The Capacity on Degraded Relay Broadcast Channel

TL;DR

This paper investigates the capacity limits of the relay broadcast channel with different degradation orders, deriving tight bounds and establishing the capacity region for the Gaussian case.

Contribution

It introduces three types of physically degraded relay broadcast channels and derives capacity bounds, fully characterizing the Gaussian case.

Findings

Bounds are tight for two degradation types.

Capacity region is established for the Gaussian PDRBC.

Theoretical bounds match in the Gaussian case.

Abstract

The relay broadcast channel (RBC) is considered, in which a transmitter communicates with two receivers with the assistance of a relay. Based on different degradation orders among the relay and the receivers' outputs, three types of physically degraded RBCs (PDRBCs) are introduced. Inner bounds and outer bounds are derived on the capacity region of the presented three types. The bounds are tight for two types of PDRBCs: 1) one receiver's output is a degraded form of the other receiver's output, and the relay's output is a degraded form of the weaker receiver's output; 2) one receiver's output is a degraded form of the relay's output, and the other receiver's output is a degraded form of the relay's output. For the Gaussian PDRBC, the bounds match, i.e., establish its capacity region.