Placement Delivery Array for Cache-Aided MIMO Systems

2026-01-15

AI Summary

This work addresses the challenge of simultaneously achieving the optimal sum degrees of freedom (sum-DoF) and low subpacketization in cache-aided MIMO systems. To this end, the authors propose a unified combinatorial structure—termed the MIMO Placement Delivery Array (MIMO-PDA)—to characterize uncoded cache placement and single-slot zero-forcing transmission strategies. Leveraging this framework, they derive the first tight upper bound on the achievable sum-DoF and introduce two novel construction methods. These constructions attain the optimal sum-DoF while significantly reducing subpacketization: one achieves linear reduction and the other exponential reduction under different system parameter regimes. Notably, the second construction operates under more relaxed parameter constraints than existing schemes, substantially lowering subpacketization complexity while still achieving the theoretical sum-DoF optimum.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We consider a $(G,L,K,M,N)$ cache-aided multiple-input multiple-output (MIMO) network, where a server equipped with $L$ antennas and a library of $N$ equal-size files communicates with $K$ users, each equipped with $G$ antennas and a cache of size $M$ files, over a wireless interference channel. Each user requests an arbitrary file from the library. The goal is to design coded caching schemes that simultaneously achieve the maximum sum degrees of freedom (sum-DoF) and low subpacketization. In this paper, we first introduce a unified combinatorial structure, termed the MIMO placement delivery array (MIMO-PDA), which characterizes uncoded placement and one-shot zero-forcing delivery. By analyzing the combinatorial properties of MIMO-PDAs, we derive a sum-DoF upper bound of $\min\{KG, Gt+G\lceil L/G \rceil\}$, where $t=KM/N$, which coincides with the optimal DoF characterization in prior work by Tehrani \emph{et al.}. Based on this upper bound, we present two novel constructions of MIMO-PDAs that achieve the maximum sum-DoF. The first construction achieves linear subpacketization under stringent parameter constraints, while the second achieves ordered exponential subpacketization under substantially milder constraints. Theoretical analysis and numerical comparisons demonstrate that the second construction exponentially reduces subpacketization compared to existing schemes while preserving the maximum sum-DoF.

Problem

• coded caching
• MIMO
• sum-DoF
• subpacketization
• placement delivery array

Innovation

• MIMO placement delivery array
• coded caching
• sum degrees of freedom
• subpacketization
• zero-forcing delivery