Interference alignment at finite SNR: General message sets

Interference alignment has proven to be a powerful tool in characterizing the high SNR behavior of wireless networks. Using this technique, Cadambe and Jafar showed that the sum degrees-of-freedom for the K-user interference channel is K/2 rather than 1 as was originally expected. In recent work, we showed that these gains are not limited to the high SNR regime. In fact, for the interference channel, each user can achieve at least half its interference-free capacity at any SNR. The key to this result was a new achievability technique called ergodic interference alignment. In this paper, we extend this technique to include more general message sets. Specifically, we consider the multicast case where each transmitter has a message destined for more than one receiver. We also look at the X channel configuration for 2 receivers where each transmitter has an independent message for each receiver.