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.
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机译：本文表明，对于任何随机变量$ X $和$ Y $，可以将$ Y $表示为$（X，Z）$的函数，使得$ Z $独立于$ X $和$ I（X ; Z | Y）\ le \ log（I（X; Y）+1）+ 4 $位。我们使用这种强大的功能表示引理（SFRL）来确定一般（离散或连续）随机变量一次精确通道仿真所需速率的界限，从而增强了Harsha等人的结果。以及Braverman和Garg，并为一击变长有损源编码，多描述编码和Gray-Wynersystem建立新的，简单的可实现性结果。我们还表明，SFRL可用于将编码器处因非已知状态的信道减少为点对点信道，这提供了Gelfand-Pinsker定理的简单可实现性证明。
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