Relay channel


In information theory, a relay channel is a probability model of the communication between a sender and a receiver aided by one or more intermediate relay nodes.

General discrete-time memoryless relay channel

A discrete memoryless single-relay channel can be modelled as four finite sets, and, and a conditional probability distribution on these sets. The probability distribution of the choice of symbols selected by the encoder and the relay encoder is represented by.

 o------------------o
 | Relay Encoder |
 o------------------o
 Λ |
 | y1 x2 |
 | V
o---------o x1 o------------------o y o---------o
o---------o o------------------o o---------o

There exist three main relaying schemes: Decode-and-Forward, Compress-and-Forward and Amplify-and-Forward. The first two schemes were first proposed in the pioneer article by Cover and El-Gamal.
The first upper bound on the capacity of the relay channel is derived in the pioneer article by Cover and El-Gamal and is known as the Cut-set upper bound. This bound says where C is the capacity of the relay channel. The first term and second term in the minimization above are called broadcast bound and multi-access bound, respectively.

Degraded relay channel

A relay channel is said to be degraded if y depends on only through and, i.e.,. In the article by Cover and El-Gamal it is shown that the capacity of the degraded relay channel can be achieved using Decode-and-Forward scheme. It turns out that the capacity in this case is equal to the Cut-set upper bound.

Reversely degraded relay channel

A relay channel is said to be reversely degraded if. Cover and El-Gamal proved that the Direct Transmission Lower Bound is tight when the relay channel is reversely degraded.

Feedback relay channel

Relay without delay channel

In a relay-without-delay channel, each transmitted relay symbol can depend on relay's past as well as present received symbols. Relay Without Delay was shown to achieve rates that are outside the Cut-set upper bound. Recently, it was also shown that instantaneous relays are capable of improving not only the capacity, but also Degrees of Freedom of the 2-user interference channel.