  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
waterfilling 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.
