# 1-Bit Compressive Sensing for Efficient Federated Learning Over the Air

arXiv: https://arxiv.org/abs/2103.16055 · HTML: https://mlsanity.com/paper/2103.16055/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 60 references that are in the map.
- First posted on arXiv 30 Mar 2021.

## Builds on (most cited first, 27 of 27)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [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)
- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [signSGD: Compressed Optimisation for Non-Convex Problems](https://mlsanity.com/paper/1802.04434/) (2018)
- [Deep Gradient Compression: Reducing the Communication Bandwidth for Distributed Training](https://mlsanity.com/paper/1712.01887/) (2017)
- [Sparsified SGD with Memory](https://mlsanity.com/paper/1809.07599/) (2018)
- [FedPAQ: A Communication-Efficient Federated Learning Method with Periodic Averaging and Quantization](https://mlsanity.com/paper/1909.13014/) (2019)
- [A Joint Learning and Communications Framework for Federated Learning over Wireless Networks](https://mlsanity.com/paper/1909.07972/) (2019)
- [Sparse Communication for Distributed Gradient Descent](https://mlsanity.com/paper/1704.05021/) (2017)
- [Federated Learning via Over-the-Air Computation](https://mlsanity.com/paper/1812.11750/) (2018)
- [Gradient Sparsification for Communication-Efficient Distributed Optimization](https://mlsanity.com/paper/1710.09854/) (2017)
- [Broadband Analog Aggregation for Low-Latency Federated Edge Learning (Extended Version)](https://mlsanity.com/paper/1812.11494/) (2018)
- [Federated Learning over Wireless Fading Channels](https://mlsanity.com/paper/1907.09769/) (2019)
- [Asynchronous Parallel Stochastic Gradient for Nonconvex Optimization](https://mlsanity.com/paper/1506.08272/) (2015)
- [One-Bit Over-the-Air Aggregation for Communication-Efficient Federated Edge Learning: Design and Convergence Analysis](https://mlsanity.com/paper/2001.05713/) (2020)
- [UVeQFed: Universal Vector Quantization for Federated Learning](https://mlsanity.com/paper/2006.03262/) (2020)
- [Cooperative SGD: A unified Framework for the Design and Analysis of Communication-Efficient SGD Algorithms](https://mlsanity.com/paper/1808.07576/) (2018)
- [LAG: Lazily Aggregated Gradient for Communication-Efficient Distributed Learning](https://mlsanity.com/paper/1805.09965/) (2018)
- [Sparse Binary Compression: Towards Distributed Deep Learning with minimal Communication](https://mlsanity.com/paper/1805.08768/) (2018)
- [On Nonconvex Decentralized Gradient Descent](https://mlsanity.com/paper/1608.05766/) (2016)
- [Energy-Aware Analog Aggregation for Federated Learning with Redundant Data](https://mlsanity.com/paper/1911.00188/) (2019)
- [Optimal parameter selection for the alternating direction method of multipliers (ADMM): quadratic problems](https://mlsanity.com/paper/1306.2454/) (2013)
- [Collaborative Machine Learning at the Wireless Edge with Blind Transmitters](https://mlsanity.com/paper/1907.03909/) (2019)
- [COKE: Communication-Censored Decentralized Kernel Learning](https://mlsanity.com/paper/2001.10133/) (2020)
- [Optimized Power Control for Over-the-Air Computation in Fading Channels](https://mlsanity.com/paper/1906.06858/) (2019)
- [Gradient Statistics Aware Power Control for Over-the-Air Federated Learning](https://mlsanity.com/paper/2003.02089/) (2020)

## Built on by (most cited first, 11 of 11)

- [Distributed Learning in Wireless Networks: Recent Progress and Future Challenges](https://mlsanity.com/paper/2104.02151/) (2021)
- [BEV-SGD: Best Effort Voting SGD for Analog Aggregation Based Federated Learning against Byzantine Attackers](https://mlsanity.com/paper/2110.09660/) (2021)
- [Distributed Swarm Learning for Edge Internet of Things](https://mlsanity.com/paper/2403.20188/) (2024)
- [Resilience in Online Federated Learning: Mitigating Model-Poisoning Attacks via Partial Sharing](https://mlsanity.com/paper/2403.13108/) (2024)
- [Sparse Decentralized Federated Learning](https://mlsanity.com/paper/2308.16671/) (2023)
- [Over-the-Air Federated Edge Learning with Error-Feedback One-Bit Quantization and Power Control](https://mlsanity.com/paper/2303.11319/) (2023)
- [Personalized Federated Learning with Bidirectional Communication Compression via One-Bit Random Sketching](https://mlsanity.com/paper/2511.13144/) (2025)
- [Lightweight Federated Learning over Wireless Edge Networks](https://mlsanity.com/paper/2507.09546/) (2025)
- [Multi-Worker Selection based Distributed Swarm Learning for Edge IoT with Non-i.i.d. Data](https://mlsanity.com/paper/2509.18367/) (2025)
- [Communication-Efficient Personalized Federated Learning via Layer-Wise Multi-Threshold Random Sketching](https://mlsanity.com/paper/2609.04830/) (2026)
- [AirGC-CD: Gaussian-Circulant Precoding for Exactly Debiasable PAPR Reduction in Over-the-Air Federated Learning](https://mlsanity.com/paper/2609.23084/) (2026)

## Abstract (arXiv)

For distributed learning among collaborative users, this paper develops and analyzes a communication-efficient scheme for federated learning (FL) over the air, which incorporates 1-bit compressive sensing (CS) into analog aggregation transmissions. To facilitate design parameter optimization, we theoretically analyze the efficacy of the proposed scheme by deriving a closed-form expression for the expected convergence rate of the FL over the air. Our theoretical results reveal the tradeoff between convergence performance and communication efficiency as a result of the aggregation errors caused by sparsification, dimension reduction, quantization, signal reconstruction and noise. Then, we formulate 1-bit CS based FL over the air as a joint optimization problem to mitigate the impact of these aggregation errors through joint optimal design of worker scheduling and power scaling policy. An enumeration-based method is proposed to solve this non-convex problem, which is optimal but becomes computationally infeasible as the number of devices increases. For scalable computing, we resort to the alternating direction method of multipliers (ADMM) technique to develop an efficient implementation that is suitable for large-scale networks. Simulation results show that our proposed 1-bit CS based FL over the air achieves comparable performance to the ideal case where conventional FL without compression and quantification is applied over error-free aggregation, at much reduced communication overhead and transmission latency.