  We study the capacity region of the two-user Binary Fading (or Erasure)
Interference Channel where the transmitters have no knowledge of the channel
state information. We develop new inner-bounds and outer-bounds for this
problem. We identify three regimes based on the channel parameters: weak,
moderate, and strong interference regimes. Interestingly, this is similar to
the generalized degrees of freedom of the two-user Gaussian interference
channel where transmitters have perfect channel knowledge. We show that for the
weak interference regime, treating interference as erasure is optimal while for
the strong interference regime, decoding interference is optimal. For the
moderate interference regime, we provide new inner and outer bounds. The
inner-bound is based on a modification of the Han-Kobayashi scheme for the
erasure channel, enhanced by time-sharing. We study the gap between our
inner-bound and our outer-bounds for the moderate interference regime and
compare our results to that of the Gaussian interference channel. Deriving our
new outer-bounds 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. We then prove the Correlation Lemma that shows an
outer-bound on the capacity region of the contracted channel also serves as an
outer-bound for the original channel. Finally using the Conditional Entropy
Leakage Lemma, we derive our outer-bound on the capacity region of the
contracted channel.
