  The compute-and-forward (CoF) is a relaying protocol, which uses algebraic
structured codes to harness the interference and remove the noise in wireless
networks. We propose the use of phase precoders at the transmitters of a
network, where relays apply CoF strategy. We define the {\em phase precoded
computation rate} and show that it is greater than the original computation
rate of CoF protocol. We further give a new low-complexity method for finding
network equations. We finally show that the proposed precoding scheme increases
the degrees-of-freedom (DoF) of CoF protocol. This overcomes the limitations on
the DoF of the CoF protocol, recently presented by Niesen and Whiting. Using
tools from Diophantine approximation and algebraic geometry, we prove the
existence of a phase precoder that approaches the maximum DoF when the number
of transmitters tends to infinity.
