The Capacity of the Semi-Deterministic Cognitive Interference Channel with a Common Cognitive Message and Approximate Capacity for the Gaussian Case

TL;DR

This paper investigates the capacity of the cognitive interference channel with a common message, providing exact results for the semi-deterministic case and approximate capacity bounds for the Gaussian case using innovative pre-coding strategies.

Contribution

It derives the capacity for the semi-deterministic channel and establishes approximate capacity bounds for the Gaussian channel with a novel pre-coding scheme that leverages the cognitive message as side information.

Findings

Capacity is exactly characterized for the semi-deterministic channel.

Approximate capacity within a constant gap for the Gaussian channel.

Pre-coding of the cognitive message enhances decoding without revealing interference.

Abstract

In this paper the study of the cognitive interference channel with a common message, a variation of the classical cognitive interference channel in which the cognitive message is decoded at both receivers. We derive the capacity for the semideterministic channel in which the output at the cognitive decoder is a deterministic function of the channel inputs. We also show capacity to within a constant gap and a constant factor for the Gaussian channel in which the outputs are linear combinations of the channel inputs plus an additive Gaussian noise term. Most of these results are shown using an interesting transmission scheme in which the cognitive message, decoded at both receivers, is also pre-coded against the interference experienced at the cognitive decoder. The pre-coding of the cognitive message does not allow the primary decoder to reconstruct the interfering signal. The cognitive message acts instead as a side information at the primary receiver when decoding its intended message.