Capacity Regions of Two-User Broadcast Erasure Channels with Feedback and Hidden Memory

TL;DR

This paper characterizes the capacity region of a two-user broadcast erasure channel with feedback and hidden Markov memory, providing bounds, approximations, and two optimal coding algorithms.

Contribution

It introduces the first capacity region characterization for channels with hidden Markov memory and feedback, along with practical coding algorithms.

Findings

Capacity region bounds are derived and shown to be tight.

Two coding algorithms are proposed with proven optimality in different regimes.

Approximate capacity regions can be approached exponentially fast with feedback length.

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. The channel state is unknown at the transmitter, but observations of this hidden Markov chain are available at the transmitter through feedback. Matching outer and inner bounds are derived and the capacity region is determined. The capacity region does not have a single-letter characterization and is, in this sense, uncomputable. Approximations of the capacity region are provided and two optimal coding algorithms are outlined. The first algorithm is a probabilistic coding scheme that bases its decisions on the past L feedback sequences. Its achievable rate-region approaches the capacity region exponentially fast in L. The second algorithm is a backpressure-like algorithm that performs optimally in the long run.