Deterministic relay channels

Capacity of a class of deterministic relay channels

Young-Han Kim

IEEE Transactions on Information Theory, vol. 54, no. 3, pp. 1328–1329, March 2008.
An alternative derivation of the coding theorem based on hash-and-forward coding appeared in arXiv (cs.IT/0611053) and Proceedings of IEEE International Symposium on Information Theory, pp. 591–595, Nice, France, June 2007.
IEEE AbstractPlus.

The capacity of a class of deterministic relay channels with transmitter input , receiver output , 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

$C(R_0) = sup_{p(x)} min { I(X;Y) + R_0,; I(X;Y, Y_1) }.$

Roughly speaking, every bit from the relay is worth one bit to the receiver until saturation at capacity.