Recently, network coding has been actively studied to increase the spectral efficiency of two-way relay wireless channels such as cellular systems as well as broadcasting systems. In this paper, we derive the average transmission capacity and the outage probability of a network coding system, which utilizes two-way data transmission via the best relay rather than multiple relays. Since the data unbalance between the forward and the reverse link in two-way communication systems exists, we include the asymmetric link as well as the symmetric link in the analysis. It is noticed that the space diversity gain increases as the increase of the number of relays. Also we obtain 11.4 dB signal-to-noise ratio (SNR) gain with 9 relays compared to that with single relay in symmetrical link at the given conditions. In asymmetrical links, we denotes that the outage probability is more sensitive to the number of relays rather than data unbalance between the links.