An Optimal Decentralized Multi-access Coded Caching System

TL;DR

A delivery scheme is proposed for the generalized model and is shown to be optimal for certain user-to-cache associations and the optimality of the proposed linear delivery scheme among all linear delivery schemes is proved.

Abstract

In this paper, we consider a multi-access coded caching system with decentralized prefetching, where a server hosts $N$ files, each of size $F$ bits, and is connected to $K$ users through a shared link. There are $c$ caches distributed across the network and each of the $K$ users connects to a random set of $r\leq c$ caches. Initially, we consider the model in which each of the cache subsets is accessed by exactly a specific number of users. For this model, a novel linear delivery scheme is introduced, using which the closed-form expression for the per-user delivery rate is computed. Furthermore, using techniques from index coding, the optimality of the proposed linear delivery scheme among all linear delivery schemes is proved. The results of the decentralized shared caching and conventional decentralized caching schemes are recovered as special cases of the proposed model. The model is further generalized by allowing each cache subset to serve any number of users. This enhances the flexibility of the system, enabling it to accommodate any arbitrary number of users. A delivery scheme is proposed for the generalized model and is shown to be optimal for certain user-to-cache associations.

Figures (5)

• Figure 1: System model of the multi-access coded caching scheme for $N=K=12$, $c=4$, $L=2$, and $r=2$.
• Figure 2: Per user transmission rates of our proposed scheme $\forall r\in \{2,3,4\}$ considering $c=4$ and $N=K=12$, and the per user transmission rate in maddah2014decentralized for $c=4$ and $N=K=4$ are plotted against $\frac{M}{N}$.
• Figure 3: Per user transmission rates of our proposed scheme and the scheme in MaNAccess considering $c=7$, $r=3$, and $N=K=35$ are plotted against $M$.
• Figure 4: Proposed per user transmission rate and lower bound for the decentralized multi-access coded caching system with $N=K=12$ and $c=4$ for all $r\in\{1,2,3,4\}$, versus $M$.
• Figure 5: Performance analysis of the generalized decentralized multi-access coded caching problem with $N=K=12$, $c=4$, and $r=2$ for various user-to-cache association profiles.

Theorems & Definitions (16)

• Lemma 1
• Lemma 2
• Lemma 3
• Example 1
• Example 2
• Theorem 1
• Theorem 2
• Remark 1
• Remark 2
• Lemma 4