  A lossy source coding problem with privacy constraint is studied in which two
correlated discrete sources $X$ and $Y$ are compressed into a reconstruction
$\hat{X}$ with some prescribed distortion $D$. In addition, a privacy
constraint is specified as the equivocation between the lossy reconstruction
$\hat{X}$ and $Y$. This models the situation where a certain amount of source
information from one user is provided as utility (given by the fidelity of its
reconstruction) to another user or the public, while some other correlated part
of the source information $Y$ must be kept private. In this work, we show that
polar codes are able, possibly with the aid of time sharing, to achieve any
point in the optimal rate-distortion-equivocation region identified by
Yamamoto, thus providing a constructive scheme that obtains the optimal
tradeoff between utility and privacy in this framework.
