Two-Dimensional Multi-Access Coded Caching with Multiple Transmit Antennas
K. K. Krishnan Namboodiri, Elizabath Peter, Balaji Sundar Rajan · 2024
This work introduces a multi-antenna coded caching problem in a two-dimensional multi-access network, where a server with$L$transmit antennas and$N$files communicates to$K_{1}K_{2}$users, each with a single receive antenna, through a wireless broadcast link. The network consists of$K_{1}K_{2}$cache nodes and$K_{1}K_{2}$users. The cache nodes, each with capacity$M$, are placed on a rectangular grid with$K_{1}$rows and$K_{2}$columns, and the users are placed regularly on the square grid such that a user can access$r^{2}$neighbouring caches in a cyclic wrap-around fashion. For a given cache memory$M$, the goal of the coded caching problem is to serve the user demands with a minimum delivery time. We propose a solution for the aforementioned coded caching problem by designing two arrays: a caching array and a delivery array. Further, we present two classes of caching and delivery arrays and obtain corresponding multi-access coded caching schemes. The first scheme achieves a normalized delivery time (NDT)$\frac{K_{1}K_{3}(1-r^{2}\frac{M}{N})}{L+K_{1}K_{2}\frac{M}{N}}$. The second scheme achieves an NDT$\frac{K_{1}K_{3}(1-r^{2}\frac{M}{N})}{L+K_{1}K_{2}r^{2}\frac{M}{N}}$when$M/N=1/K_{1}K_{2}$and$L=K_{1}K_{2}-r^{2}$, which is optimal under uncoded placement and one-shot delivery.