Device-to-device (D2D) communication is one of the most promising techniques for next-generation wireless Internet of Things networks. This paper considers coded caching in a wireless multiaccess D2D network, where users communicate with each other and can access multiple cache nodes. Access topologies derived from two combinatorial designs known as thet-design andt-group divisible design (t-GDD), referred to as thet-design andt-GDD topologies, respectively, have been studied recently for the multiaccess coded caching (MACC) network. These access topologies, which subsume the other known topologies except the cyclic wrap-around topology, are extended to a multiaccess D2D coded caching (MADCC) network. Novel MADCC schemes are proposed, and schemes are also derived from existing MACC schemes witht-design andt-GDD topologies. To compare different MADCC schemes, the metrics of load per user and subpacketization level are used while keeping the number of caches, cache size, and access degree the same. A comparison of the proposed schemes with those derived from existing MACC schemes, as well as with the existing MADCC scheme under a cyclic wrap-around topology, shows that the proposed schemes have an advantage in either load per user or subpacketization level or both. Additionally, several low subpacketization level coded caching schemes are obtained for the original D2D network with dedicated caches.

Function-Correcting Codes (FCCs) are a novel class of codes designed to protect function evaluations of messages against errors while minimizing redundancy. A theoretical framework for systematic FCCs to channels matched to the Lee metric has been studied recently, which introduced function-correcting Lee distance codes (FCLCs) and also derived upper and lower bounds on their optimal redundancy. In this paper, we first propose a Plotkin-like bound for irregular Lee-distance codes. We then construct explicit FCLCs for specific classes of functions, including the Lee weight, Lee weight distribution, modular sum and locally bounded function. For these functions, lower bounds on redundancy are obtained, and our constructions are shown to be optimal in certain cases. Finally, a comparative analysis with classical Lee error-correcting codes and codes correcting errors in function values demonstrates that FCLCs can significantly reduce redundancy while preserving function correctness.

This paper studies wireless device-to-device (D2D) coded caching in a multiaccess network, where users communicate with each other and access multiple cache nodes. Access topologies derived from two combinatorial designs, the$t$-design and$t$-group divisible design ($t$-GDD), previously studied for multiaccess coded caching (MACC) network by Cheng et al. in [14], are extended to multiaccess D2D coded caching (MADCC) network. Novel MADCC schemes are proposed and also derived schemes from existing MACC schemes in [14]. To compare different MADCC schemes, the metrics of load per user and subpacketization level are used while keeping the number of caches and cache memory size fixed. Comparison of the proposed schemes with the schemes derived from existing MACC schemes in [14] and the existing MADCC scheme with cyclic wrap-around topology shows that the proposed schemes have an advantage in either load per user or subpacketization level or both.

This paper studies a two-layer hierarchical network in which some users are offline during the content delivery phase. A two-layer hierarchical network consists of a single server connected to multiple cache-aided mirror sites, and each mirror site is connected to a distinct set of cache-aided users. A scheme for such a hierarchical system with offline users has been proposed recently, but considered a special case where all mirror caches have zero memory, which is a significant limitation. We propose an array known as a hierarchical hotplug placement delivery array (HHPDA), which describes the placement and delivery phases of a coded caching scheme for a general two-layer hierarchical network with offline users. Further, we construct a class of HHPDAs using combinatorial t-designs.

Coded caching in a wireless device-to-device (D2D) network was first studied by Ji et al. in [4] (referred to as the JCM scheme). Wang et al. in [7] proposed the D2D placement delivery array (DPDA) that characterizes coded caching in a D2D network and derived a lower bound on the transmission load of a DPDA. Only the JCM scheme achieves this bound but requires a subpacketization level that grows exponentially with the number of users. This paper proposes two new classes of DPDA constructions that give low subpacketization level D2D schemes using cross resolvable designs. The first class of constructed DPDA achieves the known lower bound on the transmission load of DPDA while requiring a subpacketization level lesser than that of the JCM scheme. A new lower bound on the transmission load of a DPDA is proposed and shows that the second class of constructed DPDA achieves this lower bound.

Multi-layer cache structures are commonly used in various IoT environments due to their distributed architecture. This paper considers coded caching for a two-layer hierarchical network consisting of a single server connected to multiple cache-aided mirror sites, and each mirror site connected to a distinct set of cache-aided users. The placement delivery array (PDA) and the hierarchical placement delivery array (HPDA) were proposed as tools for designing coded caching schemes with reduced subpacketization levels for single-layer and two-layer networks, respectively. This paper proposes construction of a novel class of HPDAs by first constructing a class of PDAs using combinatorial t-designs. The proposed class of HPDAs yields hierarchical coded caching schemes at several memory points for a given number of mirrors and users. Additionally, we introduce the concept of hierarchical memory sharing to achieve the lower envelope of the convex hull of these points. It is shown that the proposed hierarchical schemes have significantly lower subpacketization levels compared to many known schemes. In cases where the system parameters and subpacketization levels of the proposed and existing schemes match, the proposed scheme achieves a better coding delay. Furthermore, the class of PDAs constructed either subsumes several known PDA constructions or achieves a better transmission load for the same system parameters.

Coded caching scheme originally proposed by Maddah-Ali and Niesen (MN) achieves optimal transmission rate$R$under uncoded placement but requires a subpacketization level$F$which increases exponentially with the number of users$K$where the number of files$N\geq K$. Placement delivery array (PDA) was proposed as a tool to design coded caching schemes with reduced subpacketization level by Yan et al. in [4]. This paper proposes two novel classes of PDA constructions from combinatorial t-designs which achieve improved transmission rate for a given low subpacketization level, cache size and number of users compared to existing coded caching schemes from t- designs. A$(K,F, Z,S)$PDA composed of a specific symbol$\star$and$S$nonnegative integers corresponds to a coded caching scheme with subpacketization level F, K users each caching$Z$packets and the demands of all the users are met with a rate$R=\frac{S}{F}$. For a given K, F and Z, a lower bound on$S$such that a (K, F, Z, S) PDA exists is given by Cheng et al. in [16]. The first class of proposed PDA achieves this lower bound on S. The second class of PDA also achieves this lower bound in some cases.