On the Rate Region of I.I.D. Discrete Signaling and Treating Interference as Noise for the Gaussian Broadcast Channel

TL;DR

This paper analyzes the rate region of the Gaussian broadcast channel using discrete inputs with treating interference as noise, showing it is within a constant gap of capacity and sometimes outperforming Gaussian signaling.

Contribution

It introduces a simple superposition coding scheme with discrete inputs for GBC and proves its achievable rate region is within a constant gap of the capacity.

Findings

Achievable rate region within a constant gap to the capacity

Discrete PAM inputs can outperform Gaussian signaling for the weak user in some cases

The scheme is simple and effective for GBC with TIN decoding

Abstract

We revisit the Gaussian broadcast channel (GBC) and explore the rate region achieved by purely discrete inputs with treating interference as noise (TIN) decoding. Specifically, we introduce a simple scheme based on superposition coding with identically and independently distributed (i.i.d.) inputs drawn from discrete constellations, e.g., pulse amplitude modulations (PAM). Most importantly, we prove that the resulting achievable rate region under TIN decoding is within a constant gap to the capacity region of the GBC, where the gap is independent of all channel parameters. In addition, we show via simulation that the weak user can achieve a higher rate with PAM than with Gaussian signaling in some cases.