  In this paper, we investigate the privacy-utility trade-off (PUT) problem,
which considers the minimal privacy loss at a fixed expense of utility. Several
different kinds of privacy in the PUT problem are studied, including
differential privacy, approximate differential privacy, maximal information,
maximal leakage, Renyi differential privacy, Sibson mutual information and
mutual information. The average Hamming distance is used to measure the
distortion caused by the privacy mechanism. We consider two scenarios: global
privacy and local privacy. In the framework of global privacy framework, the
privacy-distortion function is upper-bounded by the privacy loss of a special
mechanism, and lower-bounded by the optimal privacy loss with any possible
prior input distribution. In the framework of local privacy, we generalize a
coloring method for the PUT problem.
