We consider the $(K,L,M,N)$ multi-access coded caching system introduced by Hachem et al., which consists of a central server with $N$ files and $K$ cache nodes, each of memory size $M$, where each user can access $L$ cache nodes in a cyclic wrap-around fashion. At present, several existing schemes achieve competitive transmission performance, but their subpacketization levels grow exponentially with the number of users. In contrast, schemes with linear or polynomial subpacketization always incur higher transmission loads. We aim to design a multi-access coded caching scheme with linear subpacketization $F$ while maintaining low transmission load. Recently, Cheng et al. proposed a construction framework for coded caching schemes with linear subpacketization (i.e., $F=K$) called non-half-sum disjoint packing (NHSDP). Inspired by this structure, we introduce a novel combinatorial structure named cyclic multi-access non-half-sum disjoint packing (CMA-NHSDP) by extending NHSDP to MACC system. By constructing CMA-NHSDP, we obtain a new class of multi-access coded caching schemes. Theoretical and numerical analyses show that our scheme achieves lower transmission loads than some existing schemes with linear subpacketization. Moreover, the proposed schemes achieves lower transmission load compared to existing schemes with exponential subpacketization in some case.

翻译：我们考虑由Hachem等人提出的$(K,L,M,N)$多接入编码缓存系统，该系统包含一个拥有$N$个文件的中央服务器和$K$个缓存节点，每个节点的存储容量为$M$，其中每个用户以循环环绕方式访问$L$个缓存节点。目前，已有若干方案实现了具有竞争力的传输性能，但其子分组化阶数随用户数量呈指数级增长。相比之下，具有线性或多项式子分组化的方案总是导致更高的传输负载。我们的目标是设计一种具有线性子分组化$F$，同时保持低传输负载的多接入编码缓存方案。最近，Cheng等人提出了一种具有线性子分组化（即$F=K$）的编码缓存方案构造框架，称为非半和不相交包装（NHSDP）。受此结构启发，我们通过将NHSDP扩展至MACC系统，引入了一种名为循环多接入非半和不相交包装（CMA-NHSDP）的新型组合结构。通过构造CMA-NHSDP，我们获得了一类新的多接入编码缓存方案。理论与数值分析表明，与一些现有的线性子分组化方案相比，我们的方案实现了更低的传输负载。此外，在某些情况下，所提出的方案相较于具有指数子分组化的现有方案也实现了更低的传输负载。