Coded Caching for Two-Dimensional Multi-Access Networks

This paper studies a novel multi-access coded caching (MACC) model in the two-dimensional (2D) topology, which is a generalization of the one-dimensional (1D) MACC model proposed by Hachem et al. The 2D MACC model is formed by a server containing $N$ files, $K_1\times K_2$ cache-nodes with $M$ files located at a grid with $K_1$ rows and $K_2$ columns, and $K_1\times K_2$ cache-less users where each user is connected to $L^2$ nearby cache-nodes. The server is connected to the users through an error-free shared link, while the users can retrieve the cached content of the connected cache-nodes without cost. Our objective is to minimize the worst-case transmission load over all possible users' demands. In this paper, we first propose a grouping scheme for the case where $K_1$ and $K_2$ are divisible by $L$. By partitioning the cache-nodes and users into $L^2$ groups such that no two users in the same group share any cache-node, we use the shared-link coded caching scheme proposed by Maddah-Ali and Niesen for each group. Then for any model parameters satisfying $\min\{K_1,K_2\}>L$, we propose a transformation approach which constructs a 2D MACC scheme from two classes of 1D MACC schemes in vertical and horizontal projections, respectively. As a result, we can construct 2D MACC schemes that achieve maximum local caching gain and improved coded caching gain, compared to the baseline scheme by a direct extension from 1D MACC schemes.Comment: 40 pages, 11 figure