Demand-Private Coded Caching and the Exact Trade-off for N=K=2

The distributed coded caching problem has been studied extensively in the recent past. While the known coded caching schemes achieve an improved transmission rate, they violate the privacy of the users since in these schemes the demand of one user is revealed to others in the delivery phase. In this paper, we consider the coded caching problem under the constraint that the demands of the other users remain information theoretically secret from each user. We first show that the memory-rate pair (M, min{ N, K}(1- M / N)) is achievable under information theoretic demand privacy, while using broadcast transmissions. Using this, we show that perfectly demand-private coded caching rate is order optimal for all parameter regimes. We then show that a demand-private scheme for $N$ files and $K$ users can be obtained from a non-private scheme that satisfies only a restricted subset of demands of N K users for $N$ files. We then focus on the demand-private coded caching problem for $K$ = 2 users, $N$ = 2 files. We characterize the exact memory-rate trade-off for this case. To show the achievability, we use our first result to construct a demand-private scheme from a non-private scheme satisfying a restricted demand subset that is known from an earlier work by Tian. Further, by giving a converse based on the extra requirement of privacy, we show that the obtained achievable region is the exact memory-rate trade-off.