The two-user causal cognitive interference channel: Novel outer bounds and constant gap result for the symmetric Gaussian noise channel in weak interference

This paper studies the two-user causal cognitive interference channel (CCIC), where two transmitters aim to communicate independent messages to two different receivers via a common channel. One source, referred to as the cognitive, is capable of overhearing the other source, referred to as the primary, through a noisy in-band link and thus can assist in sending the primary's data. The authors of this paper recently characterized to within a constant gap the capacity of the symmetric Gaussian CCIC in: 1) the strong interference regime and 2) for a subset of the weak interference regime when the cooperation link is larger than a given threshold. This paper characterizes to within a constant gap the capacity for the symmetric Gaussian CCIC in the regime that was still open. To this end, two novel outer bounds of the types 2 Rp+ Rc and Rp+2 Rc are derived for the class of injective semideterministic CCICs, where the noises at the different source-destination pairs are independent. These outer bounds, as well as an achievable rate region based on Gelfand-Pinsker binning, superposition coding, and simultaneous decoding at the receivers, are then specialized to the Gaussian noise case. It is shown that the novel outer bounds are necessary to characterize the capacity within a constant gap when the cooperation link is weaker than the direct links, that is, in this regime unilateral cooperation leaves some system resources underutilized.