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

2025-06-30

AI Summary

This paper investigates coded caching under intersection constraints—i.e., users’ requested file index sets must share a nonempty intersection—to model resource-constrained edge IoT scenarios, such as small private caches accessing a limited shared cache. To address this setting, we propose a centralized coded caching scheme based on combinatorial design: it employs uncoded prefetching, introduces intersection classes and their uniform subclass partitions to establish system parameter feasibility conditions, and constructs a structured delivery scheme yielding an explicit rate–memory trade-off. Leveraging theoretical analysis—including an exponential information-theoretic lower bound under general coding and modeling via multi-access topology—we derive the worst-case achievable rate. Numerical evaluations demonstrate that the proposed scheme significantly outperforms baseline schemes and the newly derived information-theoretic lower bound.

Technology Category

• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Combinatorial Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Cloud, edge and content delivery systems for the Web
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements

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.

Problem

• Optimizing coded caching for private caches under intersecting index constraints
• Modeling resource-limited IoT systems with shared and private caches
• Characterizing rate-memory trade-offs for intersection class caching schemes

Innovation

• Private and access caches with uncoded placement
• Intersection class for constrained indexing regime
• Uniform-intersection subclass with regular transmission