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Asymptotic Coupling and Its Applications in Information Theory by Yu, Lei; Tan, Vincent Y. F. is a scholarly article available to read on EtoBox.

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A coupling of two distributions $P_{X}$ and $P_{Y}$ is a joint distribution $P_{XY}$ with marginal distributions equal to $P_{X}$ and $P_{Y}$. Given marginals $P_{X}$ and $P_{Y}$ and a real-valued function $f$ of the joint distribution $P_{XY}$, what is its minimum over all couplings $P_{XY}$ of $P_{X}$ and $P_{Y}$? We study the asymptotics of such coupling problems with different $f$'s and with $X$ and $Y$ replaced by $X^{n}=(X_{1},\ldots,X_{n})$ and $Y^{n}=(Y_{1},\ldots,Y_{n})$ where $X_{i}$ and $Y_{i}$ are i.i.d.\ copies of random variables $X$ and $Y$ with distributions $P_{X}$ and $P_{Y}$ respectively. These include the maximal coupling, minimum distance coupling, maximal guessing coupling, and minimum entropy coupling problems. We characterize the limiting values of these coupling problems as $n$ tends to infinity. We show that they typically converge at least exponentially fast to their limits. Moreover, for the problems of maximal coupling and minimum excess-distance probability coupling, we also characterize (or bound) the optimal convergence rates (exponents). Furthermore, for the maximal guessing coupling problem we show that it is equivalent to the distribution approxim

Author

Yu, Lei; Tan, Vincent Y. F.

Published

2017

Language

EN