Wireless relay and network coding are two critical techniques to increase the reliability and throughput of wireless cooperative communication systems. In this paper, a complex field network coding （CFNC） scheme with the K-th best relay selection （KBS） is proposed and investigated, wherein the K-th best relay is selected to forward the multiplexed signal to the destination. First, the upper bound of the symbol error probability （SEP）, the diversity order, and the coding gain are derived for the CFNC scheme with KBS. Then, the coding gain is utilized as the optimized cri- terion to determine the optimal power allocation. It is validated through analysis and simulation that the CFNC scheme with KBS can achieve full diversity only when K=I, while the diversity order decreases with increasing parameter K, and the optimal power allocation can significantly improve the performance of the CFNC scheme with KBS.
