Hierarchical Coded Caching in Satellite-Terrestrial Networks with Nonuniform User Cache and Geographic Distributions

Coded caching shows great potential for reducing delivery latency in satellite networks by exploiting multicast opportunities among users with different requests and leveraging predictable mobility. Unlike previous studies focusing on direct satellite-user connections with uniform cache sizes, we investigate a more practical scenario where satellites serve users through arbitrarily distributed terrestrial relays, with users connected to different relays having heterogeneous cache sizes. To address this, two basic schemes are introduced to develop a hybrid decentralized hierarchical coded caching scheme, which integrates zero-padding, pipelined-forwarding, and concurrent transmissions across layers. By balancing these two basic schemes, an upper bound of the global transmission delay is derived. Additionally, a new converse bound is established by decoupling satellite-relay/user connections, classifying users by cache sizes, constructing cyclic wrap-around request patterns and deriving the cut-set bound for selected users. Furthermore, a more tractable lower bound is derived by introducing a selection threshold that effectively captures user density and cache heterogeneities, identifying performance-limiting head users. Theoretical analysis shows that the transmission delay is within a constant factor of the lower bound, which constitutes a constant-gap result for hierarchical and satellite-terrestrial networks with heterogeneous user caches. Numerical results demonstrate the superior performance of our proposed scheme.