This paper presents a novel achievable scheme for coded caching systems with $N$ files and $K$ users, specifically when $N \leq K$. This new scheme employs linear coding both during the placement phase - where cache contents are linear combinations of files from the library - and the delivery phase. The multi-step delivery phase enables users to decode the cached coded content and eliminate interference effectively. In the small memory regime, the proposed scheme outperforms existing methods, particularly when $K$ and $N$ values are similar, it maintains manageable sub-packetization levels, and operates over a finite field of size $3$ regardless of the system parameters.

翻译：本文提出了一种适用于具有$N$个文件和$K$个用户的编码缓存系统的新颖可实现方案，特别针对$N \leq K$的场景。该方案在放置阶段（缓存内容为文件库中文件的线性组合）和传输阶段均采用线性编码技术。多步骤的传输阶段使用户能够有效解码缓存的编码内容并消除干扰。在小内存区域，所提方案性能优于现有方法，尤其在$K$与$N$值相近时，该方案能保持可控的子分组化水平，且无论系统参数如何变化，其运算始终在大小为$3$的有限域上进行。