Sum-capacity of a class of K-user Gaussian interference channels within O(K) bits

Though the capacity of the 2-user Gaussian interference channel has long eluded information theorists, recent progress has been made by focussing on approximations with provable bounds. However, extensions to a general K-user network has proven to be non-obvious, in particular due to the role of interference alignment in these cases. In this paper, we look at a special case of a K-user Gaussian interference network where only one of the users interferes with and is also interfered by all the other users. We determine the sum-capacity of such a network within O(K) bits for all possible values of the channel parameters, provided the direct signal is stronger than the receiver noise.