# Compute-Update Federated Learning: A Lattice Coding Approach Over-the-Air

arXiv: https://arxiv.org/abs/2409.06343 · HTML: https://mlsanity.com/paper/2409.06343/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 48 references that are in the map.
- First posted on arXiv 10 Sep 2024.

## Builds on (most cited first, 22 of 22)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [signSGD: Compressed Optimisation for Non-Convex Problems](https://mlsanity.com/paper/1802.04434/) (2018)
- [Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Condition](https://mlsanity.com/paper/1608.04636/) (2016)
- [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)
- [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)
- [On Analog Gradient Descent Learning over Multiple Access Fading Channels](https://mlsanity.com/paper/1908.07463/) (2019)
- [Communication-Efficient and Distributed Learning Over Wireless Networks: Principles and Applications](https://mlsanity.com/paper/2008.02608/) (2020)
- [Optimized Power Control Design for Over-the-Air Federated Edge Learning](https://mlsanity.com/paper/2106.09316/) (2021)
- [Blind Federated Edge Learning](https://mlsanity.com/paper/2010.10030/) (2020)
- [Federated Learning via Intelligent Reflecting Surface](https://mlsanity.com/paper/2011.05051/) (2020)
- [Joint Privacy Enhancement and Quantization in Federated Learning](https://mlsanity.com/paper/2208.10888/) (2022)
- [Accelerated Gradient Descent Learning over Multiple Access Fading Channels](https://mlsanity.com/paper/2107.12452/) (2021)
- [Scalable Hierarchical Over-the-Air Federated Learning](https://mlsanity.com/paper/2211.16162/) (2022)
- [Hierarchical Over-the-Air Federated Learning with Awareness of Interference and Data Heterogeneity](https://mlsanity.com/paper/2401.01442/) (2024)
- [Federated Learning via Lattice Joint Source-Channel Coding](https://mlsanity.com/paper/2403.01023/) (2024)
- [Communication-Efficient Federated Learning over MIMO Multiple Access Channels](https://mlsanity.com/paper/2206.05723/) (2022)
- [Accelerating Distributed Optimization via Over-the-Air Computing](https://mlsanity.com/paper/2212.14003/) (2022)
- [Wireless Network Coding with Intelligent Reflecting Surfaces](https://mlsanity.com/paper/2103.11982/) (2021)

## Built on by (most cited first, 5 of 5)

- [Over-the-Air Federated Learning via Weighted Aggregation](https://mlsanity.com/paper/2409.07822/) (2024)
- [Over-the-Air Federated Learning: Rethinking Edge AI Through Signal Processing](https://mlsanity.com/paper/2512.03719/) (2025)
- [Out-of-Air Computation: Enabling Structured Function Extraction from Wireless Superposition](https://mlsanity.com/paper/2604.04312/) (2026)
- [AirPASS: Over-the-Air Federated Learning via Pinching Antenna Systems](https://mlsanity.com/paper/2607.06768/) (2026)
- [Progressive-Resolution Secure Aggregation for Federated Learning](https://mlsanity.com/paper/2610.00695/) (2026)

## Abstract (arXiv)

This paper introduces a federated learning framework that enables over-the-air computation via digital communications, using a new joint source-channel coding scheme. Without relying on channel state information at devices, this scheme employs lattice codes to both quantize model parameters and exploit interference from the devices. We propose a novel receiver structure at the server, designed to reliably decode an integer combination of the quantized model parameters as a lattice point for the purpose of aggregation. We present a mathematical approach to derive a convergence bound for the proposed scheme and offer design remarks. In this context, we suggest an aggregation metric and a corresponding algorithm to determine effective integer coefficients for the aggregation in each communication round. Our results illustrate that, regardless of channel dynamics and data heterogeneity, our scheme consistently delivers superior learning accuracy across various parameters and markedly surpasses other over-the-air methodologies.