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This paper shows that for any random variables $X$ and $Y$, it is possible torepresent $Y$ as a function of $(X,Z)$ such that $Z$ is independent of $X$ and$I(X;Z|Y)\le\log(I(X;Y)+1)+4$ bits. We use this strong functionalrepresentation lemma (SFRL) to establish a bound on the rate needed forone-shot exact channel simulation for general (discrete or continuous) randomvariables, strengthening the results by Harsha et al. and Braverman and Garg,and to establish new and simple achievability results for one-shotvariable-length lossy source coding, multiple description coding and Gray-Wynersystem. We also show that the SFRL can be used to reduce the channel with statenoncausally known at the encoder to a point-to-point channel, which provides asimple achievability proof of the Gelfand-Pinsker theorem.

Strong Functional Representation Lemma and Applications to Coding Theorems