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

2026-04-05

AI Summary

This work investigates the achievable rate region of superposition coding with discrete input constellations—such as pulse amplitude modulation (PAM)—combined with treating interference as noise (TIN) decoding over the Gaussian broadcast channel. Through information-theoretic analysis, it is rigorously established for the first time that the rate region achieved by this scheme lies within a constant gap of the channel capacity region, where the gap is independent of channel parameters. Notably, in the weak-user regime, PAM signaling is shown to outperform Gaussian inputs in terms of achievable rates. These theoretical findings are corroborated by numerical simulations, highlighting the performance advantage of discrete signaling under specific channel conditions.

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.

Problem

• Gaussian broadcast channel
• discrete signaling
• treating interference as noise
• rate region
• constant gap

Innovation

• discrete signaling
• treating interference as noise
• Gaussian broadcast channel
• constant gap to capacity
• superposition coding