A New Construction Structure on Coded Caching with Linear Subpacketization: Non-Half-Sum Disjoint Packing

Coded caching is a promising technique to effectively reduce peak traffic by using local caches and the multicast gains generated by these local caches. We aim to design a coded caching scheme to minimize subpacketization $F$ and transmission load $R$, since these two metrics are key measures of scheme implementation complexity and transmission efficiency, respectively. In this paper, we focus on studying linear subpacketization coded caching schemes with low transmission load. We first introduce a new combinatorial structure, called non-half-sum disjoint packing (NHSDP), which can be used to construct coded caching schemes where the number of users is equal to the subpacketization, i.e. $K=F$. Then by constructing NHSDPs, we obtain a new class of coded caching schemes which achieve lower load compared to the existing schemes with linear subpacketization and even some of the existing schemes with polynomial subpacketization. Moreover, the novel concept of NHSDPs is closely related to the classical combinatorial structures, including cyclic difference packing, non-three-term arithmetic progressions, and perfect hash family.