Device-to-Device (D2D) assisted coded caching is a promising approach to improve the communication efficiency over networks. However, the basic D2D coded caching scheme requires a subpacketization size that increases exponentially with the number of users. This is infeasible since the file size needs to be extremely large in the server. It is desirable to design a scheme that achieves a small subpacketization size while keeping the rate low. Recently, D2D placement delivery array (DPDA) was proposed to address the high subpacketization issue of D2D coded caching. This paper investigates the design of DPDA from the perspectives of linear algebraic and additive combinatorics. It is shown that a linear subspace possessing certain property can be employed in the design of DPDA. Based on this, a new D2D coded caching scheme with a subquadratic subpacketization size is derived through shortening the binary Reed-Muller codes. In order to obtain a D2D coded caching scheme with a linear subpacketization size, a new combinatorial structure called proper disjoint 3-term arithmetic progression (3-AP) free set is further introduced, and a deterministic algorithm for constructing it is provided with a polynomial complexity. Both the theoretical and numerical results reveal that the proposed schemes have a superior performance in terms of subpacketization size or transmission rate.

Large-scale Internet of Things (IoT) networks enable intelligent services such as smart cities and autonomous driving, but often face resource constraints. Collecting heterogeneous sensory data, especially in small-scale datasets, is challenging, and independent edge nodes can lead to inefficient resource utilization and reduced learning performance. To address these issues, this paper proposes a collaborative optimization framework for energy-efficient federated edge learning with small-scale datasets. We first derive an expected learning loss to quantify the relationship between the number of training samples and learning objectives. A stochastic online learning algorithm is then designed to adapt to data variations, and a resource optimization problem with a convergence bound is formulated. Finally, an online distributed algorithm efficiently solves large-scale optimization problems with high scalability. Extensive simulations and autonomous navigation case studies with collision avoidance demonstrate that the proposed approach significantly improves learning performance and resource efficiency compared to state-of-the-art benchmarks.