标题： 非线性函数计算广播 显示英文标题

标题： Non-Linear Function Computation Broadcast

摘要： 这项工作解决了包含一个主节点的$K$用户计算广播问题，该主节点拥有所有数据集和用户对于有限域上的函数需求的一般类，包括线性和非线性函数。主节点发送一个广播消息，以使每个$K$个分布式用户能够以渐近无损的方式利用用户的辅助信息计算其所需函数。我们推导了允许用户通过捕捉计算结构和可用辅助信息来计算其所需函数的最优$K$用户计算广播速率的界限。我们的可达方案涉及设计一种基于图的新编码模型，通过利用数据集、用户需求和每个用户的辅助信息之间的结构依赖关系，构建一个满足每个用户需求的广播消息，借鉴Körner的特征图框架。反证部分利用了$K$个用户拥有的需求和辅助信息结构，得出广播速率的紧致下界。通过示例，我们展示了我们的方案在通信速率方面优于现有技术。 显示英文摘要

摘要： This work addresses the $K$-user computation broadcast problem consisting of a master node, that holds all datasets and users for a general class of function demands, including linear and non-linear functions, over finite fields. The master node sends a broadcast message to enable each of $K$ distributed users to compute its demanded function in an asymptotically lossless manner with user's side information. We derive bounds on the optimal $K$-user computation broadcast rate that allows the users to compute their demanded functions by capturing the structures of the computations and available side information. Our achievability scheme involves the design of a novel graph-based coding model to build a broadcast message to meet each user's demand, by leveraging the structural dependencies among the datasets, the user demands, and the side information of each user, drawing on K{\"o}rner's characteristic graph framework. The converse uses the structures of the demands and the side information available at $K$ users to yield a tight lower bound on the broadcast rate. With the help of examples, we demonstrate our scheme achieves a better communication rate than the existing state of the art.