This paper introduces a 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. We propose a novel receiver structure at the server, designed to reliably decode an integer combination of the quantized model parameters as a lattice point for the purpose of aggregation. We present a mathematical approach to derive a convergence bound for the proposed scheme and offer design remarks. In this context, we suggest an aggregation metric and a corresponding algorithm to determine effective integer coefficients for the aggregation in each communication round. Our results illustrate that, regardless of channel dynamics and data heterogeneity, our scheme consistently delivers superior learning accuracy across various parameters and markedly surpasses other over-the-air methodologies.

翻译：本文提出了一种联邦学习框架，通过数字通信实现空中计算，采用了一种新颖的联合信源-信道编码方案。该方案无需依赖设备端的信道状态信息，而是利用格码对模型参数进行量化，并有效利用来自设备的干扰。我们提出了一种新颖的服务器端接收机结构，旨在可靠地将量化模型参数的整数组合解码为一个格点，以实现聚合目的。我们提出了一种数学方法来推导所提方案的收敛界，并提供了设计要点。在此背景下，我们建议了一种聚合度量指标及相应的算法，以确定每个通信轮次中用于聚合的有效整数系数。我们的结果表明，无论信道动态特性和数据异质性如何，所提方案在各种参数设置下均能持续提供更优的学习精度，并显著超越其他空中计算方法。