Coded Caching for Two-Dimensional Multi-Access Networks

This paper formulates the multi-access coded caching (MACC) problem under the two-dimensional (2D) topology, which is a generalization of the one-dimensional (1D) MACC problem originally considered by Hachem et al. The novel 2D MACC system includes a server containing N files, K
1
×K
2
cache-nodes (each of size M units) placed on a grid with K
1
rows and K
2
columns, and K
1
×K
2
cache-less users, each of which accesses to L
²
nearby cache-nodes. More precisely, focus on any row (or column) of the grid, each user can access L consecutive cache-nodes in a cyclic wrap-around fashion, referred to as row (or column) 1D MACC problem in the 2D MACC system. The users are connected to the server through an error-free shared link, while they can also retrieve the content stored at the accessible cache-nodes without cost. Our objective is to minimize the worst-case transmission load among all possible users’ demands. This work proposes a baseline scheme firstly, which directly extends an existing 1D MACC scheme to the 2D model by using a Minimum Distance Separable (MDS) code. Then two improved schemes are designed. In the grouping scheme, we divide the cache-nodes and users into L
²
groups by their positions, such that any two users in the same group do not share any cache-node, and then utilize the seminal shared-link coded caching scheme proposed by Maddah-Ali and Niesen for each group. Then we propose the hybrid scheme, consisting in a highly non-trivial way to construct a 2D MACC scheme by using two 1D MACC problems under vertical and horizontal projections.