  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.
