Capacity Upper Bounds for the Relay Channel via Reverse Hypercontractivity

TL;DR

This paper introduces new upper bounds on the capacity of the primitive relay channel using reverse hypercontractivity, providing simpler proofs and improving upon previous bounds in network information theory.

Contribution

It recovers, generalizes, and improves existing upper bounds on relay channel capacity with novel, simpler proofs based on reverse hypercontractivity, a first in network information theory.

Findings

New upper bounds tighter than previous cutset bounds.

Simpler proof techniques using reverse hypercontractivity.

First application of reverse hypercontractivity for first-order converses.

Abstract

The primitive relay channel, introduced by Cover in 1987, is the simplest single-source single-destination network model that captures some of the most essential features and challenges of relaying in wireless networks. Recently, Wu and Ozgur developed upper bounds on the capacity of this channel that are tighter than the cutset bound. In this paper, we recover, generalize and improve their upper bounds with simpler proofs that rely on a converse technique recently introduced by Liu, van Handel and Verd\'u that builds on reverse hypercontractivity. To our knowledge, this is the first application of reverse hypercontractivity for proving first-order converses in network information theory.