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Energy-Efficient Channel Decoding for Wireless Federated Learning: Convergence Analysis and Adaptive Design

Linping Qu, Yuyi Mao, Shenghui Song, Chi-Ying Tsui

TL;DR

It is theoretically proved that wireless FL with communication errors can converge at the same rate as the case with error-free communication provided the bit error rate (BER) is properly constrained.

Abstract

One of the most critical challenges for deploying distributed learning solutions, such as federated learning (FL), in wireless networks is the limited battery capacity of mobile clients. While it is a common belief that the major energy consumption of mobile clients comes from the uplink data transmission, this paper presents a novel finding, namely channel decoding also contributes significantly to the overall energy consumption of mobile clients in FL. Motivated by this new observation, we propose an energy-efficient adaptive channel decoding scheme that leverages the intrinsic robustness of FL to model errors. In particular, the robustness is exploited to reduce the energy consumption of channel decoders at mobile clients by adaptively adjusting the number of decoding iterations. We theoretically prove that wireless FL with communication errors can converge at the same rate as the case with error-free communication provided the bit error rate (BER) is properly constrained. An adaptive channel decoding scheme is then proposed to improve the energy efficiency of wireless FL systems. Experimental results demonstrate that the proposed method maintains the same learning accuracy while reducing the channel decoding energy consumption by ~20% when compared to an existing approach.

Energy-Efficient Channel Decoding for Wireless Federated Learning: Convergence Analysis and Adaptive Design

TL;DR

It is theoretically proved that wireless FL with communication errors can converge at the same rate as the case with error-free communication provided the bit error rate (BER) is properly constrained.

Abstract

One of the most critical challenges for deploying distributed learning solutions, such as federated learning (FL), in wireless networks is the limited battery capacity of mobile clients. While it is a common belief that the major energy consumption of mobile clients comes from the uplink data transmission, this paper presents a novel finding, namely channel decoding also contributes significantly to the overall energy consumption of mobile clients in FL. Motivated by this new observation, we propose an energy-efficient adaptive channel decoding scheme that leverages the intrinsic robustness of FL to model errors. In particular, the robustness is exploited to reduce the energy consumption of channel decoders at mobile clients by adaptively adjusting the number of decoding iterations. We theoretically prove that wireless FL with communication errors can converge at the same rate as the case with error-free communication provided the bit error rate (BER) is properly constrained. An adaptive channel decoding scheme is then proposed to improve the energy efficiency of wireless FL systems. Experimental results demonstrate that the proposed method maintains the same learning accuracy while reducing the channel decoding energy consumption by ~20% when compared to an existing approach.
Paper Structure (19 sections, 7 theorems, 35 equations, 12 figures, 3 tables, 1 algorithm)

This paper contains 19 sections, 7 theorems, 35 equations, 12 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Motivation
  3. Contributions
  4. Organization
  5. System Model and Energy Consumption Evaluation
  6. Wireless FL
  7. Energy Consumption Evaluation
  8. LDPC Decoding
  9. Energy-Efficient LDPC Decoding Design
  10. Effect of BER on the Convergence Rate of Wireless FL
  11. BER vs. Number of LDPC Decoding Iterations
  12. LDPC Decoding Iteration Control
  13. Experimental Results
  14. Experimental Settings
  15. Learning Performance of the Baseline Scheme
  16. ...and 4 more sections

Key Result

Lemma 1

Denote $\tilde{\mathbf{w}}$ as the decoded model of $\mathbf{w}$. Based on Assumptions assumption_ber and onebit_error, the $d$-th dimension of $\tilde{\mathbf{w}}$ is given as where $w_{d}$ is the $d$-th dimension of $\mathbf{w}$ and $\delta\left(w_{d}\right)$ is the distortion term. The mean square model error caused by bit errors is given as where $b$ is the BER and $M_{\mathbf{w}} \triangleq

Figures (12)

  • Figure 1: Wireless FL with digital communication and its operations.
  • Figure 2: Digitalization for each parameter in $\tilde{\mathbf{w}}_{r}$ (an example with $N=3$), where a continuous model parameter is mapped to the binary sequence of the nearest boundary.
  • Figure 3: Distortion between the decoded and broadcast global model. Different error bits, e.g., the most significant bit (MSB) and least significant bit (LSB), lead to different model distortion.
  • Figure 4: Validation of the model error analysis in (\ref{['model_error']}) by experiments on the Fashion-MNIST dataset. The experimental setting is detailed in Section \ref{['ex_setting']}. In each communication round, we compute the actual model error between the decoded and broadcast global model on a selected client, and compare with the value calculated by the RHS in (\ref{['model_error']}) with $\mathbf{w}$ setting as $\mathbf{w}_{r}$. It is observed that the analytical and simulation results match closely for different BER conditions. The model errors also show a trend of boundness, which demonstrates the rationality of Assumption \ref{['range_bound']}.
  • Figure 5: Mappings between BER and the maximum number of LDPC decoding iterations at different receive SNRs.
  • ...and 7 more figures

Theorems & Definitions (15)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Remark 1
  • Theorem 1
  • Corollary 1
  • proof
  • Remark 2
  • Lemma 3
  • ...and 5 more