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arXiv 2201.10585cs.ITmath.IT
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多天线编码缓存方案中的扩展放置传送阵列

Extended Placement Delivery Arrays for Multi-Antenna Coded Caching Scheme

K. K. Krishnan Namboodiri, Elizabath Peter, B. Sundar Rajan

摘要:

多天线编码缓存问题,其中具有$L$发送天线的服务器通过无线广播链路与$K$用户通信,得到解决。在问题设置中,服务器有一个$N$文件库,每个用户都配备了一个容量为$M$的专用缓存。针对上述多天线编码缓存问题,提出了扩展放置传递阵列(EPDA)的思想,该阵列由特殊符号$\star$和集合$\{1,2,\dots,S\}$中的整数组成.从$(K,L,F,Z,S)$ EPDA,可以获得具有$K$用户的多天线编码缓存方案和具有$L$发射天线的服务器,其中归一化存储器$\frac{M}{N}=\frac{Z}{F}$和递送时间$T=\frac{S}{F}$。放置交付阵列(用于单天线编码缓存方案)是一类特殊的具有$L=1$的EPDA。对于多天线编码缓存方案构造EPDA,它示出了,可以实现的最大可能的自由度(DoF)是$t+L$,其中$t=\frac{KM}{N}$是一个整数。此外,提出了两种EPDA的构造:a)$ K=t+L$,和b)$K=nt+(n-1)L, \hspace{0.1cm}L\geq t$,其中$n\geq 2$是整数。在从这些EPDA得到的多天线方案中,实现了完整的DoF,同时需要子分组化数$\frac{K}{\text{gcd}(K,t,L)}$。该子分组数小于文献中先前已知的方案所需的子分组数。

英文摘要:

The multi-antenna coded caching problem, where the server having $L$ transmit antennas communicating to $K$ users through a wireless broadcast link, is addressed. In the problem setting, the server has a library of $N$ files, and each user is equipped with a dedicated cache of capacity $M$. The idea of extended placement delivery array (EPDA), an array which consists of a special symbol $\star$ and integers in a set $\{1,2,\dots,S\}$, is proposed to obtain a novel solution for the aforementioned multi-antenna coded caching problem. From a $(K,L,F,Z,S)$ EPDA, a multi-antenna coded caching scheme with $K$ users, and the server with $L$ transmit antennas, can be obtained in which the normalized memory $\frac{M}{N}=\frac{Z}{F}$, and the delivery time $T=\frac{S}{F}$. The placement delivery array (for single-antenna coded caching scheme) is a special class of EPDAs with $L=1$. For the multi-antenna coded caching schemes constructed from EPDAs, it is shown that the maximum possible Degree of Freedom (DoF) that can be achieved is $t+L$, where $t=\frac{KM}{N}$ is an integer. Furthermore, two constructions of EPDAs are proposed: a) $ K=t+L$, and b) $K=nt+(n-1)L, \hspace{0.1cm}L\geq t$, where $n\geq 2$ is an integer. In the resulting multi-antenna schemes from those EPDAs achieve the full DoF, while requiring a subpacketization number $\frac{K}{\text{gcd}(K,t,L)}$. This subpacketization number is less than that required by previously known schemes in the literature.

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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