Multi-antenna Coded Caching with Combinatorial Multi-access Networks

Abstract

We study the combinatorial multi-access coded caching problem, introduced by Muralidhar et al. with a single antenna at the server [P. N. Muralidhar, D. Katyal, and B. S. Rajan, "Maddah-Ali-Niesen scheme for multi-access coded caching," in IEEE ITW, 2021], under the setting of multiple transmit antennas. The problem setting consists of a server with L transmit antennas connected to a set of K users that are assisted with C ≤ K helper caches. Each user accesses a unique set of r caches, and there exists a user corresponding to every distinct set of r caches. Thus,$K = \binom {C} { r} $. For this network, the fundamental limits under uncoded placement are known for the single-antenna case [F. Brunero and P. Elia, "Fundamental limits of combinatorial multi-access caching," IEEE Trans. Inf. Theory, 2023]. Notable performance gains were achieved using multiple antennas at the server in other network models [1], [2]. The multi-antenna scenario has not been explored in any multi-access networks in the context of coded caching. In this work, we propose a multi-antenna coded caching scheme for the combinatorial multi-access setting where the number of transmit antennas is one more than the number of caches accessible to each user. When the normalized cache size equals 1/C and r = C−2, our scheme achieves the same performance obtained in a dedicated cache network having $K = \binom {C} { r} $ users, each having a normalized cache size r/C, and L = C−1 antennas. When r = 1, the proposed scheme recovers the multi-antenna coded caching scheme for the dedicated cache networks in [S. P. Shariatpanahi, G. Caire, and B. H. Khalaj, "Physical-layer schemes for wireless coded caching," IEEE Trans. Inf. Theory, 2019].