Taming Subpacketization without Sacrificing Communication: A Packet Type-based Framework for D2D Coded Caching

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.

💡 Research Summary

This paper tackles one of the most pressing practical obstacles in device‑to‑device (D2D) coded caching: the explosive growth of subpacketization required to achieve the optimal communication rate. The classical Ji‑Caire‑Molisch (JCM) scheme, which extends the Maddah‑Ali–Niesen (MAN) placement to a D2D setting, attains the optimal rate (R_{\text{JCM}} = K(1-\mu)t) (with (t = K\mu)) but forces each subfile to be split into (t) packets, leading to a subpacketization level (F_{\text{JCM}} = t\binom{K}{t}). This “double‑layer” symmetric design becomes infeasible for realistic file sizes.

The authors introduce a Packet Type (PT) framework that deliberately injects asymmetry through user grouping and then exploits this asymmetry across three stages: file splitting, cache placement, and multicast delivery. The key ideas are:

1. User Grouping & Asymmetric Splitting – Users are partitioned into groups; files are split into subfiles whose “type’’ is defined by the set of groups that store them. This breaks the global symmetry of the JCM placement.

2. Type‑Based Classification – Both subfiles and multicast groups are categorized into a finite set of “packet types”. Identical types share the same structural properties, allowing systematic analysis.

3. Two Reduction Mechanisms

   • Subfile Saving Gain – Certain subfile types become redundant once groups and transmitters are fixed. By discarding these types, the total number of subfiles drops dramatically compared with the (\binom{K}{t}) baseline.
   • Further Splitting Saving Gain – In JCM every subfile is uniformly split into (t) packets. PT observes that, depending on the chosen transmitter set for a multicast group, a subfile may need far fewer packets (a “splitting factor” (t’\le t)). A vector least‑common‑multiple (LCM) operation synchronizes the splitting requirements across all types, yielding globally consistent, often much smaller, packet‑per‑subfile ratios.

The overall subpacketization becomes
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