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The authors consider a three-node half-duplex Gaussian relay network where two nodes (say a, b) want to communicate with each other and the third node acts as a relay for this two way communication. Outer bounds and achievable rate regions for the possible rate pairs (Ra;Rb) for two-way communication are investigated. The modes (transmit or receive) of the half-duplex nodes together specify the state of the network. A relaying protocol uses a specific sequence of states and a coding scheme for each state. In this paper, they first obtain an outer bound for the rate region of all achievable (Ra;Rb) based on the half-duplex cut-set bound. This outer bound can be numerically computed by solving a linear program.
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