  In this paper, taking into account the effect of link delays, we investigate
the capacity region of the Cognitive Interference Channel (C-IFC), where
cognition can be obtained from either causal or non-causal generalized
feedback. For this purpose, we introduce the Causal Cognitive Interference
Channel With Delay (CC-IFC-WD) in which the cognitive user's transmission can
depend on $L$ future received symbols as well as the past ones. We show that
the CC-IFC-WD model is equivalent to a classical Causal C-IFC (CC-IFC) with
link delays. Moreover, CC-IFC-WD extends both genie-aided and causal cognitive
radio channels and bridges the gap between them. First, we derive an outer
bound on the capacity region for the arbitrary value of $L$ and specialize this
general outer bound to the strong interference case. Then, under strong
interference conditions, we tighten the outer bound. To derive the achievable
rate regions, we concentrate on three special cases: 1) Classical CC-IFC (L=0),
2) CC-IFC without delay (L=1), and 3) CC-IFC with unlimited look-ahead in which
the cognitive user non-causally knows its entire received sequence. In each
case, we obtain a new inner bound on the capacity region. Moreover, we show
that the coding strategy which we use to derive an achievable rate region for
the classical CC-IFC achieves the capacity for the classes of degraded and
semi-deterministic classical CC-IFC under strong interference conditions.
Furthermore, we extend our achievable rate regions to the Gaussian case.
Providing some numerical examples for Gaussian CC-IFC-WD, we compare the
performances of the different strategies and investigate the rate gain of the
cognitive link for different delay values.
