Subpacketization Level in Optimal Placement for Coded Caching with Nonuniform File Popularities

We consider coded caching between a server and K users and study the file subpacketization in the optimal cache placement for the coded caching scheme (CCS) with nonuniform file popularities. We formulate the cache placement optimization problem of the CCS and show the optimal cache placement has several possible structures. Analyzing these structures, we show that each file can be partitioned into subfiles of at most two different sizes. By exploring each of these placement structures, we obtain the corresponding subpacketization level. Through analysis, we show that the worst-case subpacketization level under the optimal cache placement is O(2^K/√K). Numerical studies demonstrate the impact of cache size and file popularity distribution on the subpacketization level of files.