We study the transmission over a cloud radio access network in which multiple base stations, acting as relay nodes, are connected to a central processor (CP) via error-free rate-limited backhaul links. We propose two lattice-based coding schemes. In the first scheme, each relay node decodes linear combinations of the users' messages in the spirit of compute-and-forward (CoF), but departs from it essentially in that the decoded equations are remapped to equations on the users' input symbols, sent compressed in a lossy manner to the CP, and are not required to be linearly independent. The compression accounts for the correlation between equations at the relay nodes through Wyner-Ziv coding. Also, by opposition to the standard CoF, an appropriate multi-user decoder is utilized to recover the sent messages. The second scheme generalizes the first one by also allowing, at each relay node, a joint compression of the decoded equation on the users' input symbols and the received signal. Both schemes apply in general, but are especially suited for situations in which there are more users that relays. We show that both schemes can outperform standard CoF and successive Wyner-Ziv schemes in certain regimes, and illustrate the gains through some numerical examples.
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