The sum-capacity of the symmetric linear deterministic Complete K-user Z-Interference Channel

We consider a K-user interference channel in which the channel gains from transmitter i to receiver j > i are 0, resulting in a type of Z interference channel which we term the Complete K-user Z Interference Channel which has not been explicitly studied. We first consider the symmetric linear high SNR deterministic approximation of the Gaussian noise channel. For this model, we provide an outer bound which may be achieved, thereby obtaining the sum-capacity. The outer bound is obtained by providing two types of side-information: the first reduces the channel model to one in which each receiver sees a sum of the direct and interference terms, the second is reminiscent of the Etkin-Tse-Wang side-information for the interference channel. It is noted that the sum-capacity is a function of the number of users K and is larger than the “W” curve for the fully connected K-user interference channel, but reduces to it as K → ∞.