Capacity of a Class of Deterministic Relay Channels

Abstract-- 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 variation of the usual random binning on the relay outputs, while the second scheme uses the usual "compress-andforward". In fact, these two schemes can be combined 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 output.

• Type: Journal
• Year: 2006
• Where: CORR
• Authors: Thomas M. Cover, Young-Han Kim
• Keywords: CORR 2006, Deterministic Relay Channels, Education, Relay, Relay Output