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Federated Learning via Lattice Joint Source-Channel Coding

Seyed Mohammad Azimi-Abarghouyi, Lav R. Varshney

TL;DR

This work addresses the challenge of efficient federated learning over wireless links without channel state information at devices by introducing FedCPU, a lattice-based joint source-channel coding scheme for over-the-air aggregation. The method quantizes model updates with lattice codes, uses dithering for uniform quantization error, and transmits with constant power; at the server, a two-layer receiver decodes an integer combination of quantized updates through lattice decoding, enabling robust, interference-exploiting aggregation. Key contributions include a transmission procedure with zeroCSIT operation, an aggregation scheme based on optimized equalization and lattice decoding, and an optimization framework for choosing aggregation coefficients. Experimental results on MNIST demonstrate that FedCPU outperforms prior over-the-air FL approaches and can closely match ideal untampered performance as the server antenna count grows, highlighting practical viability in heterogeneous, noisy, and low-antenna settings.

Abstract

This paper introduces a universal 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. A novel two-layer receiver structure at the server is designed to reliably decode an integer combination of the quantized model parameters as a lattice point for the purpose of aggregation. Numerical experiments validate the effectiveness of the proposed scheme. Even with the challenges posed by channel conditions and device heterogeneity, the proposed scheme markedly surpasses other over-the-air FL strategies.

Federated Learning via Lattice Joint Source-Channel Coding

TL;DR

This work addresses the challenge of efficient federated learning over wireless links without channel state information at devices by introducing FedCPU, a lattice-based joint source-channel coding scheme for over-the-air aggregation. The method quantizes model updates with lattice codes, uses dithering for uniform quantization error, and transmits with constant power; at the server, a two-layer receiver decodes an integer combination of quantized updates through lattice decoding, enabling robust, interference-exploiting aggregation. Key contributions include a transmission procedure with zeroCSIT operation, an aggregation scheme based on optimized equalization and lattice decoding, and an optimization framework for choosing aggregation coefficients. Experimental results on MNIST demonstrate that FedCPU outperforms prior over-the-air FL approaches and can closely match ideal untampered performance as the server antenna count grows, highlighting practical viability in heterogeneous, noisy, and low-antenna settings.

Abstract

This paper introduces a universal 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. A novel two-layer receiver structure at the server is designed to reliably decode an integer combination of the quantized model parameters as a lattice point for the purpose of aggregation. Numerical experiments validate the effectiveness of the proposed scheme. Even with the challenges posed by channel conditions and device heterogeneity, the proposed scheme markedly surpasses other over-the-air FL strategies.
Paper Structure (10 sections, 2 theorems, 22 equations, 3 figures)

This paper contains 10 sections, 2 theorems, 22 equations, 3 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Setup
  4. Learning Algorithm
  5. Lattice Preliminaries
  6. FedCPU: Compute-Update Scheme
  7. Transmission Scheme
  8. Aggregation Scheme
  9. Experimental Results
  10. Conclusions

Key Result

Theorem 1

The optimal equalization vector for a given coefficient vector $\mathbf{a}$ is

Figures (3)

  • Figure 1: Transmitter structure for device $k$.
  • Figure 2: Receiver structure for the server.
  • Figure 3: Test accuracy (a) for different $M$ values, (b) for different $\rho$ values, and (c) for different FL strategies.

Theorems & Definitions (8)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Theorem 1
  • Remark 1
  • Remark 2
  • Theorem 2