Superimposed XOR: Approaching Capacity Bounds of the Two-Way Relay Channels

In two-way relay channels, bitwise XOR and symbol-level superposition coding are two popularnetwork-coding based relaying schemes. However, neither of them can approach the capacity boundwhen the channels in the broadcast phase are asymmetric. In this paper, we present a new physicallayer network coding (PLNC) scheme, called superimposed XOR. The new scheme advances the existingschemes by specifically taking into account the channel asymmetry as well as information asymmetry inthe broadcast phase. We obtain its achievable rate regions over Gaussian channels when integrated withtwo known time control protocols in two-way relaying. We also demonstrate their average maximumsum-rates and service delay performances over fading channels. Numerical results show that the proposedsuperimposed XOR achieves a larger rate region than both XOR and superposition and performs muchbetter over fading channels. We further deduce the boundary of its achievable rate region of the broadcastphase in an explicit and analytical expression. Based on these results, we then show that the gap to thecapacity bound approaches zero at high signal-to-noise ratio.