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- W2964045791 abstract "A coupling of two distributions P <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>X</sub> and P <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>Y</sub> is a joint distribution P <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>XY</sub> with marginal distributions equal to P <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>X</sub> and P <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>Y</sub> . Given marginals P <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>X</sub> and P <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>Y</sub> and a real-valued function f of the joint distribution P <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>XY</sub> , what is its minimum over all couplings P <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>XY</sub> of P <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>X</sub> and P <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>Y</sub> ? We study the asymptotics of such coupling problems with different f's and with X and Y replaced by X <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</sup> = (X <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sub> , . . . , X <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</sub> ) and Y <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</sup> = (Y1, . . . , Y <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</sub> ) where X <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>i</sub> and Y <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>i</sub> are i.i.d. copies of random variables X and Y with distributions P <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>X</sub> and P <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>Y</sub> , 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 approximation problem. Therefore, some existing results for the latter problem can be used to derive the asymptotics of the maximal guessing coupling problem. We also study the asymptotics of the maximal guessing coupling problem for two general sources and a generalization of this problem, named the maximal guessing coupling through a channel problem. We apply the preceding results to several new information-theoretic problems, including exact intrinsic randomness, exact resolvability, channel capacity with input distribution constraint, and perfect stealth and secrecy communication." @default.
- W2964045791 created "2019-07-30" @default.
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- W2964045791 date "2019-03-01" @default.
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- W2964045791 title "Asymptotic Coupling and Its Applications in Information Theory" @default.
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