论文标题
多安德滕纳编码的缓存方案的扩展放置递送阵列
Extended Placement Delivery Arrays for Multi-Antenna Coded Caching Scheme
论文作者
论文摘要
多个Antenna编码的缓存问题，该问题的服务器通过无线广播链接传输了$ l $ $ $ $ k $用户的天线。在问题设置中，服务器具有$ n $文件的库，每个用户都配备了容量$ m $的专用缓存。提出了一个由特殊符号$ \ star $组成的阵列扩展放置递送阵列（EPDA）的想法，并提议在集合$ \ {1,2，\ dots，s \} $中获得一个新颖的解决方案，以获取上述多端antenna编码的缓存问题的新颖解决方案。从$（k，l，f，z，s）$ epda，一种带有$ k $用户的多安特纳编码的缓存方案，可以获得$ l $ transmit antennas的服务器，其中可以获得标准化的内存$ \ frac {m} {m} {n} {n} = \ frac {z} {z} {f} $ $ time $ t Time $ teless $ t Time $ t frac frac。放置递送阵列（用于单安坦纳编码的缓存方案）是一类特殊的EPDA，$ l = 1 $。对于由EPDAS构建的多端纳编码的缓存方案，可以证明可以实现的最大自由度（DOF）为$ t+l $，其中$ t = \ frac {km} {n} {n} $是integer。此外，提出了两个EPDA的结构：a）$ k = t+l $，b）$ k = nt+（n-1）l，\ hspace {0.1cm} l \ geq t $，其中$ n \ geq 2 $是整数。在这些EPDA的生成的多Antenna方案中，可以实现完整的DOF，同时需要一个子包装编号$ \ frac {k} {\ text {gcd} {gcd}（k，k，t，l）} $。该子包装数量小于文献中先前已知的方案所要求的。
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.
