The Gaussian Channel with Noisy Feedback: Improving Reliability via Interaction

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.