Constructions of Coded Caching Schemes with Flexible Memory Size

Coded caching scheme recently has become quite popular in the wireless network due to its effectively reducing the transmission amount (denote such an amount by $R$) during peak traffic times. However to realize a coded caching scheme, each file must be divided into $F$ packets which usually increases the computation complexity of a coded caching scheme. So we prefer to construct a caching scheme that decreases the order of $F$ for practical implementations. In this paper, we construct four classes of new schemes where two classes can significantly reduce the value of $F$ by increasing a little $R$ comparing with the well known scheme proposed by Maddah-Ali and Niesen, and $F$ in the other two classes grows sub-exponentially with $K$ by sacrificing more $R$. It is worth noting that a tradeoff between $R$ and $F$, which is a hot topic in the field of caching scheme, is proposed by our constructions. In addition, our constructions include all the results constructed by Yan et al., (IEEE Trans. Inf. Theory 63, 5821-5833, 2017) and some main results obtained by Shangguan et al., (arXiv preprint arXiv:1608.03989v1) as the special cases.