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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.Comment: 17 pages, submitted to IEEE Transactions on Information Theor
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