K-user fading interference channels: The ergodic very strong case

Sufficient conditions required to achieve the interference-free capacity region of ergodic fading K-user interference channels (IFCs) are obtained. In particular, this capacity region is shown to be achieved when every receiver decodes all K transmitted messages such that the channel statistics and the water-filling power policies for all K (interference-free) links satisfy a set of K(K - 1) ergodic very strong conditions. The result is also of independent interest in combinatorics.