Preserving ON-OFF Privacy for Past and Future Requests

We study the ON-OFF privacy problem. At each time, the user is interested in the latest message of one of $N$ sources. Moreover, the user is assumed to be incentivized to turn privacy ON or OFF whether he/she needs it or not. When privacy is ON, the user wants to keep private which source he/she is interested in. The challenge here is that the user's behavior is correlated over time. Therefore, the user cannot simply ignore privacy when privacy is OFF, because this may leak information about his/her behavior when privacy was ON due to correlation. We model the user's requests by a Markov chain. The goal is to design ON-OFF privacy schemes with optimal download rate that ensure privacy for past and future requests. The user is assumed to know future requests within a window of positive size $\omega$ and uses it to construct privacy-preserving queries. In this paper, we construct ON-OFF privacy schemes for $N=2$ sources and prove their optimality.