  We consider the two-user interference channel with rate-limited feedback.
Related prior works focus on the case where feedback links have infinite
capacity, while no research has been done for the rate-limited feedback
problem. Several new challenges arise due to the capacity limitations of the
feedback links, both in deriving inner-bounds and outer-bounds. We study this
problem under three different interference models: the El Gamal-Costa
deterministic model, the linear deterministic model, and the Gaussian model.
For the first two models, we develop an achievable scheme that employs three
techniques: Han-Kobayashi message splitting, quantize-and-binning, and
decode-and-forward. We also derive new outer-bounds for all three models and we
show the optimality of our scheme under the linear deterministic model. In the
Gaussian case, we propose a transmission strategy that incorporates lattice
codes, inspired by the ideas developed in the first two models. For symmetric
channel gains, we prove that the gap between the achievable sum-rate of the
proposed scheme and our new outer-bounds is bounded by a constant number of
bits, independent of the channel gains.
