On the Optimality of Simple Han-Kobayashi Schemes for Gaussian Interference Channels

The Generalized Degrees of Freedom (GDoF) region of the 2-user Gaussian Interference Channel (GIC) was derived by Etkin, Tse and Wang. This GDoF region is achieved using the class of Han-Kobayashi (HK) schemes. For $K$-user GICs with $K > 2$, the GDoF region is not known completely. For the $K$-user GIC, Geng et al. derived the channel conditions under which Gaussian signalling and Treating Interference as Noise (TIN) is GDoF optimal. The TIN scheme also belongs to the class of HK schemes. In this paper, we derive conditions under which Simple HK (S-HK) schemes are GDoF optimal for general $K$-user GICs. Simple HK schemes are HK schemes with Gaussian signalling, no time sharing, and no private-common power splitting. The class of simple HK schemes includes the TIN scheme and schemes that involve various levels of interference decoding and cancellation at each receiver.