Abstract
Coded caching is an effective way to reduce the network load by exploiting multicast opportunities between distinct users. In [1], a hierarchical network with two layers of caches is investigated. It is shown that the achievable rate of each layer is bounded from the corresponding converse bound within a constant multiplicative and additive gap, and can be achieved simultaneously. In this regard (with the additive gap), there is no tension between the rates of the two layers [1]. This paper takes a further investigation on this topic and shows that there is tension using a toy model. With the toy model, we derive new lower bounds and propose novel achievable schemes, which are shown to be optimal in an average sense. The involved techniques in both the lower bounds and achievable schemes could be of interest for future studies on coded caching in hierarchical networks.
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