The Capacity of the Semi-Deterministic Cognitive Interference Channel and its Application to Constant Gap Results for the Gaussian Channel

TL;DR

This paper determines the capacity of the semi-deterministic cognitive interference channel and applies these insights to establish tighter constant gap results for the Gaussian channel, improving understanding of its capacity limits.

Contribution

It provides the exact capacity for the semi-deterministic C-IFC and derives new, tighter constant gap bounds for the Gaussian C-IFC, enhancing capacity approximation.

Findings

Capacity of semi-deterministic C-IFC is established.

New constant gap bounds for Gaussian C-IFC are derived.

Results are relevant for high and low SNR regimes.

Abstract

The cognitive interference channel (C-IFC) consists of a classical two-user interference channel in which the message of one user (the "primary" user) is non-causally available at the transmitter of the other user (the "cognitive" user). We obtain the capacity of the semi-deterministic C-IFC: a discrete memoryless C-IFC in which the cognitive receiver output is a noise-less deterministic function of the channel inputs. We then use the insights obtained from the capacity-achieving scheme for the semi-deterministic model to derive new, unified and tighter constant gap results for the complex-valued Gaussian C-IFC. We prove: (1) a constant additive gap (difference between inner and outer bounds) of half a bit/sec/Hz per real dimension, of relevance at high SNRs, and (b) a constant multiplicative gap (ratio between outer and inner bounds) of a factor two, of relevance at low SNRs