We consider the multi-access coded caching problem, which contains a central server with $N$ files, $K$ caches with $M$ units of memory each and $K$ users where each one is connected to $L (\geq 1)$ consecutive caches, with a cyclic wrap-around. Caches are populated with content related to the files and each user then requests a file that has to be served via a broadcast message from the central server with the help of the caches. We aim to design placement and delivery policies for this setup that minimize the central servers' transmission rate while satisfying an additional linear sub-packetization constraint. We propose policies that satisfy this constraint and derive upper bounds on the achieved server transmission rate, which upon comparison with the literature establish the improvement provided by our results. To derive our results, we map the multi-access coded caching problem to variants of the well-known index coding problem. In this process, we also derive new bounds on the optimal transmission size for a `structured' index coding problem, which might be of independent interest.

翻译：本文研究多址编码缓存问题，该问题包含一个拥有$N$个文件的中央服务器、$K$个各具有$M$单位内存的缓存节点以及$K个用户，每个用户连接$L(\geq 1)$个连续缓存节点（采用循环环绕结构）。缓存节点预存与文件相关的内容，随后每个用户请求一个文件，需通过中央服务器的广播消息并借助缓存节点进行服务。我们旨在为这一配置设计存储与交付策略，以最小化中央服务器的传输速率，同时满足额外的线性子分组化约束。我们提出满足该约束的策略，并推导出服务器传输速率的上界，通过与现有文献的对比表明本方法能实现性能改进。为获得上述结果，我们将多址编码缓存问题映射到经典索引编码问题的变体。在此过程中，我们还为"结构化"索引编码问题推导了最优传输规模的边界，该结论可能具有独立研究价值。