Degradedness Under Cooperation

TL;DR

This paper introduces new degradedness notions in cooperative broadcast and relay networks, demonstrating that decode and forward is optimal under these conditions and deriving tight capacity bounds for various network classes.

Contribution

It proposes the concepts of strongly less noisy and strongly more capable degradedness, establishing their implications for optimality and capacity bounds in cooperative networks.

Findings

Decode and forward is optimal under new degradedness conditions.

Tight capacity bounds are derived for certain cooperative network classes.

The cut-set bound is tight for primitive relay and diamond channels.

Abstract

We study cooperation problems in broadcast and relay networks, where the receivers do not satisfy the classical physical degradedness assumptions. New notions of degradedness, \emph{strongly less noisy} and \emph{strongly more capable} are introduced. We show that under these conditions, decode and forward (D\&F) is optimal for classes of cooperative systems with limited conference rates, thus yielding new capacity results for these systems. In particular, we derive bounds on the capacity region of a class of broadcast channels with cooperation, that are tight on part of the capacity region. It is shown that the cut-set bound is tight for classes of primitive relay and diamond channels, beyond the physically or stochastically degraded models.