  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.
