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 $(K, KM/N)=(2q+1, 2r)$ 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.

• The paper introduces a heterogeneous packet type framework that reduces subpacketization in D2D coded caching while preserving the optimal communication rate.
• The methodology jointly optimizes user grouping and coordinated transmitter selection with type-dependent packet sizing to lower further-splitting factors.
• The approach enables practical deployment for odd-numbered user groups by eliminating redundant subfile types and simplifying file partitioning.

Heterogeneous File Splitting for Subpacketization Reduction in D2D Coded Caching

Introduction

The paper "Reducing Subpacketization in Device-to-Device Coded Caching via Heterogeneous File Splitting" (2603.29945) introduces a new design paradigm for device-to-device (D2D) coded caching, which aims to minimize file subpacketization while preserving the optimal communication rate. The key innovation is a heterogeneous packet type (PT) framework that allows file packets to have type-dependent sizes, in contrast to prior PT frameworks restricted to homogeneous subpacketization. This facilitates finer granularity in memory allocation and flexible user grouping, enabling packet reduction strategies that were not previously attainable, especially in the regime of odd user populations.

Background: Subpacketization and Prior Art

D2D coded caching schemes such as the Ji-Caire-Molisch (JCM) design require splitting each file into an exponential number of subpackets. While JCM is rate-optimal, its subpacketization level $F_\mathrm{JCM} = t\binom{K}{t}$ (for $K$ users and parameter $t$) is prohibitively high for practical systems. Several alternative constructions—e.g., based on projective geometry, placement delivery arrays (PDAs), or combinatorial designs—provide substantially reduced subpacketization but at the cost of increased communication rate and lack of generality.

Previous work [Zhang et al., (Zhang et al., 12 Feb 2026)] established a PT-based framework that systematically explored rate-optimal subpacketization reduction by leveraging user grouping and type-based subfile and packet classification. However, its applicability was limited due to the requirement of homogeneity in packet size, preventing further optimization under unequally sized user groups and odd $K$ values.

Heterogeneous PT Framework

The paper extends the PT framework to the heterogeneous setting, where packet sizes can vary according to type and are jointly designed with user grouping and transmitter assignment. This increased flexibility enables new D2D coded caching schemes for parameters of the form $(K, t) = (2q+1, 2r)$ with $q, r \in \mathbb{N}_+$, achieving a constant-factor reduction in subpacketization compared to JCM—without any increase in communication rate.

Core Concepts

• Refined Packet Types and Coupled Groups: Each subfile type is further partitioned into subtypes, grouped so that packets within a group have uniform size, but groups themselves can have heterogeneous sizes.
• Coordinated Transmitter Selection: Transmitters for each coupled group are chosen independently, allowing vector least common multiple (LCM) coordination of local further-splitting (FS) factors to achieve globally minimal subpacketization.

Reduction in Subpacketization: Numerical Results

The proposed heterogeneous PT construction, for $(K, t) = (2q+1, 2r)$, employs unequal grouping $(q+1, q)$ and coordinated transmitter selection. The subpacketization level is

$F_\mathrm{PT} = \sum_{k=1}^{t+1} \alpha_k f_k$

where $\alpha_k$ is the (globally coordinated) further-splitting factor and $K$0 is the count of subfiles of the $K$1th type. This structure enables two sources of subpacketization savings:

1. Subfile exclusion: Certain subfile types (e.g., the first) are entirely eliminated from both placement and delivery.
2. Reduced FS factors: Many subfile types are split into fewer than $K$2 packets.

The relative reduction is illustrated in (Figure 1), which displays actual and asymptotic subpacketization ratios as a function of $K$3. For fixed $K$4, the ratio $K$5 approaches $K$6 as $K$7 grows, signifying a constant-factor improvement for practical system sizes.

Figure 2: Actual (solid) and asymptotic (dashed) subpacketization ratios for various $K$8 values. Both ratios increase with $K$9, indicating a diminishing PT reduction over JCM.

Mechanism: Subfile and Packet Type Structure

The flexibility of type-dependent packet sizing is illustrated by the subfile/packet layout. Consider the case $t$0; each subfile type is bifurcated into two subtypes, each assigned to a different coupled group (Figure 3). Packet coloring in (Figure 3) visualizes the assignment to coupled groups and consequent packet-size distinctions.

Figure 4: Illustration of subfile and packet types. Packets of the same color (i.e., belonging to the same coupled group) have identical sizes.

User grouping is orchestration-dependent; in the proposed scheme, a $t$1 split enables satisfaction of the memory constraints with heterogeneity, whereas under homogeneous constraints, such reductions are structurally precluded.

Global FS Vector Design and Subpacketization Analysis

A central technical device is the construction of the global FS vector, which prescribes the number of splits for each subfile type to ensure all users meet their memory constraints. For the case $t$2, (Figure 5) contrasts the global FS vectors for the two intermediate coupled groups with the resulting aggregate global FS vector, which is always pointwise less than or equal to the JCM FS vector.

Figure 1: Comparison of global FS vectors for $t$3.

The design ensures that for a large subset of subfile types, the further splitting factor is strictly less than $t$4, plateauing at $t$5 only for higher-index types. This gives rise to the subfile-type-specific packet splitting structure—a critical enabler for the asymptotic reduction in total subpacketization.

Implications and Theoretical Advances

The construction fills the gap left by homogeneous PT designs for rate-optimal D2D caching with odd $t$6, fully characterizing the minimal subpacketization attainable in this challenging setting. Contradicting prior limitations, the work demonstrates that heterogeneous subpacketization not only expands the class of feasible user groupings but is essential for further subpacketization reduction.

Practical implications include the ability to deploy rate-optimal D2D coded caching in larger systems where packetization overhead previously rendered such schemes infeasible. The explicit characterization of asymptotic reduction offers clear guidelines for system designers to select appropriate packetization granularity.

Theoretically, the framework underscores the necessity of relaxing symmetry/homogeneity constraints to realize unexplored subpacketization-rate trade-offs. The methodology—jointly optimizing user grouping, transmitter selection, and packet sizing—suggests a broader design principle applicable to other coded distributed systems.

Future Directions

Open problems raised by this work include extending heterogeneous PT designs to additional $t$7 regimes (especially for odd $t$8), exploring more general user-group assignments, and quantifying trade-offs under practical constraints (file size, limited field sizes, non-uniform demand). Moreover, optimizing for further subpacketization reduction beyond the rate-optimal regime (i.e., permitting slight rate loss for exponential reductions) is a compelling direction.

Conclusion

This paper systematically shows that allowing heterogeneous packet sizes in type-based D2D coded caching unlocks significant reductions in subpacketization level, achievable with optimal communication rate and feasible user groupings otherwise unattainable under previous frameworks. The approach provides a rigorous foundation and concrete construction for practical deployment, and opens new avenues in the investigation of the rate-subpacketization trade-off in coded distributed caching systems.