Capacity of a Class of Deterministic Relay Channels
<|reference_start|>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 Y_1 = f(X, Y), and a separate communication link from the relay to the receiver with capacity R_0, is shown to be   C(R_0) = \max_{p(x)} \min \{I(X;Y)+R_0, I(X;Y, Y_1) \}.   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 usual ``compress-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.<|reference_end|>
@article{cover2006capacity,
    title={Capacity of a Class of Deterministic Relay Channels},
    author={Thomas M. Cover, Young-Han Kim},
    journal={arXiv preprint arXiv:cs/0611053},
    year={2006},
    doi={10.1109/ISIT.2007.4557289},
    archivePrefix={arXiv},
    eprint={cs/0611053},
    primaryClass={cs.IT math.IT}
}