On the Rate-Memory Trade-off for Two-Dimensional Multi-Access Coded Caching

We study a two-dimensional multi-access coded caching problem involving a central server with a collection of files, cache nodes arranged in a rectangular grid, and users. Each user requests a file from the central server and has access to a specific subset of neighboring caches. The caches are prepopulated with content derived from the files, and the users request files to be served through a shared broadcast link from the central server, assisted by the cache contents. Our goal is to design placement and delivery policies that minimize the broadcast transmission from the central server. A special case, where each user accesses an equal number of caches along the rows and columns of the rectangular grid, was previously analyzed in [1], where a coloring-based grouping scheme was applied to derive an achievable rate-memory trade-off for the two-dimensional setting. In this work, we first extend the grouping scheme to the more general cases where users access different numbers of caches along rows and columns. Additionally, for scenarios where users access only one cache along the columns, we propose a new placement and delivery policy and demonstrate that it achieves better performance than the grouping scheme. Furthermore, we address the high subpacketization issue by deriving an achievable rate-memory trade-off under the constraint of linear subpacketization for the two-dimensional multi-access coded caching problem.