Extended Placement Delivery Arrays for Multi-Antenna Coded Caching Scheme
K. K. Krishnan Namboodiri, Elizabath Peter, Balaji Sundar Rajan · IEEE Transactions on Communications · 2023
This work addresses the multi-antenna coded caching problem where a server with$L$transmit antennas communicates to$K$users through a wireless broadcast link. In the problem setting, the server has a library of$N$files, and each user is equipped with a dedicated cache of capacity$M$. A novel solution for the multi-antenna coded caching problem is obtained by designing a combinatorial structure called an extended placement delivery array (EPDA). It is shown that the placement delivery arrays known for the centralized coded caching scheme are a special class of EPDAs with$L=1$. Furthermore, three constructions of EPDAs are proposed for the settings: a)$K = t+L$, b)$K = nt+ (n-1)L;L\geq t, n\geq 2$, and c)$K,L,t$such that$t + L\leq K$, where$t = KM/N$is an integer. The multi-antenna schemes resulting from the first two constructions achieve the optimal degrees of freedom (DoF)$t+L$with a subpacketization number -the number of subfiles into which a file is divided-$K/\text {gcd}(K,t,L)$, which is lower than the subpacketization number of the existing schemes. The scheme obtained from the third construction also achieves the optimal DoF with a subpacketization number$\binom {K/{\gamma }}{(t+L)/{\gamma }}\left ({{t+L}}\right)/{\gamma }$, where$\gamma =\text {gcd}(K,t,L)$.