A New Construction Structure on Coded Caching with Linear Subpacketization: Non-Half-Sum Latin Rectangle

2026-01-15

AI Summary

This work addresses the challenge in coded caching of simultaneously achieving low subpacketization and low transmission load. To this end, the authors propose a novel combinatorial structure—Non-Half-Sum Latin Rectangles (NHSLRs)—constructed via combinatorial design theory and integrated with coded multicast and local caching mechanisms, thereby extending the design framework for linear subpacketization schemes. For the first time, this approach generalizes the subpacketization level from the fixed value \( F = K \) to a broader linear scale \( F = \mathcal{O}(K) \), maintaining linear complexity with respect to the number of users while significantly reducing transmission load. The resulting scheme outperforms existing linear approaches and approaches the efficiency of certain exponential-subpacketization schemes.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

Coded caching is recognized as an effective method for alleviating network congestion during peak periods by leveraging local caching and coded multicasting gains. The key challenge in designing coded caching schemes lies in simultaneously achieving low subpacketization and low transmission load. Most existing schemes require exponential or polynomial subpacketization levels, while some linear subpacketization schemes often result in excessive transmission load. Recently, Cheng et al. proposed a construction framework for linear coded caching schemes called Non-Half-Sum Disjoint Packing (NHSDP), where the subpacketization equals the number of users $K$. This paper introduces a novel combinatorial structure, termed the Non-Half-Sum Latin Rectangle (NHSLR), which extends the framework of linear coded caching schemes from $F=K$ (i.e., the construction via NHSDP) to a broader scenario with $F=\mathcal{O}(K)$. By constructing NHSLR, we have obtained a new class of coded caching schemes that achieves linearly scalable subpacketization, while further reducing the transmission load compared with the NHSDP scheme. Theoretical and numerical analyses demonstrate that the proposed schemes not only achieves lower transmission load than existing linear subpacketization schemes but also approaches the performance of certain exponential subpacketization schemes.

Problem

• coded caching
• subpacketization
• transmission load
• linear subpacketization

Innovation

• coded caching
• linear subpacketization
• Non-Half-Sum Latin Rectangle
• transmission load reduction
• combinatorial design