This paper studies a multiaccess coded caching (MACC) where the connectivity topology between the users and the caches can be described by a class of combinatorial designs. Our model includes as special cases several MACC topologies considered in previous works. The considered MACC network includes a server containing $N$ files, $\Gamma$ cache nodes and $K$ cacheless users, where each user can access $L$ cache nodes. The server is connected to the users via an error-free shared link, while the users can retrieve the cache content of the connected cache-nodes while the users can directly access the content in their connected cache-nodes. Our goal is to minimise the worst-case transmission load on the shared link in the delivery phase. The main limitation of the existing MACC works is that only some specific access topologies are considered, and thus the number of users $K$ should be either linear or exponential to $\Gamma$. We overcome this limitation by formulating a new access topology derived from two classical combinatorial structures, referred to as the $t$-design and the $t$-group divisible design. In these topologies, $K$ scales linearly, polynomially, or even exponentially with $\Gamma$. By leveraging the properties of the considered combinatorial structures, we propose two classes of coded caching schemes for a flexible number of users, where the number of users can scale linearly, polynomially or exponentially with the number of cache nodes. In addition, our schemes can unify most schemes for the shared link network and unify many schemes for the multi-access network except for the cyclic wrap-around topology.

翻译：本文研究了一种多接入编码缓存（MACC）系统，其中用户与缓存节点之间的连接拓扑可由一类组合设计描述。该模型将先前工作中考虑的多种MACC拓扑结构作为特例纳入统一框架。考虑的网络包含一个存有$N$个文件的服务器、$\Gamma$个缓存节点以及$K$个无缓存用户，每个用户可访问$L$个缓存节点。服务器通过无差错共享链路连接用户，用户既能直接获取所连缓存节点中的内容，又可在传输阶段通过该链路请求数据。我们的目标是最小化交付阶段共享链路上的最坏情况传输负载。现有MACC研究的主要局限在于仅考虑了特定接入拓扑，导致用户数$K$需与$\Gamma$呈线性或指数关系。为突破这一限制，本文基于两种经典组合结构——$t$-设计与$t$-群可分解设计——构建了新型接入拓扑。在该拓扑中，$K$值可随$\Gamma$呈线性、多项式甚至指数级扩展。通过利用所涉组合结构的特性，我们提出了两类适用于灵活用户数量的编码缓存方案，用户数量可随缓存节点数量呈线性、多项式或指数级增长。此外，本文方案能统一共享链路网络中的多数方案，并可统一多接入网络中除环形环绕拓扑外的多数方案。