When Does Channel-Output Feedback Enlarge the Capacity Region of the Two-User Linear Deterministic Interference Channel?

The two-user linear deterministic interference channel (LDIC) with noisy channel-output feedback is fully described by six parameters that correspond to the number of bit-pipes between each transmitter and its corresponding intended receiver, i.e., −→n 11 and −→n 22; between each transmitter and its corresponding non-intended receiver i.e., n12 and n21; and between each receiver and its corresponding transmitter, i.e., ←− n 11 and ←− n 22. An LD-IC without feedback corresponds to the case in which ←− n 11 = ←− n 22 = 0. The capacity region of the linear deterministic interference channel with noisy channeloutput feedback is denoted by C(−→n 11,−→n 22, n12, n21,←− n 11,←− n 22). This paper presents the exact conditions on ←− n 11 (resp. ←− n 22) for observing an improvement in the capacity region C(−→n 11,−→n 22, n12, n21,←− n 11, 0) (resp. C(−→n 11,−→n 22, n12, n21, 0,←− n 22)) when compared to C(−→n 11, −→n 22, n12, n21, 0, 0), for any 4-tuple (−→n 11, −→n 22, n12, n21) ∈ N. Specifically, it is shown that there exists a threshold for the number of bit-pipes in the feedback link of transmitter-receiver pair 1 (resp. 2), denoted by ←− n 11 (resp. ←− n 22) for which any ←− n 11 > ←− n 11 ( resp. ←− n 22 > ←− n 22 ) enlarges the capacity region, i.e., C(−→n 11,−→n 22, n12, n21, 0, 0) ⊂ C(−→n 11,−→n 22, n12, n21,←− n 11, 0) (resp. C(−→n 11,−→n 22, n12, n21, 0, 0) ⊂ C(−→n 11,−→n 22, n12, n21, 0,←− n 22)). The exact conditions on ←− n 11 ( resp. ←− n 22 ) to observe an improvement on a single rate or the sum-rate capacity, for any 4-tuple (−→n 11,−→n 22, n12, n21) ∈ N are also presented in this paper.