On the optimality of treating interference as noise for K-user compound interference channels

For the K-user interference channel, Geng et al. identify a general condition under which power control and treating interference as noise (TIN) is optimal from the perspective of generalized degrees of freedom (GDoF). In this work, we show that for a K-user compound interference channel, if in every possible state for each receiver, the channel satisfies the TIN-optimality condition of Geng et al., then power control and TIN achieves the entire GDoF region of the compound channel. For an arbitrary compound interference channel, we find a non-trivial counterpart regular interference channel, such that the two have the same TIN region, and the GDoF-optimal power control problems for the two are equivalent.