Approximate capacity region for the symmetric Gaussian interference channel with noisy feedback,” (Submitted to

Abstract Recent results have shown that feedback can significantly increase the capacity of interference networks. This paper considers the impact of noise on the gain due to feedback. Specifically, this paper considers the two-user linear deterministic interference channel with partial feedback, as a stepping stone in order to characterize the capacity region for the two-user Gaussian interference channel with noisy feedback. The capacity region for the symmetric linear deterministic interference channel with partial feedback has been obtained. Partial feedback has been shown to increase the capacity region if and only if the amount of feedback level l is greater than a certain threshold l * , and it is found that l * is equal to the per-user symmetric capacity without feedback. One of the key ideas is a novel converse outer bound on weighted sum rates 2R1 + R2 and R1 + 2R2. The novel outer bounds are tightened by specially defined auxiliary random variables. It has been illustrated through numerous examples, that the outer bounds on the sum rate R1 + R2 alone are not sufficient to characterize the capacity region, and 2R1 + R2 and R1 + 2R2 bounds are also necessary. The result and the techniques developed for this linear deterministic model are then applied to characterize inner bounds and outer bounds for the symmetric Gaussian IC with noisy feedback. The outer bounds have been shown to be at most 11.7 bits/s/Hz away from the achievable rate region. As a corollary, the generalized-degree-of-freedom region, which approximates the capacity region of the symmetric Gaussian IC at high SNR, is found