Fundamental Limits of Demand-Private Coded Caching
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We consider the coded caching problem with an additional privacy constraint that a user should not get any information about the demands of the other users. We first show that a demand-private scheme for N files and K users can be obtained from a non-private scheme that serves only a subset of the demands for the N files and NK users problem. We further use this fact to construct a demand-private scheme for N files and K users from a particular known non-private scheme for N files and NK-K+1 users. It is then demonstrated that, the memory-rate pair (M,min{N,K}(1-M/N)), which is achievable for non-private schemes with uncoded transmissions, is also achievable under demand privacy. We further propose a scheme that improves on these ideas by removing some redundant transmissions. The memory-rate trade-off achieved using our schemes is shown to be within a multiplicative factor of 3 from the optimal when K < N and of 8 when N≤ K. Finally, we give the exact memory-rate trade-off for demand-private coded caching problems with N≥ K=2.
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