Coded Caching with Shared Caches and Private Caches

TL;DR

This work designs two centralized coded caching schemes based on uncoded placement that are shown to be optimal in specific memory regimes.

Abstract

This work studies the coded caching problem in a setting where the users are simultaneously endowed with a private cache and a shared cache. The setting consists of a server connected to a set of users, assisted by a smaller number of helper nodes that are equipped with their own storage. In addition to the helper cache, each user possesses a dedicated cache which is also used to prefetch file contents. Each helper cache can serve an arbitrary number of users, but each user gets served by only one helper cache. We consider two scenarios: (a) the server has no prior information about the user-to-helper cache association, and (b) the server knows the user-to-helper cache association at the placement phase itself. We design centralized coded caching schemes under uncoded placement for the above two settings. For case (b), two schemes are proposed that are optimal in certain memory regimes. Further, a cut-set based lower bound is derived and used to show that one of the proposed schemes for case (b) is optimal in certain memory regime.

Figures (6)

• Figure 1: Network model.
• Figure 2: An acyclic subgraph $\mathcal{J}$.
• Figure 3: For a network with $K=30$, $N=30$, $\Lambda=5$, $\mathcal{U}=\{\{1,2,\ldots,20\}$,$\{21,\ldots,24\}$,$\{25,26,27\}$,$\{28,29\},\{30\}\}$.
• Figure 4: For a network with $K=30$, $N=30$, $\Lambda=5$, $\mathcal{U}=\{\{1,\ldots,6\}$,$\{7,\ldots,12\}$,$\{13,\ldots,18\}$,$\{19,\ldots,24\},$$\textrm{\space}\{25,\ldots,30\}\}$.
• Figure 5: For a network with $K=30$, $N=30$, $\Lambda=5$

Theorems & Definitions (18)

• Lemma 1
• Corollary 1
• Theorem 1
• Remark 1
• Remark 2
• Lemma 2: Cut-set type converse ABKSW
• Example 1
• Theorem 2
• Example 2
• Remark 3