Ergodic Interference Alignment

Consider a K-user interference channel with time-varying fading. At any particular time, each receiver will see a signal from most transmitters. The standard approach to such a scenario results in each transmitter-receiver pair achieving a rate proportional to 1/k the single user rate. However, given two well chosen time indices, the channel coefficients from interfering users can be made to exactly cancel. By adding up these two signals, the receiver can see an interference-free version of the desired transmission. We show that this technique allows each user to achieve at least half its interference-free ergodic capacity at any SNR. Prior work was only able to show that half the interference-free rate was achievable as the SNR tended to infinity. We examine a finite field channel model and a Gaussian channel model. In both cases, the achievable rate region has a simple description and, in the finite field case, we prove it is the ergodic capacity region.