The approximate sum capacity of the symmetric Gaussian K-user interference channel

We derive a new achievable sum rate for the symmetric Gaussian K-user interference channel. This sum rate is shown to be within a constant gap of the outer bound on the sum capacity of this channel for all values of interference level outside some outage set. The result is established through the use of lattice interference alignment. A new lattice-based extension to the Han-Kobayshi scheme is also introduced.