This paper considers a communication network comprised of two nodes, which have no mutual direct communication links, communicating two-way with the aid of a common relay node (RN), also known as separated two-way relay (TWR) channel. We first recall a cut-set outer bound for the set of rates in the context of this network topology assuming full-duplex transmission capabilities. Then, we derive a new achievable rate region based on hash-and-forward (HF) relaying where the RN does not attempt to decode but instead hashes its received signal, and show that under certain channel conditions it coincides with Shannon's inner-bound for the two-way channel [1]. Moreover, for binary adder TWR channel with additive noise at the nodes and the RN we provide a detailed capacity achieving coding scheme based on structure codes.
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