On Gaussian MACs with Variable-Length Feedback and Non-Vanishing Error~Probabilities

TL;DR

This paper investigates the fundamental limits of Gaussian MACs with variable-length feedback and non-zero error probabilities, introducing new techniques to characterize capacity regions and second-order bounds.

Contribution

It develops novel achievability and converse methods for continuous channels with power constraints, comparing VLFT and stop-feedback codes.

Findings

VLFT codes outperform stop-feedback codes significantly.

Established ε-capacity regions for Gaussian MAC with variable-length feedback.

Derived bounds on second-order asymptotics using renewal theory.

Abstract

We characterize the fundamental limits of transmission of information over a Gaussian multiple access channel (MAC) with the use of variable-length feedback codes and under a non-vanishing error probability formalism. We develop new achievability and converse techniques to handle the continuous nature of the channel and the presence of expected power constraints. We establish the $\varepsilon$-capacity regions and bounds on the second-order asymptotics of the Gaussian MAC with variable-length feedback with termination (VLFT) codes and stop-feedback codes. We show that the former outperforms the latter significantly. Due to the multi-terminal nature of the channel model, we leverage tools from renewal theory developed by Lai and Siegmund to bound the asymptotic behavior of the maximum of a finite number of stopping times.