Posterior Matching for Gaussian Broadcast Channels with Feedback

TL;DR

This paper extends the posterior matching scheme to Gaussian broadcast channels with feedback, deriving error probabilities and achievable rates, and demonstrates its advantages over existing codes in symmetric scenarios.

Contribution

It introduces a generalized coding scheme based on posterior matching for Gaussian broadcast channels with feedback, unifying and extending previous codes.

Findings

Achieves the linear-feedback sum-capacity in symmetric channels.

Outperforms the Kramer code in symmetric Gaussian broadcast channels.

Special case includes a variant of the Ozarow-Leung code.

Abstract

In this paper, the posterior matching scheme proposed by Shayevits and Feder is extended to the Gaussian broadcast channel with feedback, and the error probabilities and achievable rate region are derived for this coding strategy by using the iterated random function theory. A variant of the Ozarow-Leung code for the general two-user broadcast channel with feedback can be realized as a special case of our coding scheme. Furthermore, for the symmetric Gaussian broadcast channel with feedback, our coding scheme achieves the linear-feedback sum-capacity like the LQG code and outperforms the Kramer code.