Interference alignment and the generalized degrees of freedom of the X channel

We study the sum capacity of the X channel generalization of the symmetric 2-user interference channel. In this X channel, there are 4 independent messages, one from each transmitter to each receiver. We characterize the sum capacity of a deterministic version of this channel, and obtain the generalized degrees of freedom characterization for the Gaussian version. The regime where the X channel outperforms the underlying interference channel is explicitly identified, and an interesting interference alignment scheme based on a cyclic decomposition of the signal space is shown to be optimal in this regime.