  We present a nested lattice-code-based strategy that achieves the
random-coding based Compress-and-Forward (CF) rate for the three node Gaussian
relay channel. To do so, we first outline a lattice-based strategy for the
$(X+Z_1,X+Z_2)$ Wyner-Ziv lossy source-coding with side-information problem in
Gaussian noise, a re-interpretation of the nested lattice-code-based Gaussian
Wyner-Ziv scheme presented by Zamir, Shamai, and Erez. We use the notation
$(X+Z_1,X+Z_2)$ Wyner-Ziv to mean that the source is of the form $X+ Z_1$ and
the side-information at the receiver is of the form $X+ Z_2$, for independent
Gaussian $X, Z_1$ and $Z_2$. We next use this $(X+Z_1,X+Z_2)$ Wyner-Ziv scheme
to implement a "structured" or lattice-code-based CF scheme which achieves the
classic CF rate for Gaussian relay channels. This suggests that lattice codes
may not only be useful in point-to-point single-hop source and channel coding,
in multiple access and broadcast channels, but that they may also be useful in
larger relay networks. The usage of lattice codes in larger networks is
motivated by their structured nature (possibly leading to rate gains) and
decoding (relatively simple) being more practically realizable than their
random coding based counterparts. We furthermore expect the proposed
lattice-based CF scheme to constitute a first step towards a generic structured
achievability scheme for networks such as a structured version of the recently
introduced "noisy network coding".
