Cooperative Compute-and-Forward

We propose a class of signaling schemes that leverage transmitter cooperation in wireless networks employing compute-and-forward or physical-layer network coding. We devise a lattice-coding approach to superposition block Markov encoding from which we construct a cooperative lattice coding strategy. Transmitters broadcast lattice codewords, decode each other's messages, and then cooperatively transmit resolution information which aids relays in decoding finite-field linear combinations of the incoming messages. We show that cooperation provides a substantial improvement in achievable computation rate and outage probability over noncooperative strategies. Using this strategy, we derive a new achievability scheme for the multiway relay channel, the rates of which are near capacity in many regimes and enjoy a diversity advantage over noncooperation.