Capacity Region of the Symmetric Linear Deterministic Interference Channel with Partial Feedback

The symmetric linear deterministic interference channel (LD-IC) with partial feedback is considered. Partial feedback for the symmetric LD-IC models a scenario in which the top l most-significant-bits of the channel output of receiver j are received as feedback at transmitter j, for j = 1, 2. It is shown that the LD-IC with partial feedback can serve as a good approximation to the Gaussian interference channel with additive white Gaussian noise (AWGN) corrupted feedback (commonly referred to as noisy feedback). The main contribution of this paper is to characterize the capacity region of the symmetric LD-IC with partial feedback. One of the key ideas is a novel converse proof which includes outer bounds on the sum rate R1 + R2, and on weighted sum rates 2R1 +R2 and R1 + 2R2. It is shown that partial feedback increases the capacity region if 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. The application of this result to the Gaussian interference channel with noisy feedback is presented in a companion paper.