For a network with one sender, $n$ receivers (users) and $m$ possiblemessages (files), caching side information at the users allows to satisfyarbitrary simultaneous demands by sending a common (multicast) coded message.In the worst-case demand setting, explicit deterministic and random cachingstrategies and explicit linear coding schemes have been shown to be orderoptimal. In this work, we consider the same scenario where the user demands arerandom i.i.d., according to a Zipf popularity distribution. In this case, wepose the problem in terms of the minimum average number of equivalent messagetransmissions. We present a novel decentralized random caching placement and acoded delivery scheme which are shown to achieve order-optimal performance. Asa matter of fact, this is the first order-optimal result for the caching andcoded multicasting problem in the case of random demands.
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机译：对于具有一个发送者，$ n $个接收者（用户）和$ m $个可能的消息（文件）的网络，在用户处缓存辅助信息可以通过发送公共（多播）编码消息来满足任意同时需求。设置，显式确定性和随机缓存策略以及显式线性编码方案已被证明是最优的。在这项工作中，根据Zipf流行度分布，我们考虑了用户需求即i.d.是随机的同一场景。在这种情况下，我们以等效消息传输的最小平均数来解决问题。我们提出了一种新颖的分散式随机缓存放置和编码的交付方案，它们被证明可以实现最佳的性能。实际上，这是在随机需求情况下缓存和编码的多播问题的一阶最佳结果。
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