In this paper, we study the coded caching scheme for the $(K,L,M_{\text{T}},M_{\text{U}},N)$ partially connected linear network, where there are $N$ files each of which has an equal size, $K+L-1$ transmitters and $K$ users; each user and transmitter caches at most $M_{\text{U}}$ and $M_{\text{T}}$ files respectively; each user cyclically communicates with $L$ transmitters. The goal is to design caching and delivery schemes to reduce the transmission latency measured by the metric normalized delivery time (NDT). By delicately designing the data placement of the transmitters and users according to the topology, we show that a combinatorial structure called multiple-antenna placement delivery array (MAPDA), which was originally proposed for the multiple-input single-output broadcast channels, can be also used to design schemes for the partially connected linear network. Then, based on existing MAPDAs and our constructing approach, we propose new schemes that achieve the optimal NDT when $ {M_\text{T}}+ {M_\text{U}}\geq N$ and smaller NDT than that of the existing schemes when (${M_\text{T}}+ {M_\text{U}}\leq N$, $\frac{M_\text{U}}{N}+\frac{M_\text{T}}{N} \frac{L}{K}\left\lceil \frac{K}{L} \right\rceil \geq 1$) or ($ {M_\text{U}}+ {M_\text{T}}< N, \frac{K}{L}\notin\mathbb{Z}^+$). Moreover, our schemes operate in one-shot linear delivery and significantly reduce the subpacketizations compared to the existing scheme, which implies that our schemes have a wider range of applications and lower complexity of implementation.

翻译：本文研究了$(K,L,M_{\text{T}},M_{\text{U}},N)$部分连接线性网络的编码缓存方案，其中包含$N$个大小相等的文件、$K+L-1$个发射机和$K$个用户；每个用户和发射机分别最多缓存$M_{\text{U}}$和$M_{\text{T}}$个文件；每个用户循环与$L$个发射机通信。目标是设计缓存和传输方案，以降低由归一化传输时延（NDT）度量的传输延迟。通过根据拓扑结构精细设计发射机和用户的数据放置，我们证明了一种称为多天线放置传输阵列（MAPDA）的组合结构——该结构最初针对多输入单输出广播信道提出——也可用于设计部分连接线性网络的方案。然后，基于现有MAPDA和我们的构造方法，我们提出了新方案，这些方案在$ {M_\text{T}}+ {M_\text{U}}\geq N$下实现了最优NDT，并在（${M_\text{T}}+ {M_\text{U}}\leq N$，$\frac{M_\text{U}}{N}+\frac{M_\text{T}}{N} \frac{L}{K}\left\lceil \frac{K}{L} \right\rceil \geq 1$）或（$ {M_\text{U}}+ {M_\text{T}}< N, \frac{K}{L}\notin\mathbb{Z}^+$）条件下获得了比现有方案更低的NDT。此外，我们的方案采用单次线性传输，并显著降低了子包化程度（相比现有方案），这意味着我们的方案具有更广泛的应用范围和更低的实现复杂度。