发表机构
Southeast University（东南大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种阶最优的编码缓存方案，在文件和需求隐私下实现最坏情况速率至多9/2倍最优，并给出下界与精确权衡。
AI 中文摘要
我们研究了具有联合文件和需求隐私性的编码缓存：每个用户恢复其请求的文件，同时联合地不学习关于其余文件和其他用户请求的任何信息。设$N$和$K$分别为文件和用户的数量，设$M$和$R$分别表示缓存内存和传输速率，两者均按文件大小归一化。对于每个$N,K\ge2$和每个可行的缓存大小，我们给出一个方案，其最坏情况传输速率至多为最优值的$9/2$倍。为了减少用于文件份额的内存，该方案对相对于参考文件的$N-1$个差异进行秘密共享。缓存的掩码提供从差异中恢复所请求文件所需的校正。对于每个整数$t\in\{0,\ldots,K-1\}$，该方案实现$M=1+(N-1)t/(K-t)$和$R=K/(t+1)$。为了对传输速率进行下界，我们在替代需求向量下比较用户组的联合缓存熵，使用一个固定用户的隐私约束。两组的选择在$M>1$时在尺度$\min\{K,1+(N-1)/(M-1)\}$上确定最优传输速率直至常数因子。在$M=1$时，精确最优值为$K$。联合广播熵的互补界给出了单位传输速率的最小内存$1+(N-1)(K-1)$，以及在该内存结束的区间上的精确权衡。所有方案和界适用于重复请求和不同请求。
英文摘要
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 $N,K\ge2$ 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 $t\in\{0,\ldots,K-1\}$, 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.
Comments14 pages, 2 figures, 1 table
