We consider the coded caching problem with shared caches where several users share a cache, but each user has access to only a single cache. For this network, the fundamental limits of coded caching are known for centralized and decentralized settings under uncoded placement. In the centralized case, to achieve the gains offered by coded caching, one requires a sub-packetization which increases exponentially with the number of caches. The dedicated cache networks had a similar issue, and placement delivery arrays (PDAs) were introduced as a solution to it. Using the PDA framework, we propose a procedure to obtain new coded caching schemes for shared caches with lower sub-packetization requirements. The advantage of this procedure is that we can transform all the existing PDA structures into coded caching schemes for shared caches, thus resulting in low sub-packetization schemes. We also show that the optimal scheme given by Parrinello, Unsal and Elia (Fundamental Limits of Coded Caching with Multiple Antennas, Shared Caches and Uncoded Prefetching) can be recovered using a Maddah-Ali Niesen PDA.
翻译:我们考虑了共享缓存的编码缓存问题, 有几个用户共享缓存, 但每个用户只能访问一个单个缓存 。 对于这个网络, 编码缓存的基本限制在未编码的集中和分散环境中是已知的。 在集中的情况下, 要实现编码缓存带来的收益, 需要一个子包装, 随着缓存数量的增加而成倍增长。 专用缓存网络也有类似的问题, 并且引入了放置交付阵列( PDA ) 作为解决办法 。 我们使用 PDA 框架, 提议了一个程序, 以获得新的编码缓存计划, 用于使用较低次包装要求的共享缓存 。 这个程序的优点是, 我们可以将所有现有的 PDA 结构转换为共享缓存的编码缓存计划, 从而导致子包装计划的减少 。 我们还表明, Parrinello, Unsal 和 Elia ( 与多个安滕纳、 共享缓存和未编码预缓存) 的最佳计划可以使用Maddah- Ali Niesen PDA 来回收。