  We consider the problem of ON-OFF privacy in which a user is interested in
the latest message generated by one of n sources available at a server. The
user has the choice to turn privacy ON or OFF depending on whether he wants to
hide his interest at the time or not. The challenge of allowing the privacy to
be toggled between ON and OFF is that the user's online behavior is correlated
over time. Therefore, the user cannot simply ignore the privacy requirement
when privacy is OFF. We represent the user's correlated requests by an n-state
Markov chain. Our goal is to design ON-OFF privacy schemes with optimal
download rate that ensure privacy for past and future requests. We devise a
polynomial-time algorithm to construct an ON-OFF privacy scheme. Moreover, we
present an upper bound on the achievable rate. We show that the proposed scheme
is optimal and the upper bound is tight for some special families of Markov
chains. We also give an implicit characterization of the optimal achievable
rate as a linear programming (LP).
