Outage behavior of bidirectional half-duplex relaying schemes

Two-phase and three-phase decode-and-forward schemes with network coding for the two-way (bidirectional) relay channel with Rayleigh-fading are considered. All nodes are half-duplex constrained. Closed form expressions of the outage probability for the two-phase scheme and the three-phase scheme with symmetric rate and time-allocation with Gaussian distributed channel inputs are derived, necessary conditions on achieving diversity for discrete channel inputs are given and practical coding schemes based on turbo codes are considered. It is shown analytically as well as by simulating the practical coding schemes that a diversity gain is achievable for the three-phase scheme as opposed to the two-phase scheme. Moreover, it is shown that for discrete channel inputs the three-phase scheme allows a diversity gain for higher rates compared to a conventional relaying scheme without network coding.