  In this paper, the capacity region of the linear deterministic interference
channel with noisy channel-output feedback (LD-IC-NF) is fully characterized.
The proof of achievability is based on random coding arguments and rate
splitting; block-Markov superposition coding; and backward decoding. The proof
of converse reuses some of the existing outer bounds and includes new ones
obtained using genie-aided models. Following the insight gained from the
analysis of the LD-IC-NF, an achievability region and a converse region for the
two-user Gaussian interference channel with noisy channel-output feedback
(GIC-NF) are presented. Finally, the achievability region and the converse
region are proven to approximate the capacity region of the G-IC-NF to within
4.4 bits.
