Multi-Antenna Coded Caching for Multi-Access Networks With Cyclic Wrap-Around

This work explores a multiple transmit antenna setting in a multi-access coded caching (MACC) network where each user accesses more than one cache. A MACC network has K users and K caches, and each user has access to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$r \lt K$ </tex-math></inline-formula> consecutive caches in a cyclic wrap-around manner. There are L antennas at the server, and each cache has a normalized size <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M/N \leq 1$ </tex-math></inline-formula>. The cyclic wrap-around MACC network with a single antenna at the server has been well-investigated, and several coded caching schemes and improved lower bounds on the performance are derived for the same. However, this MACC network has not yet been studied under multi-antenna settings in the coded caching literature. We study the multi-antenna MACC problem and propose a solution for the same by constructing a pair of arrays called caching and delivery arrays. We present four constructions of caching and delivery arrays for different scenarios and obtain corresponding multi-antenna MACC schemes. Three of the above schemes achieve optimal performance under uncoded placement and one-shot delivery. The optimality is shown by matching the performance of the multi-antenna MACC scheme to the optimal performance in a dedicated cache network having K users and normalized cache size <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$rM/N$ </tex-math></inline-formula>. Further, as a special case, one of the proposed schemes subsumes an existing optimal MACC scheme for the single-antenna setting.