The technique of coded caching proposed by Madddah-Ali and Niesen is a promising approach to alleviate the load of networks during peak-traffic 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 reinterpret PDA from a new perspective, i.e., the strong edge coloring of bipartite graph (bigraph). We prove that, a PDA is equivalent to a strong edge colored bigraph. Thus, we can construct a class of PDAs from existing structures in bigraphs. The class subsumes the scheme proposed by Maddah-Ali et al. and a more general class of PDAs proposed by Shangguan et al. as special cases.

Coded caching scheme recently has become quite popular in the wireless network since the maximum transmission amount R reduces effectively during the peak-traffic times. 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 design a scheme with R and F as small as possible in practice. However there exists a tradeoff between R and F. In this paper, we generalize the schemes constructed by Shangguan et al. (IEEE Trans. Inf. Theory, 64, 5755-5766, 2018) and Yan et al. (IEEE Trans. Inf. Theory 63, 5821-5833, 2017) respectively. These two classes of schemes have a wider range of application due to the more flexible memory size than the original ones. By comparing with the previous known deterministic schemes, our new schemes have advantages on R or F.

In coded caching system, we prefer to design a scheme with the rate R and the packet number F of each file split as small as possible since the efficiency of transmission in the peak traffic times increases with the decreasing of R and the realizing complexity increases with the increasing of F. Up to now, almost all of the previously known schemes can be realized by the combinatorial structure which is called placement delivery array (PDA). In this paper, we also study the schemes by means of PDAs. We first show that given the minimum rate, the scheme proposed by Maddah-Ali and Niesen (MN scheme) has the minimum packet number which is too large in practice. From the view point of combinatorial design, two variant MN schemes, which can significantly reduce the packet number by increasing some rate, are obtained. Especially one of these schemes has better performance than the scheme generated by the well known grouping method.

In caching system, it is desirable to design a coded caching scheme with the transmission load $R$ and subpacketization $F$ as small as possible, in order to improve efficiency of transmission in the peak traffic times and to decrease implementation complexity. Yan et al. reformulated the centralized coded caching scheme as designing a corresponding $F\times K$ array called placement delivery array (PDA), where $F$ is the subpacketization and $K$ is the number of users. Motivated by several constructions of PDAs, we introduce a framework for constructing PDAs, where each row is indexed by a row vector of some matrix called row index matrix and each column’s index is labelled by an element of a direct product set. Using this framework, a new scheme is obtained, which can be regarded as a generalization of some previously known schemes. When $K$ is equal to ${\binom{m}{ t}}q^{t}$ for positive integers $m$ , $t$ with $t < m$ and $q\geq 2$ , we show that the row index matrix must be an orthogonal array if all the users have the same memory size. Furthermore, the row index matrix must be a covering array if the coded gain is ${\binom{m}{ t}}$ , which is the maximal coded gain under our framework. Consequently the lower bounds on the transmission load and subpacketization of the schemes are derived under our framework. Finally, using orthogonal arrays as the row index matrix, we obtain two more explicit classes of schemes which have significantly advantages on the subpacketization while the transmission load is equal or close to that of the schemes constructed by Shangguan et al. for the same number of users and memory size.

Ji et al. ( IEEE Trans. Inform. Theory, 62(2): 849- 869,2016) first studied coded caching in Device-to-Device (D2D) networks, and proposed a D2D coded caching scheme, which is referred to as the JCM scheme. In practice we prefer to design a scheme with its two important targets, i.e., the rate (the maximal total amount of transmission) and packet number F, as small as possible. In this paper we first propose a simple array called D2D placement delivery array (DPDA) to characterize the placement phase and the delivery phase in D2D networks. Consequently some D2D coded caching schemes can be realized by an appropriate DPDA. Secondly a lower bound on the rate of a DPDA is derived. And we show that the JCM scheme achieves our lower bound. However, it is well known that its packet number F increases exponentially with the number of users K. So we propose two classes of new schemes by constructing DPDAs. One reduces the packet number exponentially with K compared with the JCM scheme while keeping the rate near to our lower bound. The other further reduces F to increasing sub-exponentially with K.

This paper considers the multiaccess coded caching systems formulated by Hachem et al. , including a central server containing $N$ files connected to $K$ cache-less users through an error-free shared link, and $K$ cache-nodes, each equipped with a cache memory size of $M$ files. Each user has access to $L$ neighbouring cache-nodes with a cyclic wrap-around topology. The coded caching scheme proposed by Hachem et al. suffers from the case that $L$ does not divide $K$ , where the needed number of transmissions (a.k.a. load) is at most four times the load expression for the case where $L$ divides $K$ . Our main contribution is to propose a novel transformation approach to smartly extend the schemes satisfying some conditions for the well known shared-link caching systems to the multiaccess caching systems. Then we can get many coded caching schemes with different subpacketizations for multiaccess coded caching system. These resulting schemes have the maximum local caching gain (i.e., the cached contents stored at any $L$ neighbouring cache-nodes are different such that the number of retrieval packets by each user from the connected cache-nodes is maximal) and the same coded caching gain as the original schemes. Applying the transformation approach to the well-known shared-link coded caching scheme proposed by Maddah-Ali and Niesen, we obtain a new multiaccess coded caching scheme that achieves the same load as the scheme of Hachem et al. but for any system parameters. Under the constraint of the cache placement used in this new multiaccess coded caching scheme, our delivery strategy is approximately optimal when $K$ is sufficiently large. Finally, we also show that the transmission load of the proposed scheme can be further reduced by compressing the multicast message.