In the coded caching problem, as originally formulated by Maddah-Ali and Niesen, a server communicates via a noiseless shared broadcast link to multiple users that have local storage capability. In order for a user to decode its demanded file from the coded multicast transmission, the demands of all the users must be globally known, which may violate the privacy of the users. To overcome this privacy problem, Wan and Caire recently proposed several schemes that attain coded multicasting gain while simultaneously guarantee information theoretic privacy of the users’ demands. In Device-to-Device (D2D) networks, the demand privacy problem is further exacerbated by the fact that each user is also a transmitter, which appears to be needing the knowledge of the files demanded by the remaining users in order to form its coded multicast transmission. This paper shows how to solve this seemingly infeasible problem. The main contribution of this paper is the development of new achievable and converse bounds for D2D coded caching that are to within a constant factor of one another when privacy of the users’ demands must be guaranteed even in the presence of colluding users (i.e., when some users share cached contents and demanded file indices). First, a D2D private caching scheme is proposed, whose key feature is the addition of virtual users in the system in order to “hide” the demands of the real users. By comparing the achievable D2D private load with an existing converse bound for the shared-link model without demand privacy constraint, the proposed scheme is shown to be order optimal, except for the very low memory size regime with more files than users. Second, in order to shed light into the open parameter regime, a new achievable scheme and a new converse bound under the constraint of uncoded cache placement (i.e., when each user stores directly a subset of the bits of the library) are developed for the case of two users, and shown to be to within a constant factor of one another for all system parameters. Finally, the two-user converse bound is extended to any number of users by a cut-set type argument. With this new converse bound, the virtual users scheme is shown to be order optimal in all parameter regimes under the constraint of uncoded cache placement and user collusion.

中文翻译：

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论未编码缓存放置和用户共谋下设备到设备私有缓存的基本限制


在编码缓存问题中，正如 Maddah-Ali 和 Niesen 最初提出的那样，服务器通过无噪声共享广播链路与具有本地存储能力的多个用户进行通信。为了使用户从编码的多播传输中解码其所请求的文件，所有用户的需求必须是全局已知的，这可能侵犯用户的隐私。为了克服这个隐私问题，Wan 和 Caire 最近提出了几种方案，在获得编码多播增益的同时保证用户需求的信息论隐私。在设备到设备（D2D）网络中，需求隐私问题由于每个用户也是发射器这一事实而进一步加剧，发射器似乎需要了解其余用户所需求的文件以形成其编码多播传输。本文展示了如何解决这个看似不可行的问题。本文的主要贡献是为 D2D 编码缓存开发了新的可实现的逆边界，当即使存在共谋用户时，也必须保证用户需求的隐私（即，当一些用户共享缓存内容和所需的文件索引）。首先，提出了一种D2D私有缓存方案，其主要特点是在系统中添加虚拟用户以“隐藏”真实用户的需求。通过将可实现的 D2D 私有负载与没有需求隐私约束的共享链路模型的现有逆界进行比较，所提出的方案被证明是顺序最优的，除了文件数量多于用户的非常低的内存大小机制之外。 其次，为了阐明开放参数机制，在未编码缓存放置（即，当每个用户直接存储库位的子集时）的约束下，开发了一种新的可实现方案和新的逆边界，用于两个用户的情况，并且对于所有系统参数来说，都显示在彼此的常数因子之内。最后，两个用户的逆界通过割集类型参数扩展到任意数量的用户。通过这个新的逆界，虚拟用户方案在未编码的缓存放置和用户串通的约束下在所有参数机制中被证明是顺序最优的。