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The bidirectional relay channel, in which two users communicate with each other through a relay node, is a simple but fundamental and practical network architecture. In this paper, we consider the block fading bidirectional relay channel with a decode-and-forward relay and propose efficient transmission strategies that exploit the block fading property of the channel. We assume that a direct link between the two users is not present and consider two transmission modes: 1) the multiple-access mode (both users transmit to the relay) and 2) the broadcast mode (the relay transmits to both users). Most existing relaying protocols assume a fixed schedule for using these transmission modes. In contrast, we abandon the restriction of having a fixed and predefined schedule and propose to optimize the selection of the transmission modes and the associated transmission rates based on the instantaneous channel state …