Finite-length design is essential for making coded caching practical, as the optimal communication gains of existing schemes often require prohibitively large subpacketization. This paper studies rate-optimal device-to-device (D2D) coded caching with reduced subpacketization. We propose a packet type-based (PT) framework that exploits the geometric structure induced by user grouping. Under this structure, subfiles, packets, and multicast groups are classified into types, allowing the originally symmetric Ji-Caire-Molisch (JCM) design~\cite{ji2016fundamental} to be systematically relaxed without sacrificing the optimal D2D communication rate. The key feature of the PT framework is that subpacketization reduction is achieved through two complementary mechanisms: \emph{subfile saving}, by excluding redundant subfile types, and \emph{further-splitting saving}, by assigning type-dependent further-splitting factors to subfiles through transmitter selection. The type-dependent splitting factors are then coordinated across multicast group types to produce a globally consistent file-splitting structure. Based on this framework, we construct several classes of rate-optimal D2D coded caching schemes that strictly improve upon the JCM subpacketization. The proposed schemes achieve either order-wise reductions in the number of users or constant-factor reductions over broad memory regimes, while preserving the optimal rate. These results reveal a structural distinction between D2D and shared-link coded caching: unlike in the shared-link setting, full symmetric subpacketization is not necessary for rate-optimal D2D caching.

翻译：有限长度设计对于使编码缓存实用化至关重要，因为现有方案的最优通信增益往往要求过大的子分组化。本文研究了降低子分组化条件下速率最优的设备到设备（D2D）编码缓存。我们提出了一种基于分组类型（PT）的框架，该框架利用用户分组诱导的几何结构。在此结构下，子文件、分组和多播组被分类为不同类型，从而允许在牺牲最优D2D通信速率的前提下，系统性地松弛原始对称的Ji-Caire-Molisch（JCM）设计~\cite{ji2016fundamental}。PT框架的关键特征在于，通过两种互补机制实现子分组化缩减：《子文件节省》，即排除冗余的子文件类型，以及《进一步分割节省》，即通过发射机选择为子文件分配类型相关的进一步分割因子。然后，这些类型相关的分割因子在多播组类型之间协调，以产生全局一致的文件分割结构。基于该框架，我们构造了若干类速率最优的D2D编码缓存方案，这些方案严格改进了JCM的子分组化。所提出的方案在用户数量上实现了阶次缩减，或在宽泛的内存区域内实现了常数因子缩减，同时保持了最优速率。这些结果揭示了D2D与共享链路编码缓存之间的结构性区别：与共享链路设置不同，在速率最优的D2D缓存中，完全对称的子分组化并非必要。