New inner and outer bounds for the discrete memoryless cognitive interference channel and some capacity results

The cognitive interference channel is an interference channel in which one transmitter is non-causally provided with the message of the other transmitter. This channel model has been extensively studied in the past years and capacity results for certain classes of channels have been proved. In this paper we present new inner and outer bounds for the capacity region of the cognitive interference channel as well as new capacity results. Previously proposed outer bounds are expressed in terms of auxiliary random variables for which no cardinality constraint is known. Consequently it is not possible to evaluate such outer bounds explicitly for a given channel model. The outer bound we derive is based on an idea originally devised by Sato for the broadcast channel and does not contain auxiliary random variables, allowing it to be more easily evaluated. The inner bound we derive is the largest known to date and is explicitly shown to include all previously proposed achievable rate regions. This comparison highlights which features of the transmission scheme - which includes rate-splitting, superposition coding, a broadcast channel-like binning scheme, and Gel'fand Pinsker coding - are most effective in approaching capacity. We next present new capacity results for a class of discrete memoryless channels that we term the "better cognitive decoding regime" which includes all previously known regimes in which capacity results have been derived as special cases. Finally, we determine the capacity region of the semi-deterministic cognitive interference channel, in which the signal at the cognitive receiver is a deterministic function of the channel inputs.