| Relay without delay is defined as a relay channel where each transmitted relay symbol can depend on the relay's current symbols as well as the past. This is in contrast to the classical relay channel which is an information theoretical model of a three node communication system where a relay, using only its past received symbols, helps a transmitter to send information to a receiver. The capacity of the relay channel is known only for a few special cases.; In this thesis, the classical max-flow min-cut bound is shown to be inapplicable to the relay without delay. A general new upper bound on the capacity of the discrete memoryless relay without delay is established and shown to coincide with a lower bound achieved by a combination of instantaneous relaying and block Markov encoding, yielding capacity results for several classes of relay without delay channels. By using a discrete memoryless example, it is shown that instantaneous relaying by itself can be optimal and can achieve rates higher than the classical max-flow min-cut bound.; Instantaneous relaying and complete decode and forward at the relay are shown to be optimal for the additive white Gaussian noise relay without delay, for ranges of parameters.; These schemes achieve rates which are higher than the max-flow min-cut bound on the capacity of the classical Gaussian relay channel. Unlike the general classical Gaussian relay channel, whose capacity is not known for any range of channel characteristics, the capacity of the Gaussian relay without delay is known for all but a limited set of parameters.; Therefore, introducing delay as an additional design factor in a relay channel makes higher rates achievable using simpler relaying strategies. |
