Placement Delivery Array for Cache-Aided MIMO Systems

TL;DR

This paper introduces a new combinatorial structure called MIMO-PDA for cache-aided MIMO networks, achieving maximum sum-DoF with reduced subpacketization through novel constructions.

Contribution

The paper proposes the MIMO-PDA framework and two new schemes that attain maximum sum-DoF with significantly lower subpacketization levels.

Findings

Achieves the sum-DoF upper bound matching prior optimal results.

Provides a linear subpacketization scheme under certain parameters.

Offers an exponential subpacketization scheme with practical advantages.

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.