# Relay channel

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Relay channel

In information theory, a relay channel is a probability model on the communication between a sender and a receiver aided by one or more intermediate relay nodes. It is a combination of the broadcast channel (from sender to relays and receiver) and multiple access channel (from sender and relays to receiver).

General discrete-time memoryless relay channel

A discrete memoryless single-relay channel can be modelled as four finite sets, $X_1, X_2, Y_1,$ and $Y$, and a conditional probability distribution $p\left(y,y_1|x_1,x_2\right)$ on these sets. The probability distribution of the choice of symbols selected by the encoder and the relay encoder is represented by $p\left(x_1,x_2\right)$.

o------------------o
Relay Encoder
o------------------o A
y1 x2
Vo---------o x1 o------------------o y o---------o
Encoder |--->| p(y,y1|x1,x2) |--->| Decoder
o---------o o------------------o o---------o

Such a relay channel is said to be degraded if "y" depends on $x_1$ only through $y_1$ and $x_2$, i.e., $p\left(y | x_1, x_2, y_1\right) = p\left(y | x_2, y_1\right)$.

Feedback relay channel

Relay without delay channel

References

* Thomas M. Cover and Abbas El Gamal, " [http://yreka.stanford.edu/~cover/papers/transIT/0572cove.pdf Capacity theorems for the relay channel] ," " IEEE Transactions on Information Theory" (1979), pp. 572-584

* Many resources on the Relay Channel and Cooperative Communications are available at " [http://utdallas.edu/~ramy/relaying.htm] ," - from Ramy Medhat Tannious webpage - UT Dallas.

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