On Capacity Regions of Two-Receiver Broadcast Packet Erasure Channels with Feedback and Memory

TL;DR

This paper characterizes the capacity region of a two-receiver broadcast packet erasure channel with feedback and memory, providing bounds that are tight in most cases and demonstrating significant feedback gains.

Contribution

It derives matching inner and outer bounds on the capacity region for channels with feedback and memory, extending previous results to include delayed feedback.

Findings

Bounds are tight in most cases, accurately describing the capacity region.

Feedback can significantly increase the achievable rates.

Numerical results confirm the bounds are close and demonstrate large feedback gains.

Abstract

The two-receiver broadcast packet erasure channel with feedback and memory is studied. Memory is modeled using a finite-state Markov chain representing a channel state. Outer and inner bounds on the capacity region are derived when the channel state is strictly causally known at the transmitter. The bounds are both formulated in terms of feasibility problems and they are matching in all but one of the constraints. The results are extended to feedback with larger delay. Numerical results show that the bounds are close in many examples and the gains offered through feedback can be quite large. The presented outer bound meets the inner bound recently derived in \cite{Kuo_Wang2014} and hence describes the capacity region.