  In this letter, the problem of implementing compute and forward (CF) is
addressed. We present a practical signal model to implement CF which is built
on the basis of Gaussian integer lattice partitions. We provide practical
decoding functions at both relay and destination nodes thereby providing a
framework for complete analysis of CF. Our main result is the analytical
derivation and simulations based validation of union bound of probability of
error for end to end performance of CF. We show that the performance is not
limited by the linear combination decoding at the relay but by the full rank
requirement of the coefficient matrix at the destination.
