Linear Coded Caching Scheme for Centralized Networks

Coded caching systems have been widely studied to reduce the data transmission during the peak traffic time. In practice, two important parameters of a coded caching system should be considered, i.e., the transmission rate which is the maximum amount of the data transmission during the peak traffic time, and the subpacketization level, the number of divided packets of each file when we implement a coded caching scheme. Although there exists a tradeoff between transmission rate and subpacketization, we prefer to design a scheme with transmission rate and subpacketization as small as possible since they reflect the transmission efficiency and complexity of the caching scheme, respectively. In this paper, we first characterize a coded caching scheme from the viewpoint of linear algebra and show that designing a linear coded caching scheme is equivalent to constructing three classes of matrices satisfying some rank conditions. Then based on the invariant subspaces in linear algebra and combinatorial design theory, a new class of coded caching schemes over F
₂
is obtained by constructing these three classes of matrices. It turns out that the transmission rate of our new scheme is the same as the scheme construct by Yan et al. (IEEE Trans. Inf. Theory 63, 5821-5833, 2017), but the subpacketization is significantly reduced. Finally by means of these matrices, we show that the minimum storage regenerating codes can also be used to construct coded caching schemes.