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,
X1,X2,Y1,
Y
p(y,y1|x1,x2)
p(x1,x2)
<nowiki> o------------------o | Relay Encoder | o------------------o Λ | | y1 x2 | | V o---------o x1 o------------------o y o---------o | Encoder |--->| p(y,y1|x1,x2) |--->| Decoder | o---------o o------------------o o---------o </nowiki>
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.
max | |
p(x1,x2) |
min\left(I\left(x1;y1|x2\right),I\left(x1,x2;y\right)\right)
max | |
p(x1)p(\haty1|y1)p(x2) |
I\left(x1;\hat{y1},y|x2\right)
I(x2;y)\geqI(y1;\haty1|y)
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
C\leq
max | |
p(x1,x2) |
min\left(I\left(x1;y1,y|x2\right),I\left(x1,x2;y\right)\right)
A relay channel is said to be degraded if y depends on
x1
y1
x2
p(y|x1,x2,y1)=p(y|x2,y1)
A relay channel is said to be reversely degraded if
p(y,y1|x1,x2)=p(y|x1,x2)p(y1|y,x2)
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.