# Federated Learning over Noisy Channels: Convergence Analysis and Design Examples

arXiv: https://arxiv.org/abs/2101.02198 · HTML: https://mlsanity.com/paper/2101.02198/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 52 of its 65 references that are in the map.
- First posted on arXiv 6 Jan 2021.

## Builds on (most cited first, 30 of 52)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Towards Federated Learning at Scale: System Design](https://mlsanity.com/paper/1902.01046/) (2019)
- [LEAF: A Benchmark for Federated Settings](https://mlsanity.com/paper/1812.01097/) (2018)
- [Local SGD Converges Fast and Communicates Little](https://mlsanity.com/paper/1805.09767/) (2018)
- [Weight Normalization: A Simple Reparameterization to Accelerate Training of Deep Neural Networks](https://mlsanity.com/paper/1602.07868/) (2016)
- [Adaptive Federated Learning in Resource Constrained Edge Computing Systems](https://mlsanity.com/paper/1804.05271/) (2018)
- [Federated Learning in Mobile Edge Networks: A Comprehensive Survey](https://mlsanity.com/paper/1909.11875/) (2019)
- [Fair Resource Allocation in Federated Learning](https://mlsanity.com/paper/1905.10497/) (2019)
- [FedPAQ: A Communication-Efficient Federated Learning Method with Periodic Averaging and Quantization](https://mlsanity.com/paper/1909.13014/) (2019)
- [Client Selection for Federated Learning with Heterogeneous Resources in Mobile Edge](https://mlsanity.com/paper/1804.08333/) (2018)
- [A Joint Learning and Communications Framework for Federated Learning over Wireless Networks](https://mlsanity.com/paper/1909.07972/) (2019)
- [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)
- [Energy Efficient Federated Learning Over Wireless Communication Networks](https://mlsanity.com/paper/1911.02417/) (2019)
- [On the Linear Speedup Analysis of Communication Efficient Momentum SGD for Distributed Non-Convex Optimization](https://mlsanity.com/paper/1905.03817/) (2019)
- [Expanding the Reach of Federated Learning by Reducing Client Resource Requirements](https://mlsanity.com/paper/1812.07210/) (2018)
- [QSGD: Communication-Efficient SGD via Gradient Quantization and Encoding](https://mlsanity.com/paper/1610.02132/) (2016)
- [Scheduling Policies for Federated Learning in Wireless Networks](https://mlsanity.com/paper/1908.06287/) (2019)
- [Protection Against Reconstruction and Its Applications in Private Federated Learning](https://mlsanity.com/paper/1812.00984/) (2018)
- [One-Bit Over-the-Air Aggregation for Communication-Efficient Federated Edge Learning: Design and Convergence Analysis](https://mlsanity.com/paper/2001.05713/) (2020)
- [Local SGD with Periodic Averaging: Tighter Analysis and Adaptive Synchronization](https://mlsanity.com/paper/1910.13598/) (2019)
- [Cooperative SGD: A unified Framework for the Design and Analysis of Communication-Efficient SGD Algorithms](https://mlsanity.com/paper/1808.07576/) (2018)
- [Client Selection and Bandwidth Allocation in Wireless Federated Learning Networks: A Long-Term Perspective](https://mlsanity.com/paper/2004.04314/) (2020)
- [DoubleSqueeze: Parallel Stochastic Gradient Descent with Double-Pass Error-Compensated Compression](https://mlsanity.com/paper/1905.05957/) (2019)

## Built on by (most cited first, 8 of 8)

- [Federated Learning over Wireless Device-to-Device Networks: Algorithms and Convergence Analysis](https://mlsanity.com/paper/2101.12704/) (2021)
- [On the Convergence of Decentralized Federated Learning Under Imperfect Information Sharing](https://mlsanity.com/paper/2303.10695/) (2023)
- [A Hybrid Architecture for Federated and Centralized Learning](https://mlsanity.com/paper/2105.03288/) (2021)
- [Federated Multi-Armed Bandits Under Byzantine Attacks](https://mlsanity.com/paper/2205.04134/) (2022)
- [Resource Rationing for Wireless Federated Learning: Concept, Benefits, and Challenges](https://mlsanity.com/paper/2104.06990/) (2021)
- [Improved Convergence Analysis and SNR Control Strategies for Federated Learning in the Presence of Noise](https://mlsanity.com/paper/2307.07406/) (2023)
- [Energy-Efficient Channel Decoding for Wireless Federated Learning: Convergence Analysis and Adaptive Design](https://mlsanity.com/paper/2407.13703/) (2024)
- [Noise-Robust and Resource-Efficient ADMM-based Federated Learning](https://mlsanity.com/paper/2409.13451/) (2024)

## Abstract (arXiv)

Does Federated Learning (FL) work when both uplink and downlink communications have errors? How much communication noise can FL handle and what is its impact to the learning performance? This work is devoted to answering these practically important questions by explicitly incorporating both uplink and downlink noisy channels in the FL pipeline. We present several novel convergence analyses of FL over simultaneous uplink and downlink noisy communication channels, which encompass full and partial clients participation, direct model and model differential transmissions, and non-independent and identically distributed (IID) local datasets. These analyses characterize the sufficient conditions for FL over noisy channels to have the same convergence behavior as the ideal case of no communication error. More specifically, in order to maintain the O(1/T) convergence rate of FedAvg with perfect communications, the uplink and downlink signal-to-noise ratio (SNR) for direct model transmissions should be controlled such that they scale as O(t^2) where t is the index of communication rounds, but can stay constant for model differential transmissions. The key insight of these theoretical results is a "flying under the radar" principle - stochastic gradient descent (SGD) is an inherent noisy process and uplink/downlink communication noises can be tolerated as long as they do not dominate the time-varying SGD noise. We exemplify these theoretical findings with two widely adopted communication techniques - transmit power control and diversity combining - and further validating their performance advantages over the standard methods via extensive numerical experiments using several real-world FL tasks.