Data](https://mlsanity.com/paper/2510.04927/) (2025)
- [Learned Digital Codes for Over-the-Air Computation in Federated Edge Learning](https://mlsanity.com/paper/2512.19777/) (2025)
- [MD-AirComp+: Adaptive Quantization for Blind Massive Digital Over-the-Air Computation](https://mlsanity.com/paper/2602.18332/) (2026)
- [Out-of-Air Computation: Enabling Structured Function Extraction from Wireless Superposition](https://mlsanity.com/paper/2604.04312/) (2026)
- [A Stable Aggregation Method for Quantum Federated Learning](https://mlsanity.com/paper/2609.00356/) (2026)
- [AirGC-CD: Gaussian-Circulant Precoding for Exactly Debiasable PAPR Reduction in Over-the-Air Federated Learning](https://mlsanity.com/paper/2609.23084/) (2026)
- [Logit-Aware MIMO AirComp for Distributed Mixture-of-Experts LLM Inference over Wireless Edge Networks](https://mlsanity.com/paper/2610.03741/) (2026)

## Abstract (arXiv)

Over-the-air computation (AirComp) is a promising technology converging communication and computation over wireless networks, which can be particularly effective in model training, inference, and more emerging edge intelligence applications. AirComp relies on uncoded transmission of individual signals, which are added naturally over the multiple access channel thanks to the superposition property of the wireless medium. Despite significantly improved communication efficiency, how to accommodate AirComp in the existing and future digital communication networks, that are based on discrete modulation schemes, remains a challenge. This paper proposes a massive digital AirComp (MD-AirComp) scheme, that leverages an unsourced massive access protocol, to enhance compatibility with both current and next-generation wireless networks. MD-AirComp utilizes vector quantization to reduce the uplink communication overhead, and employs shared quantization and modulation codebooks. At the receiver, we propose a near-optimal approximate message passing-based algorithm to compute the model aggregation results from the superposed sequences, which relies on estimating the number of devices transmitting each code sequence, rather than trying to decode the messages of individual transmitters. We apply MD-AirComp to the federated edge learning (FEEL), and show that it significantly accelerates FEEL convergence compared to state-of-the-art while using the same amount of communication resources. To support further research and ensure reproducibility, we have made our code available at https://github.com/liqiao19/MD-AirComp.