In device-to-device (D2D) coded caching problems, it is possible that not all users will make file requests in the delivery phase. Hence, we propose a new D2D centralized coded caching problem, named the 3-user D2D coded caching with two random requesters and one sender (2RR1S), where in the delivery phase, any two of the three users will make file requests, and the user that does not make any file request is the designated sender. We find the optimal caching and delivery scheme, denoted as the 2RRIS scheme, for any number of files N by proving matching converse and achievability results. It is shown that coded cache placement is needed to achieve the optimal performance. Furthermore, the optimal rate-memory tradeoff has a uniform expression for N>=4 and different expressions for N=2 and 3. To examine the usefulness of the proposed model and scheme, we adapt the 2RR1S scheme to two scenarios. The first one is the 3-user D2D coded caching model proposed by Ji et al. By characterizing the optimal rate-memory tradeoff for the 3-user D2D coded caching when N=2, which was previously unknown, we show that the adapted 2RR1S scheme is in fact optimal for the 3-user D2D coded caching problem when N=2 and the cache size is medium. The benefit comes from coded cache placement which is missing from existing D2D coded caching schemes. The second scenario is where in the delivery phase, each user makes a file request randomly and independently with the same probability p. We call this model the request-random D2D coded caching problem. Adapting the 2RR1S scheme to this scenario, we show the superiority of our adapted scheme over other existing D2D coded caching schemes for medium to large cache size.

翻译：在设备到设备（D2D）编码缓存问题中，交付阶段可能出现并非所有用户都会发出文件请求的情况。为此，我们提出了一种新的D2D集中式编码缓存问题，即"三用户两随机请求者一发送者"（2RR1S）模型：在交付阶段，三个用户中的任意两个将发出文件请求，而未发出任何文件请求的用户则被指定为发送者。通过证明匹配的逆命题与可达性结果，我们针对任意文件数量N，找到了最优缓存与交付方案（记为2RR1S方案）。研究表明，为达到最优性能，必须采用编码缓存放置策略。此外，最优速率-内存权衡关系在N≥4时具有统一表达式，而在N=2和3时则呈现不同形式。为验证所提模型与方案的实用性，我们将2RR1S方案适配至两个场景。第一个场景是Ji等人提出的三用户D2D编码缓存模型。通过刻画此前未知的N=2时三用户D2D编码缓存的最优速率-内存权衡，我们证明适配后的2RR1S方案在N=2且缓存大小适中时，对该三用户D2D编码缓存问题具有最优性——其优势源于现有D2D编码缓存方案所缺失的编码缓存放置策略。第二个场景中，交付阶段每个用户以相同概率p随机且独立地发出文件请求，我们将此模型称为"请求随机型D2D编码缓存问题"。将2RR1S方案适配至该场景后，我们证明：在中等到较大缓存容量区间内，本适配方案优于其他现有D2D编码缓存方案。