互信息、拟阵与极值依赖
Mutual information, matroids and extremal dependencies
摘要：
本文证明了拟阵的秩函数可用“互信息函数”表示当且仅当拟阵是二元拟阵。所考虑的互信息函数是测量多址信道（MAC）的输入（二进制均匀）和输出之间的信息量的函数。此外，它示出的MAC的互信息功能是整数值是“等同于”的线性确定性MAC，在这个意义上说，它基本上包含在输出没有更多的信息比一些线性形式的输入。这些笔记把重点放在连接之间的互信息泛函和秩函数在拟阵理论，而不假设先验知识对这两个问题。第一部分介绍了互信息泛函，第二部分介绍了拟阵理论的基本概念，第三部分将这两个主题联系起来。它还表明，熵拟阵在文献中研究对应的MAC拟阵的具体情况。
英文摘要：
In this paper, it is shown that the rank function of a matroid can be represented by a "mutual information function" if and only if the matroid is binary. The mutual information function considered is the one measuring the amount of information between the inputs (binary uniform) and the output of a multiple access channel (MAC). Moreover, it is shown that a MAC whose mutual information function is integer valued is "equivalent" to a linear deterministic MAC, in the sense that it essentially contains at the output no more information than some linear forms of the inputs. These notes put emphasis on the connection between mutual information functionals and rank functions in matroid theory, without assuming prior knowledge on these two subjects. The first section introduces mutual information functionals, the second section introduces basic notions of matroid theory, and the third section connects these two subjects. It is also shown that entropic matroids studied in the literature correspond to specific cases of MAC matroids.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
