Outage Performance for Compute-and-Forward in Generalized Multi-Way Relay Channels

The compute-and-forward (CPF) relaying strategy proposed by Nazer and Gastpar has been proven to achieve a significant improvement in "computation rate" than conventional relaying strategies in the multiple-access channel (MAC). Although there has been some recent work on the implementations of CPF, to our best knowledge, there is no published work that has analysed the outage performance of CPF for the multi-way relay channel (MWRC). In this paper, we apply the CPF strategy in generalized MWRCs. Outage probabilities for both non-network coding (Non-NC) and CPF are derived. The numerical results show that CPF can achieve a 7 dB gain in comparison with Non-NC at the outage probability of 10^-2 in the canonical two-way relay channel. It is also demonstrated that CPF is superior to Non-NC in outage performance in the MWRCs with relatively small number of users.