Finite-length analysis is critical for bringing coded caching closer to practical deployment. In this work, we study the design of communication rate-optimal device-to-device (D2D) coded caching schemes with minimal subpacketization levels, a key bottleneck in finite-length settings. We present a novel \tit{packet type-based} (PT) design framework that (i) strategically introduces \tit{asymmetry} into file splitting through user grouping, and (ii) systematically exploits such asymmetry in both cache placement and multicast delivery to create subpacketization reduction opportunities. In particular, the induced asymmetry gives rise to two fundamental forms of subpacketization reduction gains: the \emph{subfile saving gain}, achieved by eliminating certain types of subfiles through careful user grouping and transmitter selection, and the \emph{further splitting saving gain}, attained by reducing the splitting granularity for the remaining subfiles. The combined effect of these two reduction gains yields an overall subpacketization improvement over the original Ji-Caire-Molisch (JCM) caching scheme~\cite{ji2016fundamental}, as well as various state-of-the-art schemes, while preserving optimal communication rates. Under the PT framework, we formulate the caching scheme design as an integer linear program (ILP), where each feasible solution corresponds to a valid rate-optimal D2D coded caching scheme with potentially reduced subpacketization relative to the JCM baseline.

翻译：有限长度分析对于推动编码缓存走向实际部署至关重要。本文研究具有最小子分组化层级的通信速率最优设备到设备（D2D）编码缓存方案设计，子分组化是有限长度设置中的关键瓶颈。我们提出了一种新颖的**基于分组类型**的设计框架，该框架（i）通过用户分组策略性地在文件分割中引入**非对称性**，以及（ii）在缓存放置和多播传输中系统性地利用这种非对称性，以创造降低子分组化的机会。具体而言，所引入的非对称性产生了两种基本形式的子分组化降低增益：**子文件节省增益**，通过精心的用户分组和发送器选择消除特定类型的子文件实现；以及**进一步分割节省增益**，通过减少剩余子文件的分割粒度实现。这两种降低增益的联合效应，相对于原始的Ji-Caire-Molisch（JCM）缓存方案以及各种先进方案，在保持最优通信速率的同时，实现了整体子分组化的改进。在PT框架下，我们将缓存方案设计表述为一个整数线性规划问题，其中每个可行解对应一个有效的速率最优D2D编码缓存方案，且其子分组化相对于JCM基线方案可能降低。