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

TL;DR

This paper introduces a novel coded caching scheme for multi-access MISO networks that leverages a knapsack problem formulation to optimize sum-DoF and subpacketization, outperforming existing methods.

Contribution

It formulates the cache placement and delivery design as a knapsack problem, enabling efficient optimization of sum-DoF and subpacketization in multi-access MISO systems.

Findings

Achieves higher sum-DoF than existing schemes.

Maintains comparable subpacketization levels.

Attains maximum sum-DoF under certain conditions.

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. ```