On the Benefit of Network Coding in Wireless Relay Networks

Our investigation of wireless relay networks begins by studying the two-way relay channel (TRC), in which a user and a base station exchange their messages with the help of a middle relay. We model the TRC as a three-node point-to-point relay network and propose practical symbol-level network coding schemes for the three-node network. We obtain several rate regions achievable by the network coding schemes and show that the use of symbol-level network coding rather than routing alone always enlarges the achievable rate region. Inparticular, the use of symbol-level network coding always increases the maximum equal-rate throughput. Furthermore, we model a cellular relay network consisting of multiple users, multiple relays and multiple base stations as a collection of two-node point-to-point systems and three-node point-to-point relay networks where each point-to-point channel is modeled as a bandlimited Gaussian channel. We propose several practical symbol-level network coding schemes on the network and investigate the benefit of symbol-level network coding by simulation. Our simulation results show that the use of symbol-level network coding rather than routing alone increases the average maximum equal-rate throughput over all users.;Next, we investigate several models of TRC including the discrete memoryless TRC, the Gaussian TRC and the bandlimited Gaussian TRC, and prove an outer bound on the capacity region of each of the TRC models. In particular, the outer bound on the capacity region of the bandlimited Gaussian TRC is a theoretical outer bound on the capacity region achievable by physical-layer network coding (PNC). Furthermore, we model a cellular relay network consisting of multiple users, multiple relays and multiple base stations as a collection of two-node point-to-point systems and three-node networks, where each two-node point-to-point system consists of two bandlimited Gaussian channels and each three-node network consists of a bandlimited Gaussian TRC. We obtain performance bounds of PNC on the cellular relay network by simulation and our simulation results show that the average maximum equal-rate throughput over all users under every PNC strategy investigated is generally worse than the average equal-rate throughput over all users under some routing strategy. This is possibly due to larger interference among the nodes under the PNC strategies compared with the routing strategy.