The Two-user Causal Cognitive Interference Channel: Novel Outer Bounds and Constant Gap Result for the Symmetric Gaussian Noise Channel in Weak Interference

TL;DR

This paper introduces new outer bounds and characterizes the capacity within a constant gap for the symmetric Gaussian CCIC in the weak interference regime, where cooperation links are weaker than direct links.

Contribution

It derives novel outer bounds for the injective semi-deterministic CCIC and completes the capacity characterization for the symmetric Gaussian CCIC in the previously unresolved weak interference regime.

Findings

New outer bounds of the form 2Rp+Rc and Rp+2Rc are established.

Capacity is characterized within a constant gap in the weak interference regime.

Unilateral cooperation can leave system resources underutilized in certain regimes.

Abstract

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. Two novel outer bounds of the type $2R_p+R_c$ and $R_p+2R_c$ are derived for the class of injective semi-deterministic CCICs where the noises at the different source-destination pairs are independent. An achievable rate region is derived based on Gelfand-Pinsker binning, superposition coding and simultaneous decoding at the receivers. The lower and outer bounds are then specialized to the practically relevant Gaussian noise case. The authors of this paper recently characterized to within a constant gap the capacity of the symmetric Gaussian CCIC in (a) the strong interference regime, and (b) for a subset of the weak interference regime when the cooperation link is larger than a given threshold. This work characterizes to within a constant gap the capacity for the symmetric Gaussian CCIC in the regime that was still open. In particular, it is shown that the novel outer bounds are necessary to characterize the capacity to 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.