This paper investigates the coded caching problem in a multi-access multiple-input single-output (MAMISO) network with the combinatorial topology. The considered system consists of a server containing $N$ files, $Λ$ cache nodes, and $K$ cache-less users, where each user can access a unique subset of $r$ cache nodes. The server is equipped with $L$ transmit antennas. Our objective is to design a caching scheme that simultaneously achieves a high sum Degree of Freedom (sum-DoF) and low subpacketization complexity. To address this challenge, we formulate the design of multi-antenna placement delivery arrays (MAPDA) as a $0$--$1$ knapsack problem to maximize the achievable DoF, thereby transforming the complex combinatorial caching structure into a tractable optimization framework that yields efficient cache placement and flexible delivery strategies. Theoretical and numerical analyses demonstrate that: for networks with combinatorial topologies, the proposed scheme achieves a higher sum-DoF than existing schemes. Under identical cache size constraints, the subpacketization level remains comparable to existing linear subpacketization schemes. Moreover, under specific system conditions, the proposed scheme attains the theoretical maximum sum-DoF of $\min\{L+KM/N, K\}$ while achieving further reductions subpacketization. For particular combinatorial structures, we further derive optimized constructions that achieve even higher sum-DoF with lower subpacketization. ```

Coded distributed computing (CDC), introduced by Li et al., effectively reduces communication load in MapReduce systems. In cascaded CDC with$K$nodes,$N$input files, and$Q$output functions, each input file is mapped by$r \geq 1$nodes, and each output function is computed by$s>1$nodes, enabling coding for multicast opportunities. However, existing CDC schemes often require splitting data into exponentially many files or functions as$K$grows, increasing complexity and degrading performance. This paper addresses the case of$K / s \in \mathbb{N}$, proposing a low-complexity CDC scheme through carefully designing the strategies of data placement and output function assignment. The proposed scheme offers key advantages:$\mathbf{1}$) multicast gains of$(r+s-1)(1-1 / s)$and approximately$r+s-1$for large$s$, with better communication load than the well-known Li et al.'s scheme; 2) reduce input and output file requirements; and 3) binary field$\mathbb{F}_{2}$operations implement in a one-shot manner, enabling immediate decoding. We also derive a new information-theoretic bound under the proposed strategies, showing that the communication load is order-optimal within a factor of 2 and approximately optimal when$K$is sufficiently large for a given$r$.

In this paper, we study the coded caching scheme for the$(K,L,M_{\text {T}},M_{\text {U}},N)$partially connected linear network, where there are N files each of which has an equal size,$K+L-1$transmitters, and K users; each user and transmitter caches at most$M_{\text {U}}$and$M_{\text {T}}$files, respectively; each user locally communicates with L nearby transmitters. The goal is to design caching and delivery schemes to reduce the transmission latency measured by the metric named normalized delivery time (NDT). By delicately designing the data placement of the transmitters and users according to the topology, we show that a combinatorial structure called multiple-antenna placement delivery array (MAPDA), which was originally proposed for the multiple-input single-output broadcast channels, can be also helpful in designing schemes for the partially connected linear network. Then, based on existing MAPDAs and our constructing approach, we propose new schemes that achieve the optimal NDT when$ {M_{\text {T}}}+ {M_{\text {U}}}\geq N$and smaller NDT than that of the existing schemes when (${M_{\text {T}}}+ {M_{\text {U}}}\leq N$,$\frac {M_{\text {U}}}{N}+\frac {M_{\text {T}}}{N} \frac {L}{K}\left \lceil {{\frac {K}{L} }}\right \rceil \geq 1$) or ($ {M_{\text {U}}}+ {M_{\text {T}}}\lt N, \frac {K}{L}\notin \mathbb {Z}^{+}$). Moreover, our schemes operate in one-shot linear delivery and significantly reduce the subpacketizations compared to the existing scheme, which implies that our schemes have a wider range of applications and lower complexity of implementation.

An$(H,r,M,N)$combination network is a symmetric relay network that involves a central server equipped with$N$files that communicates with$K$users through$H$cache-less intermediate relays, where each user maintains a local cache of size$M$files and is connected to a distinct subset of$r$relays. In this setting, the well-known uniform scheme is proposed by Zewail and Yener via Minimum Distance Separable (MDS) codes. For practical reasons, this paper studies a more general combination network where each distinct subset of$r$relays is connected to$\Lambda $users, referred to as$(H,r,\Lambda,M,N)$dense-user combination network. Although the Zewail-Yener scheme is also feasible for the considered system, it causes high computational complexity since the use of$(H,r)_{q}$MDS code involves expensive multiplication operations in large finite field. In this paper, we aim to design coded caching schemes not only to minimize the worst-case link-load, but also to be implemented over the minimum operation field, i.e., binary field$\mathbb {F}_{2}$. First, we propose a construction which can transform any coded caching scheme for the shared-link model to the considered dense-user combination network. By applying the transformation approach based on the seminal work proposed by Maddah-Ali and Niesen, we present the MAN-based scheme that operates in binary field. To further reduce the link-load under small memory regions, we propose a hybrid scheme that can extend any caching scheme for the original$(H,r,M,N)$combination network to the considered$(H,r,\Lambda,M,N)$dense-user combination network by an ingenious outer-inner construction. From the theoretical analysis of computation complexity, the proposed schemes can significantly reduce the number of bit operations. From numerical comparisons, the link-loads of proposed schemes are close to or even better than that of Zewail-Yener scheme, while significantly reducing the operation field.

