Coded Caching With Full Heterogeneity: Exact Capacity of the Two-User/Two-File Case
Coded Caching With Full Heterogeneity: Exact Capacity of the Two-User/Two-File Case
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DOI：
10.1109/tit.2022.3181411
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发表时间：
2022-11
影响因子：
2.5
通讯作者：
Chih-Hua Chang;B. Peleato;Chih-Chun Wang
中科院分区：
文献类型：
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作者：
Chih-Hua Chang;B. Peleato;Chih-Chun Wang
编码高速缓存文献中最常用的设置包括以下四个元素：(I)均匀文件大小，(Ii)均匀高速缓存大小，(Iii)与用户无关的均匀文件流行度(即，所有用户共享相同的文件偏好)，以及(Iv)最坏情况速率分析。虽然最近的结果放宽了其中一些假设，但仍然需要更深入地了解完全异构性设置，因为传统的缓存方案对文件/缓存大小几乎没有什么假设，并且几乎总是允许每个用户通过个性化的文件请求预测来拥有他/她自己的文件偏好。采用微观方法，刻画了最小2用户/2文件($N=K=2$)问题在同时考虑(I)不同大小的文件、(Ii)不同大小的高速缓存、(Iii)与用户相关的文件流行度和(Iv)平均速率分析的最一般设置下的精确容量。完全解决$N=K=2$的情况可以进一步了解针对任意$N$和$K$的完全异构性的最优编码缓存的性能和复杂性。
The most commonly used setting in the coded caching literature consists of the following four elements: (i) homogeneous file sizes, (ii) homogeneous cache sizes, (iii) user-independent homogeneous file popularity (i.e., all users share the same file preference), and (iv) worst-case rate analysis. While recent results have relaxed some of these assumptions, deeper understanding of the full heterogeneity setting is still much needed since traditional caching schemes place little assumptions on file/cache sizes and almost always allow each user to have his/her own file preference through individualized file request prediction. Taking a microscopic approach, this paper characterizes the exact capacity of the smallest 2-user/2-file ( $N=K=2$ ) problem but under the most general setting that simultaneously allows for (i) heterogeneous files sizes, (ii) heterogeneous cache sizes, (iii) user-dependent file popularity, and (iv) average-rate analysis. Solving completely the case of $N=K=2$ could shed further insights on the performance and complexity of optimal coded caching with full heterogeneity for arbitrary $N$ and $K$ .