# Communication-Efficient Federated Learning via Quantized Compressed Sensing

arXiv: https://arxiv.org/abs/2111.15071 · HTML: https://mlsanity.com/paper/2111.15071/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 42 references that are in the map.
- First posted on arXiv 30 Nov 2021.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (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)
- [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)
- [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)
- [Gradient Sparsification for Communication-Efficient Distributed Optimization](https://mlsanity.com/paper/1710.09854/) (2017)
- [Federated Optimization:Distributed Optimization Beyond the Datacenter](https://mlsanity.com/paper/1511.03575/) (2015)
- [Federated Learning over Wireless Fading Channels](https://mlsanity.com/paper/1907.09769/) (2019)
- [Federated Learning for Wireless Communications: Motivation, Opportunities and Challenges](https://mlsanity.com/paper/1908.06847/) (2019)
- [UVeQFed: Universal Vector Quantization for Federated Learning](https://mlsanity.com/paper/2006.03262/) (2020)
- [Towards an Intelligent Edge: Wireless Communication Meets Machine Learning](https://mlsanity.com/paper/1809.00343/) (2018)
- [High-Dimensional Stochastic Gradient Quantization for Communication-Efficient Edge Learning](https://mlsanity.com/paper/1910.03865/) (2019)
- [Communicate to Learn at the Edge](https://mlsanity.com/paper/2009.13269/) (2020)
- [Machine Learning at the Wireless Edge: Distributed Stochastic Gradient Descent Over-the-Air](https://mlsanity.com/paper/1901.00844/) (2019)
- [Bayesian Federated Learning over Wireless Networks](https://mlsanity.com/paper/2012.15486/) (2020)

## Built on by (most cited first, 18 of 18)

- [Communication-Efficient Split Learning via Adaptive Feature-Wise Compression](https://mlsanity.com/paper/2307.10805/) (2023)
- [Distributed Deep Reinforcement Learning Based Gradient Quantization for Federated Learning Enabled Vehicle Edge Computing](https://mlsanity.com/paper/2407.08462/) (2024)
- [Communication-Efficient Design for Quantized Decentralized Federated Learning](https://mlsanity.com/paper/2303.08423/) (2023)
- [Federated Learning: A Cutting-Edge Survey of the Latest Advancements and Applications](https://mlsanity.com/paper/2310.05269/) (2023)
- [Communication-Efficient Federated Learning by Quantized Variance Reduction for Heterogeneous Wireless Edge Networks](https://mlsanity.com/paper/2501.11267/) (2025)
- [Towards Adapting Federated & Quantum Machine Learning for Network Intrusion Detection: A Survey](https://mlsanity.com/paper/2509.21389/) (2025)
- [Over-the-Air Federated Learning with Compressed Sensing: Is Sparsification Necessary?](https://mlsanity.com/paper/2310.03410/) (2023)
- [FedMPQ: Secure and Communication-Efficient Federated Learning with Multi-codebook Product Quantization](https://mlsanity.com/paper/2404.13575/) (2024)
- [Noise-Robust and Resource-Efficient ADMM-based Federated Learning](https://mlsanity.com/paper/2409.13451/) (2024)
- [Personalized Federated Learning with Bidirectional Communication Compression via One-Bit Random Sketching](https://mlsanity.com/paper/2511.13144/) (2025)
- [Enhancing Communication Efficiency in FL with Adaptive Gradient Quantization and Communication Frequency Optimization](https://mlsanity.com/paper/2509.23419/) (2025)
- [LSHFed: Robust and Communication-Efficient Federated Learning with Locally-Sensitive Hashing Gradient Mapping](https://mlsanity.com/paper/2511.01296/) (2025)
- [Deep Probabilistic Unfolding for Quantized Compressive Sensing](https://mlsanity.com/paper/2605.11475/) (2026)
- [Q-LocalAdam: Memory-Efficient Client-Side Adaptive Optimization for Edge Federated Learning](https://mlsanity.com/paper/2605.17552/) (2026)
- [Quantization in Federated Learning: Methods, Challenges and Future Directions](https://mlsanity.com/paper/2606.26822/) (2026)
- [Mixed-Timescale Differential Coding for Downlink Model Broadcast in Wireless Federated Learning](https://mlsanity.com/paper/2607.13119/) (2026)
- [Polar Code Based Federated Learning: Convergence Analysis and Resource Allocation](https://mlsanity.com/paper/2608.13961/) (2026)
- [FedFit: Federated Fine-Tuning of LLMs via Vector-Bank Parameterization and Quantization](https://mlsanity.com/paper/2610.01537/) (2026)

## Abstract (arXiv)

In this paper, we present a communication-efficient federated learning framework inspired by quantized compressed sensing. The presented framework consists of gradient compression for wireless devices and gradient reconstruction for a parameter server (PS). Our strategy for gradient compression is to sequentially perform block sparsification, dimensional reduction, and quantization. Thanks to gradient sparsification and quantization, our strategy can achieve a higher compression ratio than one-bit gradient compression. For accurate aggregation of the local gradients from the compressed signals at the PS, we put forth an approximate minimum mean square error (MMSE) approach for gradient reconstruction using the expectation-maximization generalized-approximate-message-passing (EM-GAMP) algorithm. Assuming Bernoulli Gaussian-mixture prior, this algorithm iteratively updates the posterior mean and variance of local gradients from the compressed signals. We also present a low-complexity approach for the gradient reconstruction. In this approach, we use the Bussgang theorem to aggregate local gradients from the compressed signals, then compute an approximate MMSE estimate of the aggregated gradient using the EM-GAMP algorithm. We also provide a convergence rate analysis of the presented framework. Using the MNIST dataset, we demonstrate that the presented framework achieves almost identical performance with the case that performs no compression, while significantly reducing communication overhead for federated learning.