Capacity of a Class of Deterministic Relay Channels

The capacity of a class of deterministic relay channels with the transmitter input X, the receiver output Y, the relay output Y1 = f(X, Y), and a separate communication link from the relay to the receiver with capacity R0, is shown to be C(R0) = \max{p(x)} \min {I(X;Y)+R0, I(X;Y, Y1) }. Thus every bit from the relay is worth exactly one bit to the receiver. Two alternative coding schemes are presented that achieve this capacity. The first scheme, hash-and-forward'', is based on a simple yet novel use of random binning on the space of relay outputs, while the second scheme uses the usualcompress-and-forward''. In fact, these two schemes can be combined together to give a class of optimal coding schemes. As a corollary, this relay capacity result confirms a conjecture by Ahlswede and Han on the capacity of a channel with rate-limited state information at the decoder in the special case when the channel state is recoverable from the channel input and the output.