Design of binary network codes for multiuser multiway relay networks

We study multiuser multiway relay networks where N user nodes exchange their information through a single-relay node. We use network coding (NC) in the relay to increase the throughput. Due to the limitation of complexity, we only consider the binary multiuser NC (BMNC) in the relay. We study the BMNC matrix [in GF(2)] and propose several design criteria on the BMNC matrix to improve the symbol error probability (SEP) performance. Closed-form expressions of the SEP of the system are provided. Moreover, an upper bound of the SEP is also proposed to provide further insights into system performance. Then, BMNC matrices are designed to minimize error probabilities.