We study a $K$-user coded-caching broadcast problem in a joint source-channel coding framework. The transmitter observes a database of files that are being generated at a certain rate per channel use, and each user has a cache, which can store a fixed fraction of the generated symbols. In the delivery phase, the transmitter broadcasts a message so that the users can decode their desired files using the received signal and their cache content. The communication between the transmitter and the receivers happens over a (deterministic) \textit{time-varying} erasure broadcast channel, and the channel state information is only available to the users. We characterize the maximum achievable source rate for the $2$-user and the degraded $K$-user problems. We provide an upper bound for any caching strategy's achievable source rates. Finally, we present a linear programming formulation to show that the upper bound is not a sharp characterization. Closing the gap between the achievable rate and the optimum rate remains open.

翻译：我们研究了一个联合信源信道编码框架下的$K$用户编码缓存广播问题。发射机观测到每信道使用次数以特定速率生成的数据库文件，每个用户拥有一个缓存，可存储固定比例生成的符号。在传输阶段，发射机广播消息，使得用户能够利用接收信号及其缓存内容解码所需的文件。发射机与接收机之间的通信通过（确定性的）时变擦除广播信道进行，且信道状态信息仅对用户可用。我们刻画了$2$用户和退化$K$用户问题的最大可达信源速率。针对任意缓存策略的可达信源速率，我们给出了一个上界。最后，我们通过线性规划公式证明该上界并非紧确刻画。缩小可达速率与最优速率之间的差距仍有待研究。