  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.
