Combinatorial Multi-Access Coded Caching with Private Caches under Intersecting Index Constraints

TL;DR

This paper studies a coded caching system with private caches and intersecting index constraints, proposing schemes and bounds relevant to resource-limited IoT scenarios with shared caches.

Contribution

It introduces a necessary and sufficient condition for the intersection class, proposes a centralized coded caching scheme, and characterizes the rate-memory trade-off within this framework.

Findings

Proposed a centralized coded caching scheme for the intersection class.

Derived a lower bound on the minimum worst-case rate with uncoded placement.

Numerical results compare the scheme's rate with bounds, showing its effectiveness.

Abstract

We consider the coded caching system where each user, equipped with a private cache, accesses a distinct r-subset of access caches. A central server housing a library of files populates both private and access caches using uncoded placement. In this work, we focus on a constrained indexing regime, referred to as the intersection class, in which the sets used to index the demands of each user must have a nonempty intersection. This regime models resource-limited IoT scenarios such as edge-assisted IoT systems, where devices with small private caches connect to a small number of shared caches. We provide a necessary and sufficient condition under which the system parameters fall within this intersection class. Under this condition, we propose a centralized coded caching scheme and characterize its rate-memory trade-off. Next, we define a uniform-intersection subclass and establish a condition under which the system belongs to this subclass. Within this subclass, the proposed scheme has a regular structure, with each transmission benefiting the same number of users, and we characterize its rate-memory trade-off. Additionally, we derive an index coding-based lower bound on the minimum achievable worst-case rate under uncoded placement. Finally, we provide numerical comparisons between the rate of the proposed scheme, the new lower bound, and bounds from the original work.