Capacity of the Degraded Half-Duplex Relay Channel

TL;DR

This paper determines the capacity of a physically degraded half-duplex relay channel, showing that modified block Markov coding with message-dependent schedules achieves capacity, simplifying management of information flow.

Contribution

It extends the classic block Markov coding approach to half-duplex relay channels with message-dependent schedules, achieving capacity in the degraded case.

Findings

Capacity is achieved with message-dependent relay schedules.

Modified coding scheme extends Cover and El Gamal's approach.

Deterministic schedules suffice for capacity achievement.

Abstract

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.