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We investigate a two-way relay (TWR) fading channel where two source nodes wish to exchange information with the help of a relay node. Given traditional TWR protocols, transmission rates in both directions are known to be limited by the hop with lower capacity, i.e., the min operations between uplink and downlink. In this paper, we propose a new transmission protocol, called alternative awaiting and broadcast (AAB), to cancel the min operations in the TWR fading channels. The operational principles, a new upper bound on ergodic sum capacity (ESC), and a convergence behavior of the average delay of signal transmission (ST) (in the relay buffer) for the proposed AAB protocol are analyzed. Moreover, we propose a suboptimal encoding/decoding solution for the AAB protocol and derive an achievable ergodic sum rate (ESR) with a corresponding average delay of ST. Numerical results show that 1) the proposed AAB protocol significantly improves the achievable ESR compared with the traditional TWR protocols, and 2) considering the average delay of system service (SS) (in the source buffer), the average delay of ST induced by the proposed AAB protocol is very small and negligible.