Coded Caching for Two-Dimensional Multi-Access Networks
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This paper studies a novel multi-access coded caching (MACC) model in two-dimensional (2D) topology, which is a generalization of the one-dimensional (1D) MACC model proposed by Hachem et al. We formulate a 2D MACC coded caching model, formed by a server containing N files, K_1× K_2 cache-nodes with limited memory M which are placed on a grid with K_1 rows and K_2 columns, and K_1× K_2 cache-less users such that each user is connected to L^2 nearby cache-nodes. More precisely, for each row (or column), every user can access L consecutive cache-nodes, referred to as row (or column) 1D MACC problem in the 2D MACC model. 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 among all possible users' demands. In this paper, we propose a baseline scheme which directly extends an existing 1D MACC scheme to the 2D model by using a Minimum Distance Separable (MDS) code, and two improved schemes. In the first scheme referred to as grouping scheme, which works when K_1 and K_2 are divisible by L, we partition the cache-nodes and users into L^2 groups according to their positions, such that no two users in the same group share any cache-node, and we utilize the seminal shared-link coded caching scheme proposed by Maddah-Ali and Niesen for each group. Subsequently, for any model parameters satisfying min{K_1,K_2}>L we propose the second scheme, referred to as hybrid scheme, consisting in a highly non-trivial way to construct a 2D MACC scheme through a vertical and a horizontal 1D MACC schemes.
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