  We introduce a generalized two-way relay channel where two sources exchange
information (not necessarily of the same rate) with help from a relay, and each
source additionally sends private information to the relay. We consider the
Gaussian setting where all point-to-point links are Gaussian channels. For this
channel, we consider a two-phase protocol consisting of a multiple access
channel (MAC) phase and a broadcast channel (BC) phase. We propose a general
decode-and-forward (DF) scheme where the MAC phase is related to computation
over MAC, while the BC phase is related to BC with receiver side information.
In the MAC phase, we time share a capacity-achieving code for the MAC and a
superposition code with a lattice code as its component code. We show that the
proposed DF scheme is near optimal for any channel conditions, in that it
achieves rates within half bit of the capacity region of the two-phase
protocol.
