Binary Fading Interference Channel with No CSIT

We characterize the capacity region of the symmetric two-user Binary Fading Interference Channel where transmitters have no knowledge of the channel state information. We show that the entire capacity region is achieved by applying point-to-point erasure codes with appropriate rates at each transmitter, and using either treat-interference-as-erasure or interference-decoding at each receiver, based on the channel parameters. The result is obtained by developing a novel outer-bound that has three main steps. We first create a contracted channel that has fewer states compared to the original channel, in order to make the analysis tractable. Using a Correlation Lemma, we then show that an outer-bound on the capacity region of the contracted channel also serves as an outer-bound for the original channel. Finally, using a Conditional Entropy Leakage Lemma, we derive our outer-bound on the capacity region of the contracted channel, and show that it coincides with the achievable region by either treat-interference-as-erasure or interference-decoding at each receiver.