Fundamental Limits of Demand-Private Coded Caching
Chinmay Gurjarpadhye, Jithin Ravi, Sneha Kamath, Bikash Kumar Dey, Nikhil Karamchandani · IEEE Transactions on Information Theory · 2022
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$N \leq K$. Finally, we give the exact memory-rate trade-off for demand-private coded caching problems with$N\geq K=2$.