# Common-Message Broadcast Channels with Feedback in the Nonasymptotic Regime: Full Feedback

## TL;DR

This paper analyzes how feedback affects the maximum coding rate in two-user broadcast channels with a common message, showing feedback improves second-order performance and can reduce dispersion, especially in antisymmetric channels.

## Contribution

It provides the first nonasymptotic bounds for broadcast channels with feedback and reveals feedback's impact on second-order coding rates and dispersion.

## Key findings

- Feedback improves the second-order term in fixed-blocklength codes.
- For certain channels, feedback halves the channel dispersion.
- Variable-length codes achieve zero dispersion.

## Abstract

We investigate the maximum coding rate achievable on a two-user broadcast channel for the case where a common message is transmitted with feedback using either fixed-blocklength codes or variable-length codes. For the fixed-blocklength-code setup, we establish nonasymptotic converse and achievability bounds. An asymptotic analysis of these bounds reveals that feedback improves the second-order term compared to the no-feedback case. In particular, for a certain class of antisymmetric broadcast channels, we show that the dispersion is halved. For the variable-length-code setup, we demonstrate that the channel dispersion is zero.