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Optimization-based Decentralized Coded Caching for Files and Caches with Arbitrary Sizes
IEEE Transactions on Communications ( IF 7.2 ) Pub Date : 2020-04-01 , DOI: 10.1109/tcomm.2019.2963031
Qi Wang , Ying Cui , Sian Jin , Junni Zou , Chenglin Li , Hongkai Xiong

Existing decentralized coded caching solutions cannot guarantee small loads in the general scenario with arbitrary file sizes and cache sizes. In this paper, we propose an optimization framework for decentralized coded caching in the general scenario to minimize the worst-case load and average load (under an arbitrary file popularity), respectively. Specifically, we first propose a class of decentralized coded caching schemes for the general scenario, which are specified by a general caching parameter and include several known schemes as special cases. Then, we optimize the caching parameter to minimize the worst-case load and average load, respectively. Each of the two optimization problems is a challenging nonconvex problem with a nondifferentiable objective function. For each optimization problem, we develop an iterative algorithm to obtain a stationary point using techniques for solving Complementary Geometric Programming (GP). We also obtain a low-complexity approximate solution by solving an approximate problem with a differentiable objective function which is an upper bound on the original nondifferentiable one, and characterize the performance loss caused by the approximation. Finally, we present two information-theoretic converse bounds on the worst-case load and average load (under an arbitrary file popularity) in the general scenario, respectively. To the best of our knowledge, this is the first work that provides optimization-based decentralized coded caching schemes and information-theoretic converse bounds for the general scenario.

中文翻译:

用于任意大小的文件和缓存的基于优化的分散编码缓存

现有的去中心化编码缓存解决方案无法保证在任意文件大小和缓存大小的一般场景下小负载。在本文中,我们提出了一种在一般情况下分散编码缓存的优化框架,以分别最小化最坏情况的负载和平均负载(在任意文件流行度下)。具体来说,我们首先针对通用场景提出了一类去中心化编码缓存方案,这些方案由通用缓存参数指定,包括几种已知方案作为特殊情况。然后,我们优化缓存参数以分别最小化最坏情况负载和平均负载。这两个优化问题中的每一个都是具有不可微目标函数的具有挑战性的非凸问题。对于每个优化问题,我们开发了一种迭代算法来使用求解互补几何规划 (GP) 的技术来获得驻点。我们还通过求解具有可微目标函数的近似问题来获得低复杂度的近似解,该可微目标函数是原始不可微函数的上限,并表征由近似引起的性能损失。最后,我们分别给出了一般情况下最坏情况负载和平均负载(在任意文件流行度下)的两个信息论逆界。据我们所知,这是第一个为一般场景提供基于优化的分散编码缓存方案和信息论逆界的工作。我们还通过求解具有可微目标函数的近似问题来获得低复杂度的近似解,该可微目标函数是原始不可微函数的上限,并表征由近似引起的性能损失。最后,我们分别给出了一般情况下最坏情况负载和平均负载(在任意文件流行度下)的两个信息论逆界。据我们所知,这是第一个为一般场景提供基于优化的分散编码缓存方案和信息论逆界的工作。我们还通过求解具有可微目标函数的近似问题来获得低复杂度的近似解,该可微目标函数是原始不可微函数的上限,并表征由近似引起的性能损失。最后,我们分别给出了一般情况下最坏情况负载和平均负载(在任意文件流行度下)的两个信息论逆界。据我们所知,这是第一个为一般场景提供基于优化的分散编码缓存方案和信息论逆界的工作。并表征由近似引起的性能损失。最后,我们分别给出了一般情况下最坏情况负载和平均负载(在任意文件流行度下)的两个信息论逆界。据我们所知,这是第一个为一般场景提供基于优化的分散编码缓存方案和信息论逆界的工作。并表征由近似引起的性能损失。最后,我们分别给出了一般情况下最坏情况负载和平均负载(在任意文件流行度下)的两个信息论逆界。据我们所知,这是第一个为一般场景提供基于优化的分散编码缓存方案和信息论逆界的工作。
更新日期:2020-04-01
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