Lossy compression for compute-and-forward in limited backhaul wireless relay networks

Abstract

We study the transmission over a cloud radio access network in which multiple relays are connected to a central processor (CP) via error-free finite-capacity links. We develop a lattice-based coding scheme in which each relay node computes a linear combination of the users' messages, in the spirit of standard compute-and-forward (CoF). However, rather than forwarding the computed equation to the CP as in standard CoF, the relay first maps this equation into one on the users' input symbols and then compresses it jointly with its channel output. The equations need not be linearly independent, and the compression also takes into account the correlation with the equations and channel outputs at other relay nodes through Wyner-Ziv coding. The CP first decompresses the signals and then decodes the users' messages successively. We analyze the sum-rate offered by this coding scheme, and show that it outperforms successive Wyner-Ziv scheme in all regimes, and it improves strictly upon the best of successive Wyner-Ziv and CoF in certain regimes.