Generalized Wireless Network Coding Schemes for Multihop Two-Way Relay Channels

Due to the overwhelming complexity of multihop transmission and intermessage interference, only a limited amount of research has been carried out in the implementation of wireless network coding (WNC) for generalized multihop two-way relay channels (MH-TRCs), let alone the generalization of multihop WNC (MH-WNC) schemes. Our recent paper has showed that the MH-WNC scheme with fixed two transmission time intervals (TTIs) was unable to always outperform conventional non-NC schemes in outage performance for the MH-TRC with an arbitrary number of nodes. In view of this fact, a generalized MH-WNC scheme with multiple TTIs is designed for the L-node K-message MH-TRC in this paper. Closed-form expressions for the upper bound of the outage probability for two prominent relaying network coding strategies (i.e., analog network coding and compute-and-forward network coding) are derived. Moreover, by investigating the relationships between the outage probability and the numbers of nodes, messages, and TTIs, we obtain an optimal MH-WNC scheme that can achieve the best outage probability and always outperform non-NC in the MH-TRC with an arbitrary number of nodes.