Recently proposed coded bi-directional relaying protocols increase the spectral efficiency by using network codes, which rely on joint packet encoding and exploitation of previously transmitted and stored information. In this letter, we derive the cumulative density function (CDF) and the probability density function (PDF) of received signal-to-noise ratios (SNRs) for two-phase and three-phase bi-directional coded relaying protocols, respectively, over Rayleigh fading channels. Using these results, we compare the outage performances as well as the average capacities of the protocols. From the numerical observations, we can see that the two-phase protocol has better link-level performances than the three-phase protocol when required data rate is greater than 2 for outate performance and transmit SNR at each node is greater than 18dB for average capacity, respectively. Otherwise, the three-phase protocol performs better.