  We consider the 2\times 2\times 2 multiple-input multipleoutput interference
channel where two source-destination pairs wish to communicate with the aid of
two intermediate relays. In this paper, we propose a novel lattice strategy
called Aligned Precoded Compute-and-Forward (PCoF). This scheme consists of two
phases: 1) Using the CoF framework based on signal alignment we transform the
Gaussian network into a deterministic finite field network. 2) Using linear
precoding (over finite field) we eliminate the end-to-end interference in the
finite field domain. Further, we exploit the algebraic structure of lattices to
enhance the performance at finite SNR, such that beyond a degree of freedom
result (also achievable by other means). We can also show that Aligned PCoF
outperforms time sharing in a range of reasonably moderate SNR, with increasing
gain as SNR increases.
