In this paper, we investigate Causal Cognitive Interference Channel (CC-IFC) with delay in which the cognitive user transmission can depend on L future received symbols as well as the past ones. We study two special cases: CC-IFC without delay (L = 1), where the cognitive user can use only current and past received symbols, and CC-IFC with a block length delay (L = n), wherein the entire received sequence can be used. In each case, we obtain an inner bound on the capacity region. Our coding schemes are based on the generalized block Markov superposition coding and instantaneous relaying for CC-IFC without delay, and non-causal partial Decode-and-Forward (DF) for CC-IFC with a block length delay. Further, providing converse proofs, we show that the derived inner bounds are tight in some cases. Hence, we characterize the capacity regions for the classes of degraded and semi-deterministic CC-IFC without delay and CC-IFC with a block length delay, under strong interference conditions.
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