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An upper bound on relaying over capacity based on channel simulation
The upper bound on the capacity of a 3-node discrete memoryless relay channel
is considered, where a source X wants to send information to destination Y with
the help of a relay Z. Y and Z are independent given X, and the link from Z to
Y is lossless with rate . A new inequality is introduced to upper-bound
the capacity when the encoding rate is beyond the capacities of both individual
links XY and XZ. It is based on generalization of the blowing-up lemma, linking
conditional entropy to decoding error, and channel simulation, to the case with
side information. The achieved upper-bound is strictly better than the
well-known cut-set bound in several cases when the latter is , with
being the channel capacity between X and Y. One particular case is
when the channel is statistically degraded, i.e., either Y is a statistically
degraded version of Z with respect to X, or Z is a statistically degraded
version of Y with respect to X. Moreover in this case, the bound is shown to be
explicitly computable. The binary erasure channel is analyzed in detail and
evaluated numerically.Comment: Submitted to IEEE Transactions on Information Theory, 21 pages, 6
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