  A discrete memoryless half-duplex relay channel is constructed from a
broadcast channel from the source to the relay and destination and a multiple
access channel from the source and relay to the destination. When the relay
listens, the channel operates in the broadcast mode. The channel switches to
the multiple access mode when the relay transmits. If the broadcast component
channel is physically degraded, the half-duplex relay channel will also be
referred to as physically degraded. The capacity of this degraded half-duplex
relay channel is examined. It is shown that the block Markov coding suggested
in the seminal paper by Cover and El Gamal can be modified to achieve capacity
for the degraded half-duplex relay channel. In the code construction, the
listen-transmit schedule of the relay is made to depend on the message to be
sent and hence the schedule carries information itself. If the schedule is
restricted to be deterministic, it is shown that the capacity can be achieved
by a simple management of information flows across the broadcast and multiple
access component channels.
