Privacy-Aware MMSE Estimation

We investigate the problem of the predictability of random variable $Y$ under a privacy constraint dictated by random variable $X$, correlated with $Y$, where both predictability and privacy are assessed in terms of the minimum mean-squared error (MMSE). Given that $X$ and $Y$ are connected via a binary-input symmetric-output (BISO) channel, we derive the optimal random mapping $P_{Z\vert \mathrm{Y}}$ such that the MMSE of $Y$ given $Z$ is …