Hierarchical Coded Caching in High Memory Regime with Coded Placement

TL;DR

This work addresses hierarchical coded caching with a two-layer network (server, mirrors, and users) by proposing two coded-placement schemes designed for high-memory regimes. The First Scheme stores coded subfiles in mirrors and derives explicit memory and rate expressions, achieving lower composite rates at selected high-memory points compared with prior KNMD-based approaches. The Second Scheme shifts coded placement to user caches, yielding different memory and rate tradeoffs; both schemes are shown to improve the composite rate $\overline{R}$ under $N \le K_1K_2$ and are analyzed against existing schemes. Overall, the results validate that coded placement can substantially reduce transmission loads in hierarchical networks with large cache sizes, offering practical gains for high-memory deployments.

Abstract

We consider a two-layer hierarchical coded caching network where a server with a library of $N$ files is connected to $K_1$ mirrors, each having a cache memory of size $M_1$. Each mirror is further connected to $K_2$ users, each equipped with a dedicated cache of size $M_2$. In this paper, we propose two distinct coded caching schemes based on coded placement, corresponding to two distinct memory pairs, \( (M_1, M_2) \). We show that the proposed schemes outperform the existing schemes at these memory points given by the proposed schemes for smaller values of $K_2$. In setups where mirrors are positioned near each other, avoiding signal interference is crucial. This can be ensured by having all mirrors transmit using orthogonal carrier frequencies. To compare our schemes with existing ones, we used the composite rate metric, which accurately represents the total bandwidth utilized in such setups. The composite rate is given by $\overline{R} = R_1 + K_1 R_2$, where $R_1$ is the rate from the server to the mirrors, and $R_2$ is the rate from the mirrors to the users, with respect to $M_1$ and $M_2$.

Figures (3)

• Figure 1: Hierarchical two-layer network.
• Figure 2: Comparison of composite rate $\overline{R}$ for the ($3,2$;$M_{1}$,$M_{2}$;6) hierarchical caching system in Example \ref{['es, x1']}.
• Figure 3: Comparison of Scheme 2 with KNMD scheme karamchandani2016hierarchical for the ($3,2$;$M_{1}$,$M_{2}$;6) hierarchical caching system.

Theorems & Definitions (4)

• Remark 1
• Remark 2
• Remark 3
• Example 1