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In this paper, achievable rates and resource allocation strategies for imperfectly known two-way relay fading channels are studied. Decode-and-forward (DF) relaying is considered. It is assumed that communication starts with the network training phase in which the users and the relay estimate the fading coefficients, albeit imperfectly. Subsequently, data transmission is performed in multiple-access and broadcast phases. In both phases, achievable rate regions are identified by treating the terms that arise due to channel estimation errors and imperfect interference cancellation as Gaussian distributed noise components. The achievable rate region of the two-way relay channel is given by the intersection of the achievable rate regions of multiple-access and broadcast phases. The impact of several training and transmission parameters (such as training power levels, time/bandwidth allocated to the multiple access and broadcast phases, and relay power allocation parameter) on the achievable rate regions and sum rates is investigated.