A Universal Coding Scheme for Remote Generation of Continuous Random Variables
IEEE Transactions on Information Theory(2016)
摘要
We consider a setup in which Alice selects a pdf $f$ from a set of prescribed pdfs $\mathscr{P}$ and sends a prefix-free codeword $W$ to Bob in order to allow him to generate a single instance of the random variable $X\sim f$. We describe a universal coding scheme for this setup and establish an upper bound on the expected codeword length when the pdf $f$ is bounded, orthogonally concave (which includes quasiconcave pdf), and has a finite first absolute moment. A dyadic decomposition scheme is used to express the pdf as a mixture of uniform pdfs over hypercubes. Alice randomly selects a hypercube according to its weight, encodes its position and size into $W$, and sends it to Bob who generates $X$ uniformly over the hypercube. Compared to previous results on channel simulation, our coding scheme applies to any continuous distribution and does not require two-way communication or shared randomness. We apply our coding scheme to classical simulation of quantum entanglement and obtain a better bound on the average codeword length than previously known.
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关键词
Universal code,channel simulation,communication complexity,simulation of quantum entanglement
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