  This paper studies the problem of interference channels with one cognitive
transmitter (ICOCT) where "cognitive" is defined from both the noncausal and
causal perspectives. For the noncausal ICOCT, referred to as interference
channels with degraded message sets (IC-DMS), we propose a new achievable rate
region that generalizes existing achievable rate regions for IC-DMS. In the
absence of the noncognitive transmitter, the proposed region coincides with
Marton's region for the broadcast channel. Based on this result, the capacity
region of a class of semi-deterministic IC-DMS is established. For the causal
ICOCT, due to the complexity of the channel model, we focus primarily on the
cognitive Z interference channel (ZIC), where the interference link from the
cognitive transmitter to the primary receiver is assumed to be absent due to
practical design considerations. Capacity bounds for such channels in different
parameter regimes are obtained and the impact of such causal cognitive ability
is carefully studied. In particular, depending on the channel parameters, the
cognitive link may not be useful in terms of enlarging the capacity region. An
optimal corner point of the capacity region is also established for the
cognitive ZIC for a certain parameter regime.
