Coded Caching for Two-Dimensional Multi-Access Networks

Abstract

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.

Coded Caching Schemes for Multi-Access Topologies via Combinatorial Design Theory

“…Under the one-dimensional (1D) MACC model, several improved schemes (with lower load or/and lower subpacketization) and converse bounds on the load were proposed in [4]- [14]. In addition, some works have extended 1D MACC to 2D MACC [13], [15]. Recently, [16] introduced a very powerful new MACC topology which proved to have stunning gains.…”