We consider a $(G,L,K,M,N)$ cache-aided multiple-input multiple-output (MIMO) network, where a server equipped with $L$ antennas and a library of $N$ equal-size files communicates with $K$ users, each equipped with $G$ antennas and a cache of size $M$ files, over a wireless interference channel. Each user requests an arbitrary file from the library. The goal is to design coded caching schemes that simultaneously achieve the maximum sum degrees of freedom (sum-DoF) and low subpacketization. In this paper, we first introduce a unified combinatorial structure, termed the MIMO placement delivery array (MIMO-PDA), which characterizes uncoded placement and one-shot zero-forcing delivery. By analyzing the combinatorial properties of MIMO-PDAs, we derive a sum-DoF upper bound of $\min\{KG, Gt+G\lceil L/G \rceil\}$, where $t=KM/N$, which coincides with the optimal DoF characterization in prior work by Tehrani \emph{et al.}. Based on this upper bound, we present two novel constructions of MIMO-PDAs that achieve the maximum sum-DoF. The first construction achieves linear subpacketization under stringent parameter constraints, while the second achieves ordered exponential subpacketization under substantially milder constraints. Theoretical analysis and numerical comparisons demonstrate that the second construction exponentially reduces subpacketization compared to existing schemes while preserving the maximum sum-DoF.

翻译：我们研究一个$(G,L,K,M,N)$缓存辅助多输入多输出（MIMO）网络，其中服务器配备$L$根天线及一个包含$N$个等大文件的库，通过无线干扰信道与$K$个用户通信；每个用户配备$G$根天线及一个容量为$M$个文件的缓存。每个用户从库中请求任意一个文件。目标是设计能够同时实现最大和自由度（sum-DoF）与低子分组复杂度的编码缓存方案。本文首先引入一种统一的组合结构，称为MIMO放置-传输阵列（MIMO-PDA），该结构刻画了未编码放置与单次迫零传输。通过分析MIMO-PDA的组合性质，我们推导出和自由度的上界为$\min\{KG, Gt+G\lceil L/G \rceil\}$，其中$t=KM/N$，该上界与Tehrani等人先前工作中给出的最优自由度表征一致。基于此上界，我们提出了两种新颖的MIMO-PDA构造，均能实现最大和自由度。第一种构造在严格的参数约束下实现线性子分组复杂度，而第二种构造在显著宽松的约束下实现有序指数级子分组复杂度。理论分析与数值比较表明，在保持最大和自由度的同时，第二种构造相较于现有方案实现了子分组复杂度的指数级降低。