On Superposition Lattice Codes for the K-User Gaussian Interference Channel

In this study, we work with lattice Gaussian coding for a K-user Gaussian interference channel. Following the procedure of Etkin et al., in which the capacity is found to be within 1 bit/s/Hz of the capacity of a two-user Gaussian interference channel for each type of interference using random codes, we work with lattices to take advantage of their structure and potential for interference alignment. We mimic random codes using a Gaussian distribution over the lattice. Imposing constraints on the flatness factor of the lattices, the common and private message powers, and the channel coefficients, we find the conditions to obtain the same constant gap to the optimal rate for the two-user weak Gaussian interference channel and the generalized degrees of freedom as those obtained with random codes, as found by Etkin et al. Finally, we show how it is possible to extend these results to a K-user weak Gaussian interference channel using lattice alignment.