This paper studies the caching system of multiple cache-enabled users with random demands. Under nonuniform file popularity, we thoroughly characterize the optimal uncoded cache placement structure for the coded caching scheme (CCS). Formulating the cache placement as an optimization problem to minimize the average delivery rate, we identify the file group structure in the optimal solution. We show that, regardless of the file popularity distribution, there are at most three file groups in the optimal cache placement, where files within a group have the same cache placement. We further characterize the complete structure of the optimal cache placement and obtain the closed-form solution in each of the three file group structures. A simple algorithm is developed to obtain the final optimal cache placement by comparing a set of candidate closed-form solutions computed in parallel. We provide insight into the file groups formed by the optimal cache placement. The optimal placement solution also indicates that coding between file groups may be explored during delivery, in contrast to the existing suboptimal file grouping schemes. Using the file group structure in the optimal cache placement for the CCS, we propose a new information-theoretic converse bound for coded caching that is tighter than the existing best one. Moreover, we characterize the file subpacketization in the CCS with the optimal cache placement solution and show that the maximum subpacketization level in the worst case scales as O(2K/K−−√){\mathcal{ O}}(2^{K}/\sqrt {K}) for KK users.

中文翻译：

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非均匀需求编码缓存优化缓存布局的基本结构


本文研究了具有随机需求的多个启用缓存的用户的缓存系统。在非均匀文件流行度下，我们彻底描述了编码缓存方案（CCS）的最佳未编码缓存放置结构。将缓存放置制定为优化问题，以最小化平均传输率，我们确定最佳解决方案中的文件组结构。我们表明，无论文件流行度分布如何，最佳缓存放置中最多存在三个文件组，其中组内的文件具有相同的缓存放置。我们进一步描述了最佳缓存放置的完整结构，并在三个文件组结构中的每一个中获得了封闭形式的解决方案。开发了一种简单的算法，通过比较一组并行计算的候选封闭式解决方案来获得最终的最佳缓存放置。我们深入了解由最佳缓存放置形成的文件组。与现有的次优文件分组方案相比，最佳放置解决方案还表明可以在交付期间探索文件组之间的编码。使用 CCS 最佳缓存放置中的文件组结构，我们提出了一种新的编码缓存信息论逆界，该界比现有的最佳界更严格。此外，我们使用最佳缓存放置解决方案来表征 CCS 中的文件子包化，并表明最坏情况下的最大子包化级别为 O(2K/K−−√){\mathcal{ O}}(2^{K }/\sqrt {K}) 对于 KK 用户。