We examine a two-layered hierarchical coded caching problem, a configuration addressed in existing research. This involves a server connected to $K_1$ mirrors, each of which serves $K_2$ users. The mirrors and the users are equipped with caches of size $M_1$ and $M_2$, respectively. We propose a hierarchical coded caching scheme with coded placements that outperforms existing schemes. To ensure a fair comparison, we introduce the notion of composite rate, defined as $\overline{R} = R_1 + K_1 R_2$, where $R_1$ is the rate from the server to mirrors and $R_2$ is the rate from mirrors to users. The composite rate has not been discussed before in the literature and is pertinent when mirrors transmit with different carrier frequencies. For the proposed scheme, we show a trade-off between the global memory $\overline{M}=K_1M_1+K_1K_2M_2$ of the system and the composite rate and compare with the existing schemes. Additionally, we conduct this comparative analysis by plotting $R_1$ + $R_2$ against global memory, which is particularly beneficial for systems wherein each mirror can utilize the same carrier frequency, given their significant spatial separation. Additionally, we propose an optimized scheme for the specific case of a single mirror, showing improved performance in this scenario.

翻译：本文研究一种分层双网络编码缓存问题，该配置在现有研究中已有涉及。该系统包含一个连接至$K_1$个镜像节点的服务器，每个镜像节点服务于$K_2$个用户。镜像节点与用户分别配备容量为$M_1$和$M_2$的缓存。我们提出了一种采用编码放置的分层编码缓存方案，其性能优于现有方案。为确保公平比较，我们引入了复合速率的概念，定义为$\overline{R} = R_1 + K_1 R_2$，其中$R_1$表示服务器到镜像节点的传输速率，$R_2$表示镜像节点到用户的传输速率。复合速率在现有文献中尚未被讨论，且在镜像节点使用不同载波频率传输时具有实际意义。针对所提方案，我们展示了系统全局内存$\overline{M}=K_1M_1+K_1K_2M_2$与复合速率之间的权衡关系，并与现有方案进行了对比。此外，我们通过绘制$R_1$ + $R_2$相对于全局内存的变化曲线进行了对比分析，这对于各镜像节点因空间分隔显著而可采用相同载波频率的系统尤为有益。另外，针对单镜像节点的特定场景，我们提出了一种优化方案，展示了该场景下的性能提升。