The Causal Cognitive Interference Channel (CCIC) models realistic causal cognitive communication between two sender-and-receiver pairs, in which the cognitive sender causally obtains a message from the primary sender and helps forward it to the primary receiver while also sending its own message to the cognitive receiver. We propose a new coding scheme combining the Han-Kobayashi scheme, partial decode-forward relaying and modified dirty-paper coding (DPC) for the Gaussian CCIC in the half-duplex mode. The proposed scheme induces correlation between the transmit signal and the state to allow traditional DPC as well as state forwarding. An achievable rate region with joint decoding is derived. Numerical results show that the rate region for the proposed scheme is better than the Han-Kobayashi scheme and several other existing schemes. We also analyze the maximum rate for the cognitive user while keeping the primary user's rate as interference-free. Results show that, by decode-and-forward relaying, the cognitive user can achieve significant rates while not affecting the primary user's rate even in the half-duplex causal case.

The causal cognitive interference channel (CCIC) is a four-node channel, in which the second sender obtains information from the first sender causally and assists in the transmission of both. We propose a new coding scheme called Han-Kobayashi partial decode-forward binning (HK-PDF-binning), which combines the ideas of Han-Kobayashi coding, partial decode-forward relaying, conditional Gelfand-Pinsker binning and relaxed joint decoding. The second sender decodes a part of the message from the first sender, then uses Gelfand-Pinsker binning to bin against the decoded codeword. When applied to the Gaussian channel, this HK-PDF-binning essentializes to a correlation between the transmit signal and the state, which encompasses the traditional dirty-paper-coding binning as a special case when this correlation factor is zero. The proposed scheme encompasses the Han-Kobayashi rate region and achieves both partial decode-forward relaying rate for the first user and interference-free rate for the second user.