# Learned Digital Over-the-Air Computing for Federated Edge Learning

arXiv: https://arxiv.org/abs/2509.16577 · HTML: https://mlsanity.com/paper/2509.16577/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 22 references that are in the map.
- First posted on arXiv 20 Sep 2025.

## Builds on (most cited first, 13 of 13)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [Sparse Communication for Distributed Gradient Descent](https://mlsanity.com/paper/1704.05021/) (2017)
- [Federated Learning over Wireless Fading Channels](https://mlsanity.com/paper/1907.09769/) (2019)
- [Distributed Learning in Wireless Networks: Recent Progress and Future Challenges](https://mlsanity.com/paper/2104.02151/) (2021)
- [One-Bit Over-the-Air Aggregation for Communication-Efficient Federated Edge Learning: Design and Convergence Analysis](https://mlsanity.com/paper/2001.05713/) (2020)
- [Addressing Representation Collapse in Vector Quantized Models with One Linear Layer](https://mlsanity.com/paper/2411.02038/) (2024)
- [AMP-Net: Denoising based Deep Unfolding for Compressive Image Sensing](https://mlsanity.com/paper/2004.10078/) (2020)
- [Dynamic Scheduling for Over-the-Air Federated Edge Learning with Energy Constraints](https://mlsanity.com/paper/2106.00490/) (2021)
- [Distributed Learning over a Wireless Network with FSK-Based Majority Vote](https://mlsanity.com/paper/2111.01850/) (2021)
- [Massive Digital Over-the-Air Computation for Communication-Efficient Federated Edge Learning](https://mlsanity.com/paper/2405.15969/) (2024)
- [OFDMA-F2L: Federated Learning With Flexible Aggregation Over an OFDMA Air Interface](https://mlsanity.com/paper/2311.15141/) (2023)
- [On the Feasibility of Distributed Phase Synchronization for Coherent Signal Superposition](https://mlsanity.com/paper/2506.22252/) (2025)

## Abstract (arXiv)

Over-the-air (OTA) aggregation enables federated edge learning (FEEL) by exploiting the superposition property of the wireless channel to merge communication with computation, eliminating the need to schedule and decode devices individually. Analog OTA schemes transmit uncoded updates but are sensitive to noise, fading, and power misalignment, motivating more robust digital alternatives. However, state-of-the-art (SoTA) digital OTA designs that combine unsourced random access (URA) with compressed sensing struggle in the low signal-to-noise ratio (SNR) regimes common in Internet of Things (IoT) deployments, where symbol recovery and active-device estimation become unreliable. We propose a learned digital OTA framework that jointly trains a URA codebook with an unrolled approximate message passing (AMP)-based decoder. The learned decoder incorporates per-layer damping, residual scaling, temperature-controlled Bayesian denoising, and a lightweight convolutional neural network (CNN) refinement, while the codebook is optimised end-to-end through a factorised parameterisation. At near-perfect-aggregation accuracy, the proposed design extends the viable SNR range by approximately 7,dB over the SoTA baseline at the same uplink overhead, and generalises across models, activity levels, and heterogeneous data.