On the Ozarow-Leung Scheme for the Gaussian Broadcast Channel with Feedback

TL;DR

This paper extends the Ozarow-Leung feedback scheme for the Gaussian broadcast channel by using estimators with memory, leading to improved achievable rates and lower error probabilities.

Contribution

It introduces a novel extension of the OL scheme with memory-based estimators, providing a recursive error analysis and demonstrating rate improvements through simulations.

Findings

Extended scheme achieves higher rates than original OL scheme.

The new estimators with memory improve error performance.

Numerical results confirm enhanced achievable rates and low error probability.

Abstract

In this work, we consider linear-feedback schemes for the two-user Gaussian broadcast channel with noiseless feedback. We extend the transmission scheme of [Ozarow and Leung, 1984] by applying estimators with memory instead of the memoryless estimators used by Ozarow and Leung (OL) in their original work. A recursive formulation of the mean square errors achieved by the proposed estimators is provided, along with a proof for the existence of a fixed point. This enables characterizing the achievable rates of the extended scheme. Finally, via numerical simulations it is shown that the extended scheme can improve upon the original OL scheme in terms of achievable rates, as well as achieve a low probability of error after a finite number of channel uses.