Interactive Schemes for the AWGN Channel with Noisy Feedback

TL;DR

This paper introduces a low-complexity, low-delay interactive coding scheme for AWGN channels with noisy feedback, achieving near-capacity performance and improved error exponents over non-feedback methods.

Contribution

It presents a novel interactive modulo-lattice coding scheme that works with noisy feedback, extending the classic S-K scheme to more realistic noisy feedback scenarios.

Findings

Achieves near-capacity performance with noisy feedback.

Provides two asymptotic constructions with high error exponents.

Demonstrates the effectiveness of feedback as side information in communication.

Abstract

We study the problem of communication over an additive white Gaussian noise (AWGN) channel with an AWGN feedback channel. When the feedback channel is noiseless, the classic Schalkwijk-Kailath (S-K) scheme is known to achieve capacity in a simple sequential fashion, while attaining reliability superior to non-feedback schemes. In this work, we show how simplicity and reliability can be attained even when the feedback is noisy, provided that the feedback channel is sufficiently better than the feedforward channel. Specifically, we introduce a low-complexity low-delay interactive scheme that operates close to capacity for a fixed bit error probability (e.g. $10^{-6}$). We then build on this scheme to provide two asymptotic constructions, one based on high dimensional lattices, and the other based on concatenated coding, that admit an error exponent significantly exceeding the best possible non-feedback exponent. Our approach is based on the interpretation of feedback transmission as a side-information problem, and employs an interactive modulo-lattice solution.