Caching is a promising solution to satisfy the ever increasing demands for the multi-media traffics. In caching networks, coded caching is a recently proposed technique that achieves significant performance gains over the uncoded caching schemes. However, to implement the coded caching schemes, each file has to be split into F packets, which usually increases exponentially with the number of users K. Thus, designing caching schemes that decrease the order of F is meaningful for practical implementations. In this paper, by reviewing the Ali-Niesen caching scheme, the placement delivery array (PDA) design problem is firstly formulated to characterize the placement issue and the delivery issue with a single array. Moreover, we show that, through designing appropriate PDA, new centralized coded caching schemes can be discovered. Secondly, it is shown that the Ali-Niesen scheme corresponds to a special class of PDA, which realizes the best coding gain with the least F . Thirdly, we present a new construction of PDA for the centralized caching system, wherein the cache size of each user M (identical cache size is assumed at all users) and the number of files N satisfies M/N = 1/q or (q − 1)/q (q is an integer such that q ≥ 2). The new construction can decrease the required F from the order O e

Abstract-The technique of coded caching proposed by Madddah-Ali and Niesen is a promising approach to alleviate the load of networks during busy times. Recently, placement delivery array (PDA) was presented to characterize both the placement and delivery phase in a single array for the centralized coded caching algorithm. In this paper, we interpret PDA from a new perspective, i.e., the strong edge coloring of bipartite graph. We prove that, a PDA is equivalent to a strong edge colored bipartite graph. Thus, we can construct a class of PDAs from existing structures in bipartite graphs. The class includes the scheme proposed by Maddah-Ali et al. and a more general class of PDAs proposed by Shangguan et al. as special cases. Moreover, it is capable of generating a lot of PDAs with flexible tradeoff between the sub-packet level and load.

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. Index TermsCoded caching scheme, placement delivery array, rate, packet number I. INTRODUCTIONRecently, the explosive increasing mobile services, especially applications such as video streaming, have imposed a tremendous pressure on the data transmission over the core network [1]. As a result, during the peak-traffic times, the communication systems are usually congested. Coded caching scheme, which was proposed by Maddah-Ali and Niesen in [12], can effectively reduce congestion during the peak-traffic times, and now is a hot topic in both industrial and academic fields (see [6]-[10], [12]-[14], [25], [28], and references therein).The benchmark work in [12] focused on the centralized caching system where a single server containing N files with the same length connects to K users over a shared link and each user has a cache memory of size M files. A coded caching scheme consists of two phases: a placement phase during off-peak times and a delivery phase during peak times. In the placement phase, the user caches are populated. This phase does not depend on the user demands which are assumed to be arbitrary. In delivery phase, each user requires a file from server. Then server sends a coded signal of at most R files to the users such that various user demands are satisfied with the help the local caches. It is meaningful to minimize the load R files in the delivery phase. Here R is always called the rate. A coded caching scheme is called F -division scheme if each file is split into F packets. If the packets of all files are directly cached in the placement phase, we call it uncoded placement. Otherwise we call it coded placement. Through an elaborate uncoded placement and a coded delivery, the first determined scheme for an F -division (K, M, N ) coded caching system with F = K KM/N , when KM N is an integer, was proposed by Maddah-Ali and Niesen in [12]. Such a scheme is referred to as MN scheme in this p...

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