The Gaussian Channel with Noisy Feedback: Improving Reliability via Interaction

TL;DR

This paper introduces an interactive communication scheme that enhances reliability over noisy feedback channels by combining Schalkwijk-Kailath coding with modulo-lattice transmission, especially when feedback SNR exceeds feedforward SNR.

Contribution

It proposes a novel interactive scheme that significantly improves communication reliability over noisy feedback channels, extending the capabilities of existing coding methods.

Findings

Reliability improves notably with noisy feedback when feedback SNR is high.

The scheme outperforms traditional no-feedback methods in specific SNR regimes.

Combines classical and lattice coding techniques for enhanced performance.

Abstract

Consider a pair of terminals connected by two independent (feedforward and feedback) Additive White Gaussian Noise (AWGN) channels, and limited by individual power constraints. The first terminal would like to reliably send information to the second terminal at a given rate. While the reliability in the cases of no feedback and of noiseless feedback is well studied, not much is known about the case of noisy feedback. In this work, we present an interactive scheme that significantly improves the reliability relative to the no-feedback setting, whenever the feedback Signal to Noise Ratio (SNR) is sufficiently larger than the feedforward SNR. The scheme combines Schalkwijk-Kailath (S-K) coding and modulo--lattice analog transmission.