Concatenated Coding Using Linear Schemes for Gaussian Broadcast Channels with Noisy Channel Output Feedback

TL;DR

This paper introduces a concatenated linear coding scheme for the Gaussian broadcast channel with noisy feedback, enabling rates beyond the no-feedback capacity by combining linear feedback codes with open-loop coding.

Contribution

It proposes a novel concatenated coding design that leverages linear feedback schemes to improve achievable rates in noisy feedback scenarios for Gaussian broadcast channels.

Findings

Achievable rate region extends beyond no-feedback capacity.

Effective single-user channels are created via linear feedback coding.

Optimized coding schemes for two-user scenarios with noisy feedback.

Abstract

Linear coding schemes have been the main choice of coding for the additive white Gaussian noise broadcast channel (AWGN-BC) with noiseless feedback in the literature. The achievable rate regions of these schemes go well beyond the capacity region of the AWGN-BC without feedback. In this paper, a concatenating coding design for the $K$-user AWGN-BC with noisy feedback is proposed that relies on linear feedback schemes to achieve rate tuples outside the no-feedback capacity region. Specifically, a linear feedback code for the AWGN-BC with noisy feedback is used as an inner code that creates an effective single-user channel from the transmitter to each of the receivers, and then open-loop coding is used for coding over these single-user channels. An achievable rate region of linear feedback schemes for noiseless feedback is shown to be achievable by the concatenated coding scheme for sufficiently small feedback noise level. Then, a linear feedback coding scheme for the $K$-user symmetric AWGN-BC with noisy feedback is presented and optimized for use in the concatenated coding scheme. Lastly, we apply the concatenated coding design to the two-user AWGN-BC with a single noisy feedback link from one of the receivers.