Design of Binary Network Codes for Multi-user Multi-way Relay Networks

We study multi-user multi-way relay networks where $N$ user nodes exchange their information through a single relay node. We use network coding in the relay to increase the throughput. Due to the limitation of complexity, we only consider the binary multi-user network coding (BMNC) in the relay. We study 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 on system performance. Then BMNC matrices are designed to minimize the error probabilities.