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Reducing Subpacketization in Device-to-Device Coded Caching via Heterogeneous File Splitting

Xiang Zhang, Giuseppe Caire, Mingyue Ji

Abstract

The packet type (PT)-based framework~\cite{zhang2026taming} provides a systematic and principled approach to designing device-to-device (D2D) coded caching schemes that achieve reduced \sbp while preserving the optimal communication rate. However, existing PT designs rely exclusively on homogeneous \sbp, where all packets have an identical size regardless of their types. This restriction limits the achievable \sbp reduction in certain parameter regimes. In this paper, we extend the PT framework to \emph{heterogeneous} \sbp, allowing packet sizes to vary across types under a refined type classification. The packet sizes, in conjunction with user grouping and multicast transmitter selection, are jointly optimized to minimize the overall \sbp level while preserving the optimal rate. Based on the heterogeneous PT framework, we construct a new class of D2D coded caching schemes for $(K, KM/N)=(2q+1, 2r)$ with $q,r \in \mathbb{N}_+$, where $K,N$ and $M$ denote the number of users, files and cache memory size, respectively. The proposed construction achieves a constant-factor reduction in \sbp compared to the Ji-Caire-Molisch (JCM) caching scheme~\cite{ji2016fundamental} and complements existing PT designs that are not applicable in this parameter regime.

Reducing Subpacketization in Device-to-Device Coded Caching via Heterogeneous File Splitting

Abstract

The packet type (PT)-based framework~\cite{zhang2026taming} provides a systematic and principled approach to designing device-to-device (D2D) coded caching schemes that achieve reduced \sbp while preserving the optimal communication rate. However, existing PT designs rely exclusively on homogeneous \sbp, where all packets have an identical size regardless of their types. This restriction limits the achievable \sbp reduction in certain parameter regimes. In this paper, we extend the PT framework to \emph{heterogeneous} \sbp, allowing packet sizes to vary across types under a refined type classification. The packet sizes, in conjunction with user grouping and multicast transmitter selection, are jointly optimized to minimize the overall \sbp level while preserving the optimal rate. Based on the heterogeneous PT framework, we construct a new class of D2D coded caching schemes for with , where and denote the number of users, files and cache memory size, respectively. The proposed construction achieves a constant-factor reduction in \sbp compared to the Ji-Caire-Molisch (JCM) caching scheme~\cite{ji2016fundamental} and complements existing PT designs that are not applicable in this parameter regime.

Paper Structure

This paper contains 24 sections, 4 theorems, 89 equations, 3 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Finite-Length D2D Coded Caching
  3. The Packet Type-based Framework
  4. Summary of Contributions
  5. Problem Setup and Overview of PT Framework
  6. Problem Setup
  7. Overview of PT Framework
  8. Main Result
  9. PT Framework with Heterogeneous Subpacketization
  10. Proposed Construction
  11. Motivating Example
  12. General PT Design
  13. Subpacketization Analysis
  14. Validation of Packet Size Ratio
  15. Discussion
  16. ...and 9 more sections

Key Result

Theorem 1

Let $(K,t) =(2q+1,2r)$ with $q,r \in \mathbb{N}_+$. The communication rate $R=N/M-1$ of D2D coded caching is achievable with subpacketization level $\hbox{$F_{\rm PT}$}$ satisfying $\hbox{$F_{\rm PT}$} \le \hbox{$F_{\rm JCM}$}$, where with Moreover, for fixed $t$,

Figures (3)

  • Figure 1: Actual (solid) and asymptotic (dashed) subpacketization ratios for various $t$ values. Both ratios increase with $t$, indicating a diminishing PT reduction over JCM.
  • Figure 2: Illustration of subfile and packet types. Packets of the same color (i.e., belonging to the same coupled group) have identical sizes.
  • Figure 3: Comparison of global FS vectors for $t=8$.

Theorems & Definitions (13)

  • Theorem 1
  • Remark 1
  • Example 1: File Splitting, $t=2$
  • Remark 2: Infeasibility of Homogeneous Subpacketization
  • Lemma 1
  • Remark 3: Subfile Count Identity
  • Lemma 2
  • Claim 1
  • Claim 2
  • Claim 3
  • ...and 3 more