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.

翻译：数据包类型（PT）框架~\cite{zhang2026taming}为设计设备到设备（D2D）编码缓存方案提供了一种系统且严谨的方法，该方案在保持最优通信速率的同时实现了 \sbp 的降低。然而，现有PT设计完全依赖于同构 \sbp，即所有数据包无论其类型如何都具有相同大小，这种限制在特定参数区间内削弱了可实现的 \sbp 降低效果。本文在精细化类型分类基础上，将PT框架扩展至\emph{异构} \sbp，允许不同类型的数据包大小存在差异。通过联合优化数据包大小、用户分组及多播发射端选择，在保持最优速率的同时最小化整体 \sbp 水平。基于异构PT框架，我们针对 $(K, KM/N)=(2q+1, 2r)$（其中 $q,r \in \mathbb{N}_+$，$K,N$ 和 $M$ 分别表示用户数、文件数和缓存内存大小）构建了一类新型D2D编码缓存方案。与Ji-Caire-Molisch (JCM) 编码方案~\cite{ji2016fundamental}相比，本文方案实现了 \sbp 的常数因子降低，并补充了现有PT设计无法适用于该参数区间的不足。