Federated edge learning (FEEL) is a popular framework for model training at an edge server using data distributed at edge devices (e.g., smart-phones and sensors) without compromising their privacy. In the FEEL framework, edge devices periodically transmit high-dimensional stochastic gradients to the edge server, where these gradients are aggregated and used to update a global model. When the edge devices share the same communication medium, the multiple access channel from the devices to the edge server induces a communication bottleneck. To overcome this bottleneck, an efficient broadband analog transmission scheme has been recently proposed, featuring the aggregation of analog modulated gradients (or local models) via the waveform-superposition property of the wireless medium. However, the assumed linear analog modulation makes it difficult to deploy this technique in modern wireless systems that exclusively use digital modulation. To address this issue, we propose in this work a novel digital version of broadband over-the-air aggregation, called one-bit broadband digital aggregation (OBDA). The new scheme features one-bit gradient quantization followed by digital modulation at the edge devices and a majority-voting based decoding at the edge server. We develop a comprehensive analysis framework for quantifying the effects of wireless channel hostilities (channel noise, fading, and channel estimation errors) on the convergence rate. The analysis shows that the hostilities slow down the convergence of the learning process by introducing a scaling factor and a bias term into the gradient norm. However, we show that all the negative effects vanish as the number of participating devices grows, but at a different rate for each type of channel hostility.

中文翻译：

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用于高效通信的联合边缘学习的一位无线聚合：设计和收敛分析

联合边缘学习 (FEEL) 是一种流行的框架，用于在边缘服务器上使用分布在边缘设备（例如，智能手机和传感器）上的数据进行模型训练，而不会损害其隐私。在 FEEL 框架中，边缘设备周期性地将高维随机梯度传输到边缘服务器，这些梯度被聚合并用于更新全局模型。当边缘设备共享相同的通信介质时，从设备到边缘服务器的多路访问通道会导致通信瓶颈。为了克服这个瓶颈，最近提出了一种有效的宽带模拟传输方案，其特点是通过无线介质的波形叠加特性聚合模拟调制梯度（或局部模型）。然而，假定的线性模拟调制使得很难在专门使用数字调制的现代无线系统中部署这种技术。为了解决这个问题，我们在这项工作中提出了一种新的数字版本的宽带无线聚合，称为一位宽带数字聚合 (OBDA)。新方案采用一位梯度量化，然后在边缘设备进行数字调制，并在边缘服务器进行基于多数投票的解码。我们开发了一个综合分析框架，用于量化无线信道敌对性（信道噪声、衰落和信道估计误差）对收敛速度的影响。分析表明，敌意通过在梯度范数中引入缩放因子和偏差项来减慢学习过程的收敛速度。然而，