In this talk, we discuss the capacity region for the Gaussian parallel two-way
relay channel (TWRC) which is a relevant model for TWRC with inter-symbol
interference, MIMO-TWRC, etc. We first consider the corresponding linear
deterministic model whose capacity region can be completely characterized and
then propose a compute-and-forward scheme for the Gaussian parallel TWRC based
on lattice codes. The coding scheme is asymptotically optimal and achieves the
capacity region to within a constant gap. We then propose a novel coding
scheme
for compute-and-forward where lattices over Eisenstein integers are used. We
show that our construction provides better performance than that provided by
the
construction of Nazer and Gastpar.