# Federated Learning over Wireless Networks: A Band-limited Coordinated Descent Approach

arXiv: https://arxiv.org/abs/2102.07972 · HTML: https://mlsanity.com/paper/2102.07972/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 29 references that are in the map.
- First posted on arXiv 16 Feb 2021.

## Builds on (most cited first, 23 of 23)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [Local SGD Converges Fast and Communicates Little](https://mlsanity.com/paper/1805.09767/) (2018)
- [signSGD: Compressed Optimisation for Non-Convex Problems](https://mlsanity.com/paper/1802.04434/) (2018)
- [Sparsified SGD with Memory](https://mlsanity.com/paper/1809.07599/) (2018)
- [Error Feedback Fixes SignSGD and other Gradient Compression Schemes](https://mlsanity.com/paper/1901.09847/) (2019)
- [TernGrad: Ternary Gradients to Reduce Communication in Distributed Deep Learning](https://mlsanity.com/paper/1705.07878/) (2017)
- [Sparse Communication for Distributed Gradient Descent](https://mlsanity.com/paper/1704.05021/) (2017)
- [The Convergence of Sparsified Gradient Methods](https://mlsanity.com/paper/1809.10505/) (2018)
- [Federated Learning via Over-the-Air Computation](https://mlsanity.com/paper/1812.11750/) (2018)
- [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)
- [Towards an Intelligent Edge: Wireless Communication Meets Machine Learning](https://mlsanity.com/paper/1809.00343/) (2018)
- [Communication-efficient distributed SGD with Sketching](https://mlsanity.com/paper/1903.04488/) (2019)
- [Error Compensated Quantized SGD and its Applications to Large-scale Distributed Optimization](https://mlsanity.com/paper/1806.08054/) (2018)
- [On Analog Gradient Descent Learning over Multiple Access Fading Channels](https://mlsanity.com/paper/1908.07463/) (2019)
- [Wireless Federated Distillation for Distributed Edge Learning with Heterogeneous Data](https://mlsanity.com/paper/1907.02745/) (2019)
- [Energy-Efficient Radio Resource Allocation for Federated Edge Learning](https://mlsanity.com/paper/1907.06040/) (2019)
- [A Distributed Synchronous SGD Algorithm with Global Top-k Sparsification for Low Bandwidth Networks](https://mlsanity.com/paper/1901.04359/) (2019)
- [Over-the-Air Computation Systems: Optimization, Analysis and Scaling Laws](https://mlsanity.com/paper/1909.00329/) (2019)
- [Over-the-air Function Computation in Sensor Networks](https://mlsanity.com/paper/1612.02307/) (2016)
- [Reduced-Dimension Design of MIMO Over-the-Air Computing for Data Aggregation in Clustered IoT Networks](https://mlsanity.com/paper/1812.02373/) (2018)
- [Blind Over-the-Air Computation and Data Fusion via Provable Wirtinger Flow](https://mlsanity.com/paper/1811.04644/) (2018)

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

- [Holistic Network Virtualization and Pervasive Network Intelligence for 6G](https://mlsanity.com/paper/2301.00519/) (2023)
- [PPA: Preference Profiling Attack Against Federated Learning](https://mlsanity.com/paper/2202.04856/) (2022)
- [Service Delay Minimization for Federated Learning over Mobile Devices](https://mlsanity.com/paper/2205.09868/) (2022)
- [Multi-Source to Multi-Target Decentralized Federated Domain Adaptation](https://mlsanity.com/paper/2304.12422/) (2023)
- [Joint Optimization of Energy Consumption and Completion Time in Federated Learning](https://mlsanity.com/paper/2209.14900/) (2022)
- [Truthful Incentive Mechanism for Federated Learning with Crowdsourced Data Labeling](https://mlsanity.com/paper/2302.00106/) (2023)
- [Fundamental limits of over-the-air optimization: Are analog schemes optimal?](https://mlsanity.com/paper/2109.05222/) (2021)
- [Communication-Efficient Distributed SGD with Compressed Sensing](https://mlsanity.com/paper/2112.07836/) (2021)
- [Over-the-Air Federated Averaging with Limited Power and Privacy Budgets](https://mlsanity.com/paper/2305.03547/) (2023)
- [Communication-Efficient Federated Learning over Wireless Channels via Gradient Sketching](https://mlsanity.com/paper/2410.23424/) (2024)
- [Timely Parameter Updating in Over-the-Air Federated Learning](https://mlsanity.com/paper/2512.19103/) (2025)

## Abstract (arXiv)

We consider a many-to-one wireless architecture for federated learning at the network edge, where multiple edge devices collaboratively train a model using local data. The unreliable nature of wireless connectivity, together with constraints in computing resources at edge devices, dictates that the local updates at edge devices should be carefully crafted and compressed to match the wireless communication resources available and should work in concert with the receiver. Thus motivated, we propose SGD-based bandlimited coordinate descent algorithms for such settings. Specifically, for the wireless edge employing over-the-air computing, a common subset of k-coordinates of the gradient updates across edge devices are selected by the receiver in each iteration, and then transmitted simultaneously over k sub-carriers, each experiencing time-varying channel conditions. We characterize the impact of communication error and compression, in terms of the resulting gradient bias and mean squared error, on the convergence of the proposed algorithms. We then study learning-driven communication error minimization via joint optimization of power allocation and learning rates. Our findings reveal that optimal power allocation across different sub-carriers should take into account both the gradient values and channel conditions, thus generalizing the widely used water-filling policy. We also develop sub-optimal distributed solutions amenable to implementation.