On the Capacity of Causal Cognitive Interference Channel With Delay

In this paper, we introduce the Causal Cognitive Interference Channel With Delay (CC-IFC-WD) in which the cognitive user transmission can depend on $L$ future received symbols as well as the past ones. Taking the effect of the link delays into account, CC-IFC-WD fills the gap between the genie-aided and causal 1cognitive radio channels. We study three special cases: 1) Classical CC-IFC (L=0), 2) CC-IFC without delay (L=1) and 3) CC-IFC with a block length delay (L=n). In each case, we obtain an inner bound on the capacity region. Our coding schemes make use of cooperative strategy by generalized block Markov superposition coding, collaborative strategy by rate splitting, and Gel'fand-Pinsker coding in order to pre-cancel part of the interference. Moreover, instantaneous relaying and non-causal partial Decode-and-Forward strategies are employed in the second and third cases, respectively. The derived regions under special conditions, reduce to several previously known results. Moreover, we show that the coding strategy which we use to derive achievable rate region for the classical CC-IFC achieves capacity for a special case of this channel. Furthermore, we extend our achievable rate regions to Gaussian case. Providing a numerical example for Gaussian CC-IFC-WD, we investigate the rate gain of the cognitive link for different delay values.