On the Capacity of the Discrete Memoryless Broadcast Channel with Feedback

TL;DR

This paper introduces a new coding scheme for the discrete memoryless broadcast channel with various types of feedback, achieving higher capacity regions than traditional no-feedback schemes through a combination of advanced strategies.

Contribution

The paper proposes a novel block-Markov coding scheme that combines Marton and Gray-Wyner strategies, extending capacity results to channels with noiseless and noisy feedback.

Findings

Achieves noiseless-feedback capacity for generalized Dueck's channel.

Attains rate points outside no-feedback capacity for generalized Blackwell's channel with noiseless feedback.

Improves capacity bounds even with low-noise feedback in certain broadcast channels.

Abstract

A coding scheme for the discrete memoryless broadcast channel with {noiseless, noisy, generalized} feedback is proposed, and the associated achievable region derived. The scheme is based on a block-Markov strategy combining the Marton scheme and a lossy version of the Gray-Wyner scheme with side-information. In each block the transmitter sends fresh data and update information that allows the receivers to improve the channel outputs observed in the previous block. For a generalization of Dueck's broadcast channel our scheme achieves the noiseless-feedback capacity, which is strictly larger than the no-feedback capacity. For a generalization of Blackwell's channel and when the feedback is noiseless our new scheme achieves rate points that are outside the no-feedback capacity region. It follows by a simple continuity argument that for both these channels and when the feedback noise is sufficiently low, our scheme improves on the no-feedback capacity even when the feedback is noisy.