论文标题
用多项式子包装编码的缓存
Coded Caching with Polynomial Subpacketization
论文作者
论文摘要
考虑具有单个服务器和$ K $用户的集中式缓存网络。该服务器具有$ n $文件的数据库，每个文件都将每个文件分为$ f $ cacket（$ f $称为子包装），并且每个用户都有一个本地高速缓存，该缓存可以存储$ \ frac {m} {n} $ n $文件的分数。我们构建了一个具有多项式子包装的集中编码缓存方案的家族。具体来说，给定$ m $，$ n $和一个整数$ n \ geq 0 $，我们为任何$（k，m，n）$ f = o（k^{n+1}）$的任何$（k，m，n）$加速系统构建了一个编码的加速方案。更一般地，对于任何$ t \ in \ {1,2，\ cdots，k-2 \} $和任何整数$ n $，以使$ 0 \ leq n \ leq t $，我们构建了一个用$ \ frac {m} {n} {n} {n} = \ frac {t} $ f \ f \ f \ f \ f \ f \ f \ f \ f \ f \ f \ f \ f \ f \ f \ f \ f \ f \ f \ f \ f \ f \ f \ f \ f \ k \ binom {\ left（1- \ frac {m} {n} \ right）k+n} {n} $。
Consider a centralized caching network with a single server and $K$ users. The server has a database of $N$ files with each file being divided into $F$ packets ($F$ is known as subpacketization), and each user owns a local cache that can store $\frac{M}{N}$ fraction of the $N$ files. We construct a family of centralized coded caching schemes with polynomial subpacketization. Specifically, given $M$, $N$ and an integer $n\geq 0$, we construct a family of coded caching schemes for any $(K,M,N)$ caching system with $F=O(K^{n+1})$. More generally, for any $t\in\{1,2,\cdots,K-2\}$ and any integer $n$ such that $0\leq n\leq t$, we construct a coded caching scheme with $\frac{M}{N}=\frac{t}{K}$ and $F\leq K\binom{\left(1-\frac{M}{N}\right)K+n}{n}$.
