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

TL;DR

The paper addresses finite-length D2D coded caching by introducing a packet type-based (PT) framework that reduces subpacketization without sacrificing the optimal rate $R_{\rm JCM}$. By leveraging user grouping and asymmetric multicast delivery, it identifies subfile saving and further splitting gains, and formalizes the design as an ILP to jointly optimize grouping and transmitter selection. It then constructs multiple rate-optimal PT schemes with order-wise or constant-factor reductions in subpacketization relative to the JCM baseline, and provides achievability proofs for three main theorems. The PT framework reveals a fundamental difference between D2D and shared-link caching: rate-optimal D2D schemes need not be perfectly symmetric, enabling practical finite-length deployments. Overall, the work offers a unified, scalable method to achieve substantial subpacketization reductions while preserving optimal communication rates, advancing the practicality of D2D coded caching.

Abstract

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.

Figures (8)

• Figure 1: Necessity of further splitting of subfiles into packets. The left figure achieves a rate of $2/3$ with $F=3$ using only subfiles, whereas the right figure (JCM scheme) attains a smaller rate $1/2$ with $F=6$ by further splitting subfiles into packets.
• Figure 2: Actual subpacketization ratio (solid lines) versus the upper bound (dotted lines) for $\hbox{$\overline{t}$}\in \{2,4,6,8\}$.
• Figure 3: Workflow of the PT design framework.
• Figure 4: Illustration of subfile types.
• Figure 5: Illustration of subfile and multicast group types.

Theorems & Definitions (38)

• Remark 1: Optimal DoF Condition
• Definition 1: Symmetric Subpacketization,ji2016fundamental
• Definition 2: Symmetric Packet Exchange,ji2016fundamental
• Example 1: JCM Scheme,ji2016fundamental
• Definition 3: Asymmetric Subpacketization
• Definition 4: Asymmetric Packet Exchange
• Remark 2
• Example 2
• Remark 3
• Theorem 1: Order-Wise Reduction