Coded Caching Scheme for Partially Connected Linear Networks via Multi-Antenna Placement Delivery Array

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 locally communicates with L nearby transmitters. The goal is to design caching and delivery schemes to reduce the transmission latency measured by the metric named 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 helpful in designing 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}}}\lt 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.