Capacity of a Class of Deterministic Relay Channels

Abstract

The capacity of a class of deterministic relay channels with transmitter input X, receiver output Y, relay output Y <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> = f(X, Y), and separate noiseless communication link of capacity R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> from the relay to the receiver, is shown to be C(R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> ) = sup min {I(X;Y) + R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> , I(X;Y,Y,)}. P(x) Roughly speaking, every bit from the relay is worth one bit to the receiver until saturation at capacity.