A discrete memoryless half-duplex relay channel is constructed from abroadcast channel from the source to the relay and destination and a multipleaccess channel from the source and relay to the destination. When the relaylistens, the channel operates in the broadcast mode. The channel switches tothe multiple access mode when the relay transmits. If the broadcast componentchannel is physically degraded, the half-duplex relay channel will also bereferred to as physically degraded. The capacity of this degraded half-duplexrelay channel is examined. It is shown that the block Markov coding suggestedin the seminal paper by Cover and El Gamal can be modified to achieve capacityfor the degraded half-duplex relay channel. In the code construction, thelisten-transmit schedule of the relay is made to depend on the message to besent and hence the schedule carries information itself. If the schedule isrestricted to be deterministic, it is shown that the capacity can be achievedby a simple management of information flows across the broadcast and multipleaccess component channels.
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