Federated learning (FL) can lead to significant communication overhead and reliance on a central server. To address these challenges, decentralized federated learning (DFL) has been proposed as a more resilient framework. DFL involves parameter exchange between devices through a wireless network. This study analyzes the performance of resource-constrained DFL using different communication schemes (digital and analog) over wireless networks to optimize communication efficiency. Specifically, we provide convergence bounds for both digital and analog transmission approaches, enabling analysis of the model performance trained on DFL. Furthermore, for digital transmission, we investigate and analyze resource allocation between computation and communication and convergence rates, obtaining its communication complexity and the minimum probability of correction communication required for convergence guarantee. For analog transmission, we discuss the impact of channel fading and noise on the model performance and the maximum errors accumulation with convergence guarantee over fading channels. Finally, we conduct numerical simulations to evaluate the performance and convergence rate of convolutional neural networks (CNNs) and Vision Transformer (ViT) trained in the DFL framework on fashion-MNIST and CIFAR-10 datasets. Our simulation results validate our analysis and discussion, revealing how to improve performance by optimizing system parameters under different communication conditions.

翻译：联邦学习（FL）可能导致显著的通信开销和对中心服务器的依赖。为解决这些挑战，去中心化联邦学习（DFL）被提出作为一种更具鲁棒性的框架。DFL通过无线网络实现设备间的参数交换。本研究分析了采用不同通信方案（数字与模拟）的资源受限DFL在无线网络中的性能，以优化通信效率。具体而言，我们为数字和模拟传输方法提供了收敛界，从而能够分析基于DFL训练的模型性能。此外，针对数字传输，我们研究并分析了计算与通信资源分配及收敛速率，获得了其通信复杂度以及保证收敛所需的最小纠错通信概率。针对模拟传输，我们讨论了信道衰落和噪声对模型性能的影响，以及衰落信道上保证收敛的最大误差累积。最后，我们利用卷积神经网络（CNN）和视觉Transformer（ViT）在Fashion-MNIST和CIFAR-10数据集上，对DFL框架下的训练性能和收敛速率进行了数值仿真。仿真结果验证了我们的分析与讨论，揭示了如何通过优化不同通信条件下的系统参数来提升性能。