Generalized Coded Caching from Set Families

Content delivery networks often suffer from communication bottlenecks during peak hours. To overcome this Maddah-Ali and Niesen proposed coded caching schemes to reduce the transmission during the peak hours. Typical constructions of coded caching schemes are for a specific number of users and homogeneous cache sizes and are not usually versatile over parameter values or extendable to other scenarios such as heterogeneous cache sizes. Optimal schemes tend to have unacceptably large subpacketization. We propose a generalized construction for coded caching schemes indexing users, subfiles and transmissions using set families with the user set family required to be a Sperner family. The proposed construction naturally extends the well-known Maddah-Ali-Niesen schemes and PDA-based schemes. We illustrate the proposed construction with specific cases based on graphs and hypergraphs. Additionally, we provide a randomized construction that is versatile over parameters, supports heterogeneous cache sizes and has low subpacketization.