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Let $X^n\in\mathcal{X}^n$ be a sequence drawn from a discrete memorylesssource, and let $Y^n\in\mathcal{Y}^n$ be the corresponding reconstructionsequence that is output by a good rate-distortion code. This paper establishesa property of the joint distribution of $(X^n,Y^n)$. It is shown that for$D>0$, the input-output statistics of a $R(D)$-achieving rate-distortion codeconverge (in normalized relative entropy) to the output-input statistics of adiscrete memoryless channel (dmc). The dmc is "backward" in that it is achannel from the reconstruction space $\mathcal{Y}^n$ to source space$\mathcal{X}^n$. It is also shown that the property does not necessarily holdwhen normalized relative entropy is replaced by variational distance.

A Connection between Good Rate-distortion Codes and Backward DMCs