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.

翻译：编码缓存被公认为一种通过利用本地缓存和编码多播增益来缓解高峰时段网络拥塞的有效方法。设计编码缓存方案的核心挑战在于同时实现低分组化水平和低传输负载。现有方案大多需要指数级或多项式级的分组化水平，而一些线性分组化方案往往导致过高的传输负载。最近，Cheng等人提出了一种称为非半和不相交填充（NHSDP）的线性编码缓存方案构造框架，其分组化数等于用户数$K$。本文引入了一种新颖的组合结构，称为非半和拉丁矩形（NHSLR），它将线性编码缓存方案的框架从$F=K$（即通过NHSDP的构造）扩展到$F=\mathcal{O}(K)$的更广泛场景。通过构造NHSLR，我们获得了一类新的编码缓存方案，该方案实现了线性可扩展的分组化，同时与NHSDP方案相比进一步降低了传输负载。理论和数值分析表明，所提出的方案不仅实现了比现有线性分组化方案更低的传输负载，而且逼近了某些指数分组化方案的性能。