an IC with more than two users. In [@ShangKramerChen2007]–[@MotahariKhandani], the sum capacity of the two user Gaussian IC has been determined for a range of “weak" interference cases.

For interference networks with more than two transmitter-receiver pairs, degrees of freedom characterization (capacity approximations within $o(\log(\mbox{SNR}))$) have been found for a class of time or frequency varying channels in [@CadambeJafarInt]–[@ShenMadsenVidal]. These results do not apply to interference networks with channels that are not time or frequency varying. For fixed interference networks, very little is known even about its degrees of freedom characterization. In [@CadambeJafarShamai], some examples of $K$ user ICs are presented which come close to achieving $K/2$ degrees of freedom. However, for general $K$ user ICs with fixed channel gains, only one degree of freedom has been achieved, whereas the best outer bound on the total degrees of freedom is $K/2$ as derived in [@MadsenNosratinia]. The fundamental problem, we believe, is the achievable strategy that forms the baseline of study - the Han-Kobayashi scheme [@HanKobayashi1981]. In this paper, we use a layered lattice coding scheme to provide rate improvements in a three user IC over what can be obtained using the layered random coding scheme used in [@HanKobayashi1981]. We also 