Coded Caching based on Combinatorial Designs
We consider the standard broadcast setup with a single server broadcasting information to a number of clients, each of which contains local storage (called cache) of some size, which can store some parts of the available files at the server. The centralized coded caching framework, consists of a caching phase and a delivery phase, both of which are carefully designed in order to use the cache and the channel together optimally. In prior literature, various combinatorial structures have been used to construct coded caching schemes. In this work, we propose a binary matrix model to construct the coded caching scheme. The ones in such a caching matrix indicate uncached subfiles at the users. Identity submatrices of the caching matrix represent transmissions in the delivery phase. Using this model, we then propose several novel constructions for coded caching based on the various types of combinatorial designs. While most of the schemes constructed in this work (based on existing designs) have a high cache requirement (uncached fraction being $\Theta \left( {\frac{1}{{\sqrt K }}} \right)$, K being the number of users), they provide a rate R that is upper bounded by a constant (R≤ 1) with increasing K, and moreover require extremely small levels of subpacketization (being O(K)), which is an extremely important parameter in practical applications of coded caching.