An Achievable Rate Region for the Broadcast Channel with Feedback

TL;DR

This paper introduces a new achievable rate region for the two-receiver broadcast channel with feedback, utilizing advanced coding strategies to improve communication rates over existing methods.

Contribution

It presents a novel single-letter achievable rate region for the broadcast channel with feedback, combining block-Markov superposition coding with correlated resolution information transmission.

Findings

Achievable rate region is strictly larger than no-feedback capacity.

Effective use of correlated resolution information enhances decoding.

Applicable to stochastically degraded AWGN broadcast channels with noisy feedback.

Abstract

A single-letter achievable rate region is proposed for the two-receiver discrete memoryless broadcast channel with generalized feedback. The coding strategy involves block-Markov superposition coding, using Marton's coding scheme for the broadcast channel without feedback as the starting point. If the message rates in the Marton scheme are too high to be decoded at the end of a block, each receiver is left with a list of messages compatible with its output. Resolution information is sent in the following block to enable each receiver to resolve its list. The key observation is that the resolution information of the first receiver is correlated with that of the second. This correlated information is efficiently transmitted via joint source-channel coding, using ideas similar to the Han-Costa coding scheme. Using the result, we obtain an achievable rate region for the stochastically degraded AWGN broadcast channel with noisy feedback from only one receiver. It is shown that this region is strictly larger than the no-feedback capacity region.