Complex Field Network Coding for Multiuser Cooperative Communications

Multi-source relay-based cooperative communications can achieve spatial diversity gains, enhance coverage and potentially increase capacity when multiuser detection is used to effect maximum likelihood demodulation. If considered for large networks, traditional relaying entails loss in spectral efficiency that can be mitigated through network coding at the physical layer. These considerations motivate the complex field network coding (CFNC) approach introduced in this paper. Different from network coding over the Galois field, where wireless throughput is limited as the number of sources increases, CFNC always achieves throughput as high as 1/2 symbol per source per channel use. In addition to improved throughput, CFNC- based relaying achieves full diversity gain regardless of the underlying signal-to-noise-ratio (SNR) and the constellation used. Furthermore, the CFNC approach is general enough to allow for transmissions from sources to a common destination as well as simultaneous information exchanges among sources.