In this paper, we study shared cache coded caching (SC-CC): a set of caches serves a larger set of users; each user access one cache, and a cache may serve many users. For this problem, under uncoded placement, Parrinello, \"Unsal, and Elia showed an optimal SC-CC scheme, in which the subpacketization level depends upon the number of caches. We show an SC-CC scheme where the subpacketization level does not directly depend upon the number of users or caches; any number of caches and users can be accommodated for a fixed subpacketization level. Furthermore, new caches can be added without re-doing the placement of the existing caches. We show that given an upper limit on the allowable subpacketization level, our SC-CC scheme may achieve a lesser rate than other relevant SC-CC schemes. Our scheme is constructed using matrices and designs. A matroid can be obtained from a matrix over a finite field; the placement of our scheme is decided by a design constructed from a matrix; the circuits of a matroid obtained from the matrix and the design is used to decide the delivery.
翻译:在本文中,我们研究了共享缓存编码缓存(SC-CC):一组缓存为更多的用户服务;每个用户访问一个缓存,一个缓存可能为许多用户服务。对于这个问题,在未编码的放置下,Parrinello,\"Unsal和Elia展示了最佳的SC-CC办法,在这种办法中,子包装水平取决于缓存的数量。我们展示了SC-CC办法,在这种办法中,子包装水平并不直接取决于用户或缓存的数量;任何数量的缓存和用户都可以容纳在固定的子包装水平上。此外,可以添加新的缓存,而不对现有缓存进行重新布置。我们表明,在允许的子包装水平上设定了一个上限,我们的SC-CC办法可能比其他相关的SC-CC办法低一个上限。我们的计划是使用矩阵和设计来构建的。从一个基质基中可以获得一个基质的基数,而不是一个限定的字段;我们的计划是由一个基质设计来决定的;从矩阵中获取的基质的电路。