In this paper, we study two models for self or loopback interference cancellation in full-duplex wireless communications. Both models are based on an underlying Z-channel with side information. We obtain achievable rate regions with suitable coding schemes under both models. Under model 1, where the self-interference channel gain is random, we employ training to estimate the unknown gain, and optimize the required training time. Under model 2, where the self-interference gain is exactly known, we show that the capacity of an ideal full-duplex node can be realized even when the side information is low rate and quantized. Our results show that loopback interference, rather than being treated as noise, can be effectively dealt with by suitable coding. © 2012 IEEE.