Multihop compute‐and‐forward for generalised two‐way relay channels

Abstract

The compute-and-forward (CaF) relaying strategy recently proposed by Nazer and Gastpar has been proven to achieve significant improvements in 'computation rate' than conventional relaying strategies in the multiple-access channel. Although there have been some recent efforts on the implementations of CaF, to the best of our knowledge, there has been no published work that analyses the outage performance of CaF in the multihop two-way relay channel (MH-TRC). In this paper, we extend the original CaF strategy to multihop CaF (MH-CaF) and investigate the outage performance of the proposed MH-CaF in the generalised MH-TRC. The transmission strategy of MH-CaF for the L-node K-message MH-TRC is generalised. The network throughput of MH-CaF is proven to be significantly better than the non-network coding (Non-NC) scheme for the MH-TRC with a large number of messages. The outage probabilities for both Non-NC and MHCaF schemes are derived for comparison. Numerical results show that for a five-node MH-TRC, MH-CaF can achieve a better outage performance than Non-NC when the number of messages is less than 12. Furthermore, it is also demonstrated that MH-CaF is always superior to Non-NC in outage performance when the number of nodes of the MH-TRC is relatively large.

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