Multi-Access Coded Caching Schemes from Maximal Cross Resolvable Designs

We study the problem of multi-access coded caching (MACC): a central server has N files, K (K ≤ N) caches each of which stores M out of the N files, K users each of which demands one out of the N files, and each user accesses z caches. The objective is to jointly design the placement, delivery, and user-to-cache association, to optimize the achievable rate. This problem has been extensively studied in the literature under the assumption that a user accesses only one cache. However, when a user accesses one or more caches, this problem has been studied only under the assumption that a user accesses z consecutive caches with a cyclic wrap-around over the boundaries. A natural question is how other user-to-cache associations fare against the cyclic wrap-around user-to-cache association. A bipartite graph can describe a general user-to-cache association. We identify a class of bipartite graphs that, when used as a user-to-cache association, achieves either a lesser rate or a lesser subpacketization than all other existing MACC schemes using a cyclic wrap-around user-to-cache association. The placement and delivery strategy of our MACC scheme is constructed using a combinatorial structure called maximal cross resolvable design.