  In a recent work, Nazer and Gastpar proposed the Compute-and-Forward strategy
as a physical-layer network coding scheme. They described a code structure
based on nested lattices whose algebraic structure makes the scheme reliable
and efficient. In this work, we consider the implementation of their scheme for
real Gaussian channels and one dimensional lattices. We relate the maximization
of the transmission rate to the lattice shortest vector problem. We explicit,
in this case, the maximum likelihood criterion and show that it can be
implemented by using an Inhomogeneous Diophantine Approximation algorithm.