This paper studies a novel multi-access coded caching (MACC) model in the two-dimensional (2D) topology, which is a generalization of the one-dimensional (1D) MACC model proposed by Hachem et al. The 2D MACC model is formed by a server containing$N$files,$K_{1}\times K_{2}$cache-nodes with$M$files located at a grid with$K_{1}$rows and$K_{2}$columns, and$K_{1}\times K_{2}$cache-less users where each user is connected to$L^{2}$nearby cache-nodes. The server is connected to the users through an error-free shared link, while the users can retrieve the cached content of the connected cache-nodes without cost. Our objective is to minimize the worst-case transmission load over all possible users’ demands. In this paper, we first propose a grouping scheme for the case where$K_{1}$and$K_{2}$are divisible by$L$. By partitioning the cache-nodes and users into$L^{2}$groups such that no two users in the same group share any cache-node, we use the shared-link coded caching scheme proposed by Maddah-Ali and Niesen for each group. Then for any model parameters satisfying$\min \{K_{1},K_{2}\}\geq L$, we propose a transformation approach which constructs a 2D MACC scheme from two classes of 1D MACC schemes in vertical and horizontal projections, respectively. As a result, we can construct 2D MACC schemes that achieve maximum local caching gain and improved coded caching gain, compared to the baseline scheme by a direct extension from 1D MACC schemes. In addition, we propose new information theoretic converse bounds under the uncoded placement constraint by leveraging the network topology.

In this paper, we consider a two-dimensional caching-aided ultra-dense network caching system, which consists of a server containing N files, K1K2cache nodes that are arranged neatly on the grid with K1rows and K2columns, and U cacheless users randomly distributed around cache nodes. The server connects to users through an error-free shared-link, and the users can be served by nearby cache nodes and freely retrieve the cache content from it. Our goal is to minimize the transmission load in the worst case while meeting all possible users’ demands. We propose a coded caching scheme based on Maddah-Ali and Niesen scheme (MN scheme), which uses the placement strategy of MN scheme to the cache nodes and uses the delivery strategy of MN scheme multiple rounds for different types of users according to their geometrical locations. We prove that our scheme is order optimal and can greatly improve the transmission performance compared with conventional uncoded caching schemes.

Coded caching technique is an efficient approach to reduce the transmission load in networks. In this paper, we consider a new widespread caching system called$(K_{1},K_{2},U,r,M,N)$two-dimensional (2D) caching-aided ultra-dense networks (UDNs) with a server containing$N$files,$K_{1}K_{2}$cache nodes arranged neatly on a grid with$K_{1}$rows and$K_{2}$columns, and$U$cache-less users randomly distributed around cache nodes. Each cache node can cache at most$M\leq N$files and has a certain service region by Euclidean distance. The server connects to users through the error-free shared link and the users in the service region of a cache node can freely retrieve all cached contents of this cache node. We aim to design a coded caching scheme for 2D caching-aided UDN system to reduce the transmission load in the worst case while meeting all possible users’ demands. First, we divide all possible users into four classes according to their geographical locations. Then our first order optimal scheme is proposed based on the Maddah-Ali and Niesen scheme. Furthermore, by compressing the transmitted signals of our first scheme based on Maximum Distance Separable (MDS) code, we obtain an improved order optimal scheme with a smaller transmission load.

This paper formulates the multi-access coded caching (MACC) problem under the two-dimensional (2D) topology, which is a generalization of the one-dimensional (1D) MACC problem originally considered by Hachem et al. The novel 2D MACC system includes a server containing N files, K1×K2cache-nodes (each of size M units) placed on a grid with K1rows and K2columns, and K1×K2cache-less users, each of which accesses to L2nearby cache-nodes. More precisely, focus on any row (or column) of the grid, each user can access L consecutive cache-nodes in a cyclic wrap-around fashion, referred to as row (or column) 1D MACC problem in the 2D MACC system. The users are connected to the server through an error-free shared link, while they can also retrieve the content stored at the accessible cache-nodes without cost. Our objective is to minimize the worst-case transmission load among all possible users’ demands. This work proposes a baseline scheme firstly, which directly extends an existing 1D MACC scheme to the 2D model by using a Minimum Distance Separable (MDS) code. Then two improved schemes are designed. In the grouping scheme, we divide the cache-nodes and users into L2groups by their positions, such that any two users in the same group do not share any cache-node, and then utilize the seminal shared-link coded caching scheme proposed by Maddah-Ali and Niesen for each group. Then we propose the hybrid scheme, consisting in a highly non-trivial way to construct a 2D MACC scheme by using two 1D MACC problems under vertical and horizontal projections.

This paper studies the multiaccess 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 MN scheme to the multiaccess caching systems, such that the load expression of the scheme by Hachem et al for the case where$L$divides$K$, remains achievable in full generality. The resulting scheme has the maximum local caching gain (i.e., the cached contents stored at any$L$neighbouring cache-nodes are different such that each user can totally retrieve$L M$files from the connected cache-nodes) and the same coded caching gain as the related MN scheme. Moreover, our transformation approach can also be used to extend other coded caching schemes (satisfying some conditions) for the original MN caching systems to the multiaccess systems, such that the resulting scheme achieves the maximum local caching gain and the same coded caching gain as the considered caching scheme.

This paper considers the multiaccess coded caching systems formulated by Hachemet 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 Hachemet 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 noveltransformationapproach 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 Hachemet 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.