Compute-forward is a coding technique that enables receiver(s) in a network to directly decode one or more linear combinations of the transmitted codewords. Initial efforts focused on Gaussian channels and derived achievable rate regions via nested lattice codes and single-user (lattice) decoding as well as sequential (lattice) decoding. Recently, these results have been generalized to discrete memoryless channels via nested linear codes and joint typicality coding, culminating in a simultaneous-decoding rate region for recovering one or more linear combinations from $K$ users. Using a discretization approach, this paper translates this result into a simultaneous-decoding rate region for a wide class of continuous memoryless channels, including the important special case of Gaussian channels. Additionally, this paper derives a single, unified expression for both discrete and continuous rate regions via an algebraic generalization of R\'enyi's information dimension.

翻译：计算前方是一种编码技术,使网络中的接收者能够直接解码传送的编码词的一个或多个线性组合。初步工作的重点是高斯河道和通过嵌套的拉蒂斯码和单一用户(拉特斯)解码以及顺序(拉特斯)解码,最近,这些结果通过嵌套的线性编码和共同的典型编码,被普遍化为离散的无记忆通道,最终形成一个同时解码率区域,以便从$K$用户中回收一个或多个线性组合。本文采用分解方法,将这一结果转化为一个同时解码率区域,用于广泛的连续无记忆的频道,包括高斯河道的重要特殊案例。此外,本文通过对R\'enyi信息层面的代谢式概括,为离散和连续速率区域提供了一个单一的统一表达方式。