Yifei Huang

In the traditional $(H,r,M,N)$ combination network, a central server storing N files communicates with $K=(\genfrac{}{}{0pt}{}{H}{r})$ users through H cache-less relays. Each user has a local cache of size M files and is connected to a distinct subset of r relays. This paper studies the $(H,r,L,\mathrm{\Lambda },M,N)$ combination network with multi-access caching, where $\mathrm{\Lambda }$ cache nodes (each of size M files) are available and each user can access L cache nodes. We show that in the regime $H\ge \mathrm{\Lambda }$ and $r\ge L$, an achievable design can be obtained via a group-wise operation, which reduces the scheme design within each group to an effective $(\mathrm{\Lambda },L,L,\mathrm{\Lambda },M,N)$ instance. For the case $\mathrm{\Lambda }=H$ and $L=r$, we further propose an explicit coded caching scheme constructed via two array-based representations (a cache-node placement array and a user-retrieve array) and a derived combinatorial placement delivery array (CPDA) based on the Maddah-Ali–Niesen (MN) placement strategy. Numerical comparisons using the user-retrievable cache ratio as the evaluation metric indicate that the proposed scheme approaches the converse bound of the traditional combination network, and the performance gap diminishes as the cache ratio increases.

We consider a $(G,L,K,M,N)$ cache-aided multiple-input multiple-output (MIMO) network, where a server equipped with $L$ antennas and a library of $N$ equal-size files communicates with $K$ users, each equipped with $G$ antennas and a cache of size $M$ files, over a wireless interference channel. Each user requests an arbitrary file from the library. The goal is to design coded caching schemes that simultaneously achieve the maximum sum degrees of freedom (sum-DoF) and low subpacketization. In this paper, we first introduce a unified combinatorial structure, termed the MIMO placement delivery array (MIMO-PDA), which characterizes uncoded placement and one-shot zero-forcing delivery. By analyzing the combinatorial properties of MIMO-PDAs, we derive a sum-DoF upper bound of $\min\{KG, Gt+G\lceil L/G \rceil\}$, where $t=KM/N$, which coincides with the optimal DoF characterization in prior work by Tehrani \emph{et al.}. Based on this upper bound, we present two novel constructions of MIMO-PDAs that achieve the maximum sum-DoF. The first construction achieves linear subpacketization under stringent parameter constraints, while the second achieves ordered exponential subpacketization under substantially milder constraints. Theoretical analysis and numerical comparisons demonstrate that the second construction exponentially reduces subpacketization compared to existing schemes while preserving the maximum sum-DoF.

Coded caching is a promising technique to create coded multicast opportunities for cache-aided networks. By splitting each file into $F$ equal packets (i.e., the subpacketization level $F$) and letting each user cache a set of packets, the transmission load can be significantly reduced via coded multicasting. It has been shown that a higher subpacketization level could potentially lead to a lower transmission load, as more packets can be combined for efficient transmission. On the other hand, a larger $F$ indicates a higher coding complexity and is problematic from a practical perspective when $F$ is extremely large. Despite many works attempting to design coded caching schemes with low subpacketization levels, a fundamental problem remains open: What is the minimum transmission load given any fixed subpacketization level? In this paper, we consider the classical cache-aided networks with identically uncoded placement and one-shot delivery strategy, and investigate the fundamental trade-off between the transmission load and the subpacketization level. We propose a \emph{general} lower bound on the transmission load for any fixed subpacketization by reformulating the centralized coded caching schemes via the combinatorial structure of the corresponding placement delivery array. The lower bound also recovers existing optimality results for the bipartite graph scheme (including the well-known Maddah-Ali and Niesen (MN) scheme and the conjugate MN scheme) as well as the grouping bipartite graph scheme. Furthermore, by carefully exploiting the combinatorial structure and computing the union size of sorted sets, we establish a new optimality result, i.e., the partition scheme can achieve the optimal rate-subpacketization trade-off.

Coded distributed computing (CDC) is a powerful approach to reduce the communication overhead in distributed computing frameworks by utilizing coding techniques. In this paper, we focus on the CDC problem in $(H,L)$-combination networks, where H APs act as intermediate pivots and $K=\left({\displaystyle \genfrac{}{}{0pt}{}{H}{L}}\right)$ workers are connected to different subsets of L APs. Each worker processes a subset of the input file and computes intermediate values (IVs) locally, which are then exchanged via uplink and downlink transmissions through the AP station to ensure that all workers compute their assigned output functions. In this paper, we first novelly characterize the transmission scheme for the shuffle phase from the view point of the coefficient matrix and then obtain the scheme by using the Combined Placement Delivery Array (CPDA). Compared with the baseline scheme, our scheme significantly improves the uplink and downlink communication loads while maintaining the robustness and efficiency of the combined multi-AP network.