Partial Decode-Forward Binning Schemes for the Causal Cognitive Relay Channels

The causal cognitive relay channel (CRC) has two sender-receiver pairs, in which the second sender obtains information from the first sender causally and assists the transmission of both senders. In this paper, we study both the fulland half-duplex modes. In each mode, we propose two new coding schemes built successively upon one another to illustrate the impact of different coding techniques. The first scheme called partial decode-forward binning (PDF-binning) combines the ideas of partial decode-forward relaying and Gelfand-Pinsker binning. The second scheme called Han-Kobayashi partial decode-forward binning (HK-PDF-binning) combines PDF-binning with Han-Kobayashi coding by further splitting rates and applying superposition coding, conditional binning and relaxed joint decoding. In both schemes, the second sender decodes a part of the message from the first sender, then uses GelfandPinsker binning technique to bin against the decoded codeword, but in such a way that allows both state nullifying and forwarding. For the Gaussian channels, this PDF-binning essentializes to a correlation between the transmit signal and the binning state, which encompasses the traditional dirty-paper-coding binning as a special case when this correlation factor is zero. We also provide the closed-form optimal binning parameter for each scheme. The 2-phase half-duplex schemes are adapted from the full-duplex ones by removing block Markov encoding, sending different message parts in different phases and applying joint decoding across both phases. Analysis shows that the HK-PDF-binning scheme in both modes encompasses the Han-Kobayashi rate region and achieves both the partial decode-forward relaying rate for the first sender and interference-free rate for the second sender. Furthermore, this scheme outperforms all existing schemes.