A Construction Framework of Coded Caching Scheme for Multi-Access MISO Systems via Knapsack Problem

2026-01-15

AI Summary

This work addresses the challenge of simultaneously achieving high sum degrees of freedom (sum-DoF) and low subpacketization complexity in combinatorial topology multi-access MIMO systems. It proposes, for the first time, modeling coded caching design as a 0–1 knapsack optimization problem. By jointly optimizing cache placement and multi-antenna content delivery strategies, the authors construct a multi-antenna placement delivery array (MAPDA). This approach significantly enhances sum-DoF while maintaining subpacketization complexity comparable to that of linear schemes, and under certain conditions, it attains the theoretical maximum sum-DoF. Consequently, the method achieves a synergistic optimization between system performance and implementation complexity.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Cloud, edge and content delivery systems for the Web
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

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, $\Lambda$ 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. ```

Problem

• coded caching
• multi-access MIMO
• sum-DoF
• subpacketization
• combinatorial topology

Innovation

• coded caching
• multi-access MIMO
• placement delivery array
• knapsack problem
• subpacketization