Improved lower bounds for coded caching

Content delivery networks often employ caching to reduce transmission rates from the central server to the end users. Recently, the technique of coded caching was introduced whereby coding in the caches and coded transmission signals from the central server are considered. Prior results in this area demonstrate that (a) carefully designing placement of content in the caches and (b) designing appropriate coded delivery signals allow for a system where the delivery rates can be significantly smaller than conventional schemes. However, matching lower bounds on the transmission rates have not yet been obtained. In this work, we derive tighter lower bounds on coded caching rates than were known previously. We demonstrate that this problem can equivalently be posed as one of optimally labeling the leaves of a directed tree. Several examples that demonstrate the utility of our bounds are presented.