Two-Dimensional Multi-Access Coded Caching with Multiple Transmit Antennas
K. K. Krishnan Namboodiri, Elizabath Peter, B. Sundar Rajan
TL;DR
The paper addresses scalable content delivery in a two-dimensional multi-access caching network where a server with $L$ transmit antennas serves $K_1K_2$ caches and users arranged on a grid, with each user accessing an $r\times r$ neighborhood of caches. It develops a design framework based on caching and delivery arrays derived from extended placement delivery arrays (EPDA) to construct multi-antenna MACC schemes, yielding two concrete schemes with closed-form NDT expressions: $T_n = \frac{K_1K_2(1-r^2\frac{M}{N})}{L+K_1K_2\frac{M}{N}}$ and $T_n = \frac{K_1K_2(1-r^2\frac{M}{N})}{L+K_1K_2r^2\frac{M}{N}}$ under $\frac{M}{N}=\frac{1}{K_1K_2}$ and $L=K_1K_2-r^2$. A construction achieving the latter (optimal under uncoded placement and one-shot delivery) demonstrates the potential of using multiple antennas to improve NDT relative to the single-antenna baseline, with explicit methodology to build caching/delivery arrays from EPDAs and to map them into MACC schemes. The work provides both general guidance and a parameter-specific optimal scheme, highlighting the practical impact of antenna count on cooperative caching gains in grid-based networks.
Abstract
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 $K_1K_2$ users, each with a single receive antenna, through a wireless broadcast link. The network consists of $K_1K_2$ cache nodes and $K_1K_2$ 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) $\frac{K_1K_2(1-r^2\frac{M}{N})}{L+K_1K_2\frac{M}{N}}$. The second scheme achieves an NDT $\frac{K_1K_2(1-r^2\frac{M}{N})}{L+K_1K_2r^2\frac{M}{N}}$ when $M/N=1/K_1K_2$ and $L=K_1K_2-r^2$, which is optimal under uncoded placement and one-shot delivery.