Sum capacity of general deterministic interference channel with channel output feedback

In a two-user interference channel, there are four possible feedback paths - two from each receiver to the transmitters. This leads to 16 possible models of feedback. In this paper, we derive the sum capacity of two user deterministic interference channel for all sixteen cases. We find that whenever any of the direct link feedback from a receiver to its own transmitter is present, the sum-capacity is the same as when all four feedback links are present. Further when no direct link feedback is present, the sum capacity with one cross-link feedback and two cross-links of feedback is the same. This sum-capacity is the same as the sum-capacity when there is no feedback except in the regime of interference in which both interfering links are weaker than both the direct-links in which case the sum-capacity is the same as sum-capacity of the feedback model with all four feedback links.