  We analyze two-user single-antenna fading interference channels with perfect
receive channel state information (CSI) and no transmit CSI. We compute the
diversity-multiplexing tradeoff (DMT) region of a fixed-power-split Han and
Kobayashi (HK)-type superposition coding scheme and provide design criteria for
the corresponding superposition codes. We demonstrate that this scheme is
DMT-optimal under moderate, strong, and very strong interference by showing
that it achieves a DMT outer bound that we derive. Further, under very strong
interference, we show that a joint decoder is DMT-optimal and "decouples" the
fading interference channel, i.e., from a DMT perspective, it is possible to
transmit as if the interfering user were not present. In addition, we show
that, under very strong interference, decoding interference while treating the
intended signal as noise, subtracting the result out, and then decoding the
desired signal, a process known as "stripping", achieves the optimal DMT
region. Our proofs are constructive in the sense that code design criteria for
achieving DMT-optimality (in the cases where we can demonstrate it) are
provided.
