Placement Delivery Array for Cache-Aided MIMO Systems

TL;DR

This work introduces MIMO-PDA, a unified combinatorial framework for cache-aided MIMO networks with uncoded placement and one-shot zero-forcing delivery. It derives a sum-DoF upper bound $g \le \min\{KG, GK\gamma + G\lceil L/G\rceil\}$ and provides two optimal constructions that achieve this bound: a cyclic, linear-subpacketization scheme under a strong parameter constraint and a hybrid, hypergraph-based scheme that yields exponential reductions in subpacketization while preserving DoF. The hybrid construction leverages Baranyai’s theorem and perfect matchings to enable scalable designs with dramatically lower $F$ compared to prior approaches. The results demonstrate that careful combinatorial design can simultaneously maximize DoF and minimize subpacketization in cache-aided MIMO systems, with practical implications for scalable wireless caching networks.

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.

Figures (8)

• Figure 1: Multiple-input-multiple-output broadcast channel (MIMO) system of one server with $L$ antennas and $K$ users with $G$ antennas.
• Figure 2: Subpacketization Comparison Between the MIMO-PDAs in Theorems \ref{['th-TST']} and \ref{['th-MAPDA-hypergraph']} with $K=120$, $G=3$, and $L=13$.
• Figure 3: The flow of constructing square $(2,3,4,8,4,2)$ MIMO-PDA.
• Figure 4: The flow diagram of constructing $\mathbf{B}$, $\mathbf{Q}$, $\mathbf{X}$, $\mathbf{T}$, $\mathbf{Y}$ and $\mathbf{P}$ .
• Figure 5: The subarray of $\mathbf{B}$ including the row $(\mathcal{T},1,1)$ where $\mathcal{T}=1234$, $1235$, $1256$, $1346$, $2456$, $3456$.

Theorems & Definitions (20)

• Definition 1: MIMO-PDA
• Theorem 1
• proof
• Example 1
• Example 2
• Remark 1: The MN PDA
• Theorem 2
• Lemma 1: MMA
• Definition 2: Consistency number
• Proposition 1