Order-Optimal Coded Caching With File and Demand Privacy

Abstract

We study coded caching with joint file and demand privacy: each user recovers its requested file while learning nothing about the remaining files and the other users' requests jointly. Let $N$ and $K$ be the numbers of files and users, and let $M$ and $R$ denote the cache memory and delivery rate, both normalized by the file size. For every $N,K\ge 2$ and every feasible cache size, we give a scheme whose worst-case delivery rate is at most $9/2$ times the optimum. To reduce the memory used for file shares, the scheme secret-shares $N-1$ differences relative to a reference file. Cached masks supply the correction needed to recover the requested file from its difference. For each integer $t\in \{0,\dots ,K-1\}$, the scheme achieves $M=1+(N-1)t/(K-t)$ and $R=K/(t+1)$. To lower-bound the delivery rate, we compare the joint cache entropy of user groups under alternative demand vectors, using one fixed user's privacy constraint. Two choices of groups determine the optimal delivery rate up to constants at the scale $\min \{K,1+(N-1)/(M-1)\}$ for $M>1$. At $M=1$, the exact optimum is $K$. A complementary bound on joint broadcast entropy gives the minimum memory for unit delivery rate, $1+(N-1)(K-1)$, and the exact tradeoff on an interval ending at that memory. All schemes and bounds apply to repeated as well as distinct requests.

14 pages, 2 figures, 1 table