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Scalable and Reliable Over-the-Air Federated Edge Learning

Maximilian Egger, Christoph Hofmeister, Cem Kaya, Rawad Bitar, Antonia Wachter-Zeh

TL;DR

Federated edge learning (FEEL) faces a communication bottleneck when aggregating high-dimensional updates. The paper investigates over-the-air computation (AirComp) and introduces two lattice-based coding schemes to enable reliable gradient aggregation over an AWGN MAC: a digital balanced numeral lattice code with constant error-correction in the number of clients, and an analog nested lattice code based on Construction A with a modulo-lattice transformation. It derives a per-dimension error bound for the digital scheme that is independent of the number of devices and provides rate and error guarantees for the nested scheme, including a regime where the nested scheme achieves capacity at $K=1$ but scales poorly with $K$. Numerical results corroborate the theoretical findings, showing that balanced numeral codes offer stable error performance as $K$ grows while nested lattices perform better at small $K$ and/or larger block lengths. These results advance scalable, reliable AirComp for FEEL in densely connected edge environments and identify trade-offs that guide practical code design.

Abstract

Federated edge learning (FEEL) has emerged as a core paradigm for large-scale optimization. However, FEEL still suffers from a communication bottleneck due to the transmission of high-dimensional model updates from the clients to the federator. Over-the-air computation (AirComp) leverages the additive property of multiple-access channels by aggregating the clients' updates over the channel to save communication resources. While analog uncoded transmission can benefit from the increased signal-to-noise ratio (SNR) due to the simultaneous transmission of many clients, potential errors may severely harm the learning process for small SNRs. To alleviate this problem, channel coding approaches were recently proposed for AirComp in FEEL. However, their error-correction capability degrades with an increasing number of clients. We propose a digital lattice-based code construction with constant error-correction capabilities in the number of clients, and compare to nested-lattice codes, well-known for their optimal rate and power efficiency in the point-to-point AWGN channel.

Scalable and Reliable Over-the-Air Federated Edge Learning

TL;DR

Federated edge learning (FEEL) faces a communication bottleneck when aggregating high-dimensional updates. The paper investigates over-the-air computation (AirComp) and introduces two lattice-based coding schemes to enable reliable gradient aggregation over an AWGN MAC: a digital balanced numeral lattice code with constant error-correction in the number of clients, and an analog nested lattice code based on Construction A with a modulo-lattice transformation. It derives a per-dimension error bound for the digital scheme that is independent of the number of devices and provides rate and error guarantees for the nested scheme, including a regime where the nested scheme achieves capacity at but scales poorly with . Numerical results corroborate the theoretical findings, showing that balanced numeral codes offer stable error performance as grows while nested lattices perform better at small and/or larger block lengths. These results advance scalable, reliable AirComp for FEEL in densely connected edge environments and identify trade-offs that guide practical code design.

Abstract

Federated edge learning (FEEL) has emerged as a core paradigm for large-scale optimization. However, FEEL still suffers from a communication bottleneck due to the transmission of high-dimensional model updates from the clients to the federator. Over-the-air computation (AirComp) leverages the additive property of multiple-access channels by aggregating the clients' updates over the channel to save communication resources. While analog uncoded transmission can benefit from the increased signal-to-noise ratio (SNR) due to the simultaneous transmission of many clients, potential errors may severely harm the learning process for small SNRs. To alleviate this problem, channel coding approaches were recently proposed for AirComp in FEEL. However, their error-correction capability degrades with an increasing number of clients. We propose a digital lattice-based code construction with constant error-correction capabilities in the number of clients, and compare to nested-lattice codes, well-known for their optimal rate and power efficiency in the point-to-point AWGN channel.
Paper Structure (6 sections, 8 theorems, 19 equations, 2 figures)

This paper contains 6 sections, 8 theorems, 19 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Over-the-Air Federated Learning Model
  3. Balanced Numeral Lattice Codes
  4. Nested Lattice Codes
  5. Comparison
  6. Conclusion

Key Result

Lemma 1

The stochastic quantizer $Q_{\textrm{stoc}}$ preserves the expectation of the gradient, i.e. where the expectation is over the randomness of the quantizer.

Figures (2)

  • Figure 1: A simplified illustration of an over-the-air federated learning setting. The $K$ edge devices transmit simultaneously to the federator. The federator observes the noisy sum.
  • Figure 2: Comparison of experimental probability of errors of Nested Lattice and Balanced Numeral codes for AirComp.

Theorems & Definitions (10)

  • Lemma 1
  • Theorem 2
  • proof
  • Corollary 1
  • Theorem 3
  • Theorem 4
  • proof : Sketch of Proof
  • Lemma 5
  • Lemma 6
  • Corollary 2