  We characterize the capacity region to within 2 bits/s/Hz and the symmetric
capacity to within 1 bit/s/Hz for the two-user Gaussian interference channel
(IC) with feedback. We develop achievable schemes and derive a new outer bound
to arrive at this conclusion. One consequence of the result is that feedback
provides multiplicative gain, i.e., the gain becomes arbitrarily large for
certain channel parameters. It is a surprising result because feedback has been
so far known to provide no gain in memoryless point-to-point channels and only
bounded additive gain in multiple access channels. The gain comes from using
feedback to maximize resource utilization, thereby enabling more efficient
resource sharing between the interfering users. The result makes use of a
deterministic model to provide insights into the Gaussian channel. This
deterministic model is a special case of El Gamal-Costa deterministic model and
as a side-generalization, we establish the exact feedback capacity region of
this general class of deterministic ICs.
