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

Modern cache-aided networks often involve users accessing multiple shared caches while possessing heterogeneous local storage resources. We consider combinatorial multi-access coded caching systems with private caches, where each user accesses multiple access caches and maintains a private memory. We study the impact of variable private cache sizes on coded multicast opportunities. We identify a structural regime, termed the intersection class, under which non-trivial coded caching is feasible, and derive a necessary and sufficient condition for this regime. For systems in this class, we characterize an achievable rate-memory trade-off. We further identify a subclass, referred to as the uniform-intersection subclass, for which the proposed scheme admits a regular transmission structure, wherein each transmission benefits the same number of users. Using an index coding formulation, we establish a converse bound and show that the proposed scheme operates close to optimality.