On the sum capacity of K-user cascade Gaussian Z-interference channel

A K-user cascade Gaussian Z-interference channel is a subclass of the general K-user Gaussian interference channel, where each user, except the first one, experiences interference only from the previous user. Under simple Han-Kobayashi schemes assuming Gaussian inputs and no time sharing, it is shown that the maximum sum rate is achieved by each user transmitting either common or private signals. For K = 3, channel conditions under which the achieved sum rate is either equal to or within 0.5 bits to the sum capacity are identified.