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.
A discrete memoryless single-relay channel can be modelled as four finite sets,
1
2
,
, and a conditional probability distribution
p ( y ,
x
2
on these sets.
The probability distribution of the choice of symbols selected by the encoder and the relay encoder is represented by
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
max
min
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.
A relay channel is said to be degraded if y depends on
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.
A relay channel is said to be reversely degraded if
Cover and El-Gamal proved that the Direct Transmission Lower Bound (wherein relay is not used) is tight when the relay channel is reversely degraded.
In a relay-without-delay channel (RWD), 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 (a special case of relay-without-delay) are capable of improving not only the capacity, but also Degrees of Freedom (DoF) of the 2-user interference channel.