In a traditional (H,r) combination network, each user connects to a unique set of r relays. However, few research efforts have considered the (H,r,u) multiaccess combination network problem wherein each unique set of r relays is connected by u users. In this paper, we focus on designing coded caching schemes for a (H,r,u) multiaccess combination network. By directly applying the well-known coding method (proposed by Zewail and Yener) for a (H,r) combination network, a coded caching scheme (called ZY scheme) for (H,r,u) multiaccess combination network is obtained. However, its subpacketization has an exponential order with the number of users which leads to high implementation complexity. In order to reduce subpacketization, a direct construction of a coded caching scheme (called the direct scheme) for (H,r,u) multiaccess combination network is proposed by means of combinational design theory, where the parameter u must be a combinatorial number. For the arbitrary parameter u, the hybrid construction of a coded caching scheme (called the hybrid scheme) for the (H,r,u) multiaccess combination network is proposed based on the direct scheme. Theoretical and numerical analysis shows that the direct scheme and the hybrid scheme have a smaller transmission load for each relay compared with the naive scheme (which is obtained by repeatedly applying the coded caching scheme for a traditional (H,r) combination network by u times) and have much lower subpacketization compared with the ZY scheme.

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In a traditional (H, r) combination network, each user is connected to a unique set of r relays. However, few research efforts to consider (H, r, u) multiaccess combination network problem where each u users are connected to a unique set of r relays. A naive strategy to obtain a coded caching scheme for (H, r, u) multiaccess combination network is by u times repeated application of a coded caching scheme for a traditional (H, r) combination network. Obviously, the transmission load for each relay of this trivial scheme is exactly u times that of the original scheme, which implies that as the number of users multiplies, the transmission load for each relay will also multiply. Therefore, it is very meaningful to design a coded caching scheme for (H, r, u) multiaccess combination network with lower transmission load for each relay. In this paper, by directly applying the well known coding method (proposed by Zewail and Yener) for (H, r) combination network, a coded caching scheme (ZY scheme) for (H, r, u) multiaccess combination network is obtained. However, the subpacketization of this scheme has exponential order with the number of users, which leads to a high implementation complexity. In order to reduce the subpacketization, a direct construction of a coded caching scheme for (H, r, u) multiaccess combination network is proposed by means of Combinational Design Theory, where the parameter u must be a combinatorial number. For arbitrary parameter u, a hybrid construction of a coded caching scheme for (H, r, u) multiaccess combination network is proposed based on our direct construction. Theoretical and numerical analysis show that our last two schemes have smaller transmission load for each relay compared with the trivial scheme, and have much lower subpacketization compared with ZY scheme.

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