Functional-decode-forward for the general discrete memoryless two-way relay channel

We consider the general discrete memoryless two-way relay channel, where two users exchange messages via a relay, and propose two functional-decode-forward coding strategies for this channel. Functional-decode-forward involves the relay decoding a function of the users´ messages rather than the individual messages themselves. This function is then broadcast back to the users, which can be used in conjunction with the user´s own message to decode the other user´s message. Via a numerical example, we show that functional-decode-forward with linear codes is capable of achieving strictly larger sum rates than those achievable by other strategies.