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arXiv 1706.07035cs.ITcs.CRcs.DCmath.IT
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Cache辅助私有信息检索的容量

The Capacity of Cache Aided Private Information Retrieval

Ravi Tandon

摘要:

考虑了允许高速缓存的私有信息检索(PIR)问题,其中用户希望从$N$分布式数据库中私有地检索$K$消息中的一个,每个消息的大小为$L$比特。用户具有存储$SL$位的本地高速缓冲存储器,其可用于存储$K$消息的任何功能。这项工作的主要贡献是准确表征的能力的高速缓存辅助PIR作为存储参数$S$的函数。特别地,对于给定的高速缓存存储参数$S$,信息理论上最优的下载成本$D^{*}(S)/L$(或容量的倒数)被示出为等于$(1- \frac{S}{K})\left(1+ \frac{1}{N}+ \ldots + \frac{1}{N^{K-1}}\right)$。该结果的特殊情况对应于当$S=0$时的设置,对于该设置,Sun和Jafar示出了最佳下载成本为$\left(1+ \frac{1}{N}+ \ldots + \frac{1}{N^{K-1}}\right)$,以及当$S=K$时的情况,即,缓存大小足够大,可以在本地存储所有消息,最佳下载成本为$0$。中间点$S\in (0, K)$可以很容易地通过一个简单的基于内存共享的PIR方案来实现。这项工作的关键技术贡献是相反的,即,下载成本的下限作为存储$S$的函数,这表明内存共享是信息理论上最优的。

英文摘要:

The problem of cache enabled private information retrieval (PIR) is considered in which a user wishes to privately retrieve one out of $K$ messages, each of size $L$ bits from $N$ distributed databases. The user has a local cache of storage $SL$ bits which can be used to store any function of the $K$ messages. The main contribution of this work is the exact characterization of the capacity of cache aided PIR as a function of the storage parameter $S$. In particular, for a given cache storage parameter $S$, the information-theoretically optimal download cost $D^{*}(S)/L$ (or the inverse of capacity) is shown to be equal to $(1- \frac{S}{K})\left(1+ \frac{1}{N}+ \ldots + \frac{1}{N^{K-1}}\right)$. Special cases of this result correspond to the settings when $S=0$, for which the optimal download cost was shown by Sun and Jafar to be $\left(1+ \frac{1}{N}+ \ldots + \frac{1}{N^{K-1}}\right)$, and the case when $S=K$, i.e., cache size is large enough to store all messages locally, for which the optimal download cost is $0$. The intermediate points $S\in (0, K)$ can be readily achieved through a simple memory-sharing based PIR scheme. The key technical contribution of this work is the converse, i.e., a lower bound on the download cost as a function of storage $S$ which shows that memory sharing is information-theoretically optimal.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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