The Optimal Constant for One-Shot Channel Simulation and Strong Functional Representation Lemma

arXiv:2611.13397v1 Announce Type: new Abstract: We prove a tight bound for one-shot channel simulation via a stronger version of the strong functional representation lemma: for any random variables $X,Y$, there exists a random variable $Z$ with $I(Z;X)=H(Y|X,Z)=0$ and $H(Y|Z)\le I+\log I+(1-\gamma)\log e-\log\log e+O(I^{-1}\log I)$, where $I=I(X;Y)$ and $\gamma$ is the Euler-Mascheroni constant. A more convenient bound is $H(Y|Z)Source：https://arxiv.org/abs/2611.13397

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