This work considers the device-to-device (D2D) multi-access coded caching problem proposed by Wu et al., where each user has access toLneighboring cache nodes in a cyclic wrap-around fashion and the users communicate with each other in the delivery phase. D2D placement delivery array (DPDA) is a combinatorial structure to design D2D coded caching schemes with uncoded placement and one-shot linear delivery. In order to achieve the maximal local caching gain with a linear subpacketization, we adopt the consecutive cyclic placement proposed for the multi-access coded caching system. First, we derive an upper bound on the coded caching gain of D2D coded caching schemes from DPDA under the consecutive cyclic placement, leading to a lower bound on the communication load. Second, we equivalently represent DPDA as a vector set satisfying certain constraints, and design a vector set satisfying the constraints, which generates a new D2D multi-access coded caching scheme with linear subpacketization for arbitrary number of users and cache node memory ratio. The new scheme either achieves the derived lower bound or achieves a coded caching gain that is only 1 less than the derived upper bound. Performance analysis demonstrates that our proposed scheme, maintaining linear subpacketization, achieves a smaller communication load compared to existing schemes with linear subpacketization. Furthermore, compared to the existing schemes employing sub-exponential subpacketization, it significantly reduces subpacketization and even achieves a lower communication load whenLis relatively large.

This work considers the multi-access caching system proposed by Hachem et al., where each user has access to$L$neighboring caches in a cyclic wrap-around fashion. We first propose a placement strategy called the consecutive cyclic placement, which achieves the maximal local caching gain. Then under the consecutive cyclic placement, we derive an upper bound on the coded caching gain of any PDA, thus obtaining a lower bound on the rate of PDA-based coded caching schemes. Finally, we construct a class of PDAs under the consecutive cyclic placement, leading to a multi-access coded caching scheme with linear subpacketization, which achieves the derived lower bound on the rate for some parameters; while for other parameters, the achieved coded caching gain is only 1 less than the derived upper bound on the coded caching gain. Analytical and numerical comparisons of the proposed scheme with existing schemes are provided to validate the performance.

Caching prefetches some library content at users’ memories during the off-peak times (i.e., placement phase), such that the number of transmissions during the peak-traffic times (i.e., delivery phase) are reduced. A coded caching strategy was originally proposed by Maddah-Ali and Niesen (MN) leading to a multicasting gain compared to the conventional uncoded caching, where each message in the delivery phase is useful to multiple users simultaneously. The load of the MN scheme is optimal under uncoded placement, but the subpacketization level is$O\left({2^{H\left({\frac {M}{N}}\right)K}}\right)$, where$K$is the number of users,$\frac {M}{N}$is the memory ratio of each user and$H\left({\frac {M}{N}}\right)$is the binary entropy at$\frac {M}{N}$. In order to reduce the subpacketization while retaining the multicast opportunities in the delivery phase, Yan et al. proposed a combinatorial structure called placement delivery array (PDA) to design coded caching schemes with uncoded placement and clique-covering delivery. In this paper, we consider the coded caching problem from the perspective of PDA. First we propose a Cartesian product method, which constructs an$mK_{1}$-user PDA based on the piece-wise$m$-fold Cartesian product of a special$K_{1}$-user PDA (called a base PDA) while keeping the memory ratio and load unchanged. Since a base PDA must satisfy some restrictive constraints, we propose a transformation from any existing PDA to a base PDA, which makes the Cartesian product method applicable to any existing PDA. As applications of the Cartesian product method, three new coded caching schemes (i.e., Schemes A, B, C) are obtained, whose performance are validated via analytical and numerical comparisons. It is worth noting that Scheme A is asymptotically optimal under uncoded placement, in the sense that the achieved coded caching gain is only decreased by 1 with respect to the coded caching gain of the MN scheme. When the number of users is$K=mq$and memory ratio is$\frac {z}{q}$, the needed subpacketization is at most$O\left ({\sqrt {\frac {K}{q}}2^{-\frac {K}{q}}}\right)$of that of the MN scheme for large$m$, which implies that for fixed number of users and memory ratio, when we choose$q$and$z$coprime, the subpacketization can be reduced the most, since the value of$\frac {K}{q}$is maximized. Moreover, Scheme A works for arbitrary memory ratio.

Caching is an efficient technique to reduce the peak-time traffic by prefetching some library content at users’ memories during the off-peak hours. Maddah-Ali and Niesen (MN) proposed the first coded caching scheme, which achieves a multicasting gain over the conventional uncoded caching. However, its high subpacketization makes it impractical. In order to reduce the subpacketization while retaining the multicast opportunities, Yan et al. proposed a combinatorial structure called placement delivery array (PDA) to design coded caching schemes. In this paper, we propose a new framework for constructing a PDA for mK1users, by taking the m-fold Cartesian product of a PDA for K1users. By applying the proposed framework to the MN scheme, a new coded caching scheme is obtained, which works for any number of users and any memory regime. While reducing the coded caching gain by only one, the needed subpacketization is at most $O\left( {\sqrt {\frac{K}{q}} {2^{ - \frac{K}{q}}}} \right)$ of that of the MN scheme, where K is the number of users, 0 < z/q < 1 is the memory ratio of each user, and q, z are coprime.