is omitted here. It should be noted that for cases (b) and (e) in the lemma, we use Han-Kobayashi style encoding and decoding for the first layer of the codebook. This is because, the power allocated to this level is not sufficient enough to reap the advantages of lattice coding. Figure \[fig : HK vs lattice 1\] compares the symmetric rate point achievable using the layered lattice coding approach with the maximum symmetric rate that can be achieved using Han-Kobayashi scheme for $a = 2.5$ and $a = \frac{1}{3}$. Note that in our layered lattice coding approach, we restrict ourselves to identical power splitting approach by all the transmitters. This can be generalized to different power splitting schemes and can possibly give better results. However, it is interesting to note that even a possibly suboptimal lattice coding scheme significantly outperforms the extension of the Han-Kobayashi scheme.

![Comparing Han-Kobayashi and Layered Lattice Coding for $a = 2.5$[]{data-label="fig : HK vs lattice 1"}](HKvsLattice){width="3.5"}

This shows that while the Han-Kobayashi coding scheme (message splitting and random coding) is optimal to within one bit for a two user Gaussian IC [@EtkinTseWang2007], it is not optimal even in terms of degrees of freedom for larger 