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arXiv 2102.02122cs.ITmath.IT
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一种通用的标量线性函数检索编码缓存方案

A General Coded Caching Scheme for Scalar Linear Function Retrieval

Yinbin Ma, Daniela Tuninetti

摘要:

编码缓存的目的是通过利用预先存储在用户本地缓存中的信息来最小化网络的峰值时间通信负载。Maddah-Ali和Niesen最初的单文件检索设置最近已由Wan等人扩展到一般标量线性函数检索(SLFR),他提出了一种线性方案,该方案令人惊讶地实现了与单个文件检索相同的最佳负载(在未编码的高速缓存放置的约束下)。本文的目标是描述一般SLFR线性方案是最优的条件,并获得实际的见解,为什么万等人的具体选择。本文证明了最佳译码系数必然是两项的乘积,一项只涉及编码系数,另一项只涉及需求。此外,编码系数之间的关系被示出为通过某些图的循环来捕获。因此,一个一般的线性计划SLFR可以找到通过解决一个生成树问题。

英文摘要:

Coded caching aims to minimize the network's peak-time communication load by leveraging the information pre-stored in the local caches at the users. The original single file retrieval setting by Maddah-Ali and Niesen has been recently extended to general Scalar Linear Function Retrieval (SLFR) by Wan et al., who proposed a linear scheme that surprisingly achieves the same optimal load (under the constraint of uncoded cache placement) as in single file retrieval. This paper's goal is to characterize the conditions under which a general SLFR linear scheme is optimal and gain practical insights into why the specific choices made by Wan et al. work. This paper shows that the optimal decoding coefficients are necessarily the product of two terms, one only involving the encoding coefficients and the other only the demands. In addition, the relationships among the encoding coefficients are shown to be captured by the cycles of certain graphs. Thus, a general linear scheme for SLFR can be found by solving a spanning tree problem.

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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