Improved Constructions of Coded Caching Schemes for Combination Networks.

In an $(H,r)$ combination network, a single content library is serving for ${\binom{H}{ r}}$ users through $H$ relays, where each user has local cache memories and simultaneously accesses a subset of $r$ relays on orthogonal non-interfering and error-free channels. The combinatorial placement delivery array (CPDA in short) can be used to realize a coded caching scheme for combination networks. In this paper, a new algorithm used to realize a scheme for combination networks based on a CPDA is proposed. Based on the fixed CPDA, the scheme realized by our algorithm has smaller subpacketization. Then we focus on directly constructing CPDAs for any positive integers $H$ and $r$ with $r< H$ and obtain two new classes of CPDAs. Compared with the previously known CPDAs, the schemes realized by our CPDAs have significant advantages on the subpacketization levels with some costing of transmission rates. [ABSTRACT FROM AUTHOR]