Improved multi-access coded caching schemes from maximal cross resolvable designs

In multi-access coded caching (MACC) schemes, most research assumes that the users access $ z $ continuous caches by the way of a cyclic wrap-around user-to-cache association. Recently, N. Das and B. S. Rajan identify a class of user-to-cache association bipartite graphs, which achieves either a lower transmission rate or subpacketization level than all other existing MACC schemes using a cyclic wrap-around user-to-cache association. In this paper, we define a class of user-to-cache association matrix, and using the matrix, we improve the MACC schemes proposed by N. Das and B. S. Rajan in [2]. The improved schemes can achieve a lower transmission rate than the original scheme of [2] with the same subpacketization level under some cases.