# On the Capacity Region of the Layered Packet Erasure Broadcast Channel with Feedback

## TL;DR

This paper investigates the capacity region of the layered packet erasure broadcast channel with feedback, deriving bounds and demonstrating the effectiveness of network coding strategies for two users and multiple layers.

## Contribution

It introduces new capacity bounds for the layered packet erasure broadcast channel with feedback, utilizing inter-user and inter-layer network coding techniques.

## Key findings

- Outer bound is tight for some channel configurations.
- Network coding improves retransmission efficiency.
- Capacity bounds generalize previous results for simpler channels.

## Abstract

In this paper, the capacity region of the Layered Packet Erasure Broadcast Channel (LPE-BC) with Channel Output Feedback (COF) available at the transmitter is investigated. The LPE-BC is a high-SNR approximation of the fading Gaussian BC recently proposed by Tse and Yates, who characterized the capacity region for any number of users and any number of layers when there is no COF. This paper derives capacity inner and outer bounds for the LPE-BC with COF for the case of two users and any number of layers. The inner bounds generalize past results for the two-user erasure BC, which is a special case of the LPE-BC with COF with only one layer. The novelty lies in the use of \emph{inter-user \& inter-layer network coding} retransmissions (for those packets that have only been received by the unintended user), where each random linear combination may involve packets intended for any user originally sent on any of the layers. Analytical and numerical examples show that the proposed outer bound is optimal for some LPE-BCs.