Fundamental Limits of Combinatorial Multi-Access Caching

This work identifies the fundamental limits of multi-access coded caching (MACC) where each user is connected to multiple caches in a manner that follows generalized combinatorial topology. topology stands out as it allows for unprecedented coding gains, even with very modest cache resources. First, we extend setting and scheme presented by Muralidhar et al. much more general supports both denser range users coexistence different numbers caches, all while maintaining astounding gains — here proven be exactly optimal associated achieved, this topology, novel information-theoretic converse present here, which establishes, together scheme, exact performance under assumption uncoded placement. We subsequently consider connectivity ensembles, including scenario entire ensemble possible network connectivities/topologies, any subset can serve arbitrary number users. For these settings, develop bounds on averaged over ensemble’s connectivities. analysis topological ensembles leaves open possibility currently-unknown topologies may yield higher hypothesis part bigger question yields most gains.