Capacity of a Class of Deterministic Relay Channels

The capacity of a class of deterministic relay channels with transmitter input X, receiver output Y, relay output Y
₁
= f(X, Y), and separate noiseless communication link of capacity R
₀
from the relay to the receiver, is shown to be C(R
₀
) = sup min {I(X;Y) + R
₀
, I(X;Y,Y,)}. P(x) Roughly speaking, every bit from the relay is worth one bit to the receiver until saturation at capacity.