This work studies a well-known shared-cache coded caching scenario where each cache can serve an arbitrary number of users, analyzing the case where there is some knowledge about such number of users (i.e., the topology) during the content placement phase. Under the assumption of regular placement and a cumulative cache size that can be optimized across the different caches, we derive the fundamental limits of performance by introducing a novel cache-size optimization and placement scheme and a novel information-theoretic converse. The converse employs new index coding techniques to bypass traditional uniformity requirements, thus finely capturing the heterogeneity of the problem, and it provides a new approach to handle asymmetric settings. The new fundamental limits reveal that heterogeneous topologies can in fact outperform their homogeneous counterparts where each cache is associated to an equal number of users. These results are extended to capture the scenario of topological uncertainty where the perceived/estimated topology does not match the true network topology. This scenario is further elevated to the stochastic setting where the user-to-cache association is random and unknown, and it is shown that the proposed scheme is robust to such noisy or inexact knowledge on the topology.

翻译：本文研究了一种广为人知的共享缓存编码缓存场景，其中每个缓存可服务任意数量的用户，并分析了在内容放置阶段对该用户数量（即拓扑结构）具有部分先验知识的情形。在规则放置假设下，且各缓存的总容量可优化调整，我们通过引入一种新颖的缓存容量优化与放置方案以及一种信息论逆界，推导了性能的基础极限。该逆界采用新的索引编码技术以突破传统的均匀性要求，从而精确刻画问题的异构性，并为处理非对称场景提供了新方法。这些基础极限揭示：异构拓扑的实际性能可优于每个缓存关联等量用户的同构拓扑。进一步将结果扩展至拓扑不确定性场景，即感知/估计的拓扑与真实网络拓扑不匹配的情形。该场景被提升至随机设定，其中用户与缓存的关联关系随机且未知，实验表明所提方案对此类拓扑信息的噪声或不精确性具有鲁棒性。