Linear block physical-layer network coding for multiple-user multiple-relay wireless networks

We propose a novel scheme for physical-layer network coding (PNC), constructed from linear block codes for multiple-user multiple-relay wireless networks. In the proposed design, each relay computes a linear combination of source symbols, namely, the network coded symbol (NCS) and forwards it to the destination. The destination collects all NCSs and the original source symbols to form a valid codeword of the linear code. The resulting codeword can be decoded to reliably extract the original source symbols. The numerical results show that our proposed design provides m-th order diversity when there are m relays. Moreover, the proposed design provides a significant sum-rate enhancement over the orthogonal multiple access scheme with network coding described in previous literature.