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

TL;DR

This work tackles coded caching in a multi-access MIMO (MAMISO) network with combinatorial cache topologies by introducing a MAPDA framework whose cache placement is optimized via a 0–1 knapsack formulation to maximize sum-DoF while controlling subpacketization. The authors develop a set of knapsack-guided MAPDA constructions, extendable to MISO scenarios, and provide rigorous theoretical comparisons against existing schemes (YWCC, NKPR, WCC, PERB) along with concrete numerical demonstrations. A key result shows that, under certain parameter regimes, the proposed schemes achieve the maximum theoretical sum-DoF of $KM/N + L$ and/or offer substantial subpacketization reductions, with special constructions reproducing known results as special cases. The framework delivers a flexible, optimization-driven approach to caching in multi-antenna networks with combinatorial access structures, offering practical gains for large-scale cache-aided wireless systems.

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, $Λ$ 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. ```

Figures (11)

• Figure 1: Multi-access multi-input single-output coded caching system
• Figure 2: The subpacketization of MAPDAs in YWCC, NKPR, WCC, and Theorem \ref{['the-olution']} and Corollary \ref{['corollary-1']}.
• Figure 3: The sum-DoF of MAPDAs in YWCC, NKPR, WCC, and Theorem \ref{['the-olution']} and Corollary \ref{['corollary-1']}.
• Figure 4: The subpacketization of MAPDAs in YWCC, NKPR, WCC, and Corollary \ref{['corollary-3']}.
• Figure 5: The sum-DoF of MAPDAs in YWCC, NKPR, WCC, and Corollary \ref{['corollary-3']}.

Theorems & Definitions (20)

• Definition 1: YWCC
• Example 1
• Lemma 1: YWCC
• Lemma 2: YWCCLBENKPR
• Definition 2: CWLZC
• Proposition 1
• Theorem 1
• Theorem 2
• Theorem 3
• Theorem 4