Matroidal Entropy Functions: A Quartet of Theories of Information, Matroid, Design, and Coding
科研大讨论系列报告
报告题目(Title)：Matroidal Entropy Functions: A Quartet of Theories of Information, Matroid, Design, and Coding
报告人(Speaker)：陈琦 副教授(西安电子科技大学)
地点(Place)：腾讯会议ID: 901 631 834
时间(Time)：2023年5月19日(周五), 10：50-11：40
邀请人(Inviter)：郭来刚
报告摘要
A matroidal entropy function is an entropy function in the form log v · r_M , where v is an integer exceeding one and r_M is the rank function of a matroid M. For a matroid M, the characterization of matroidal entropy function induced by M is to determine its probabilistic-characteristic set X_M, i.e., the set of integers v such that log v · r_M is entropic. To characterize matroidal entropy functions, we introduce variable strength orthogonal arrays(VOA), which can be considered as special cases of classic combinatorial structure orthogonal arrays(OA). We prove that whether log v · r_M is entropic depends on whether a VOA(M, v) is constructible. Leveraging the correspondences between matroidal entropy functions and VOAs, we characterize the matroidal entropy functions induced by matroids obtained from matroid operations such as deletion, contraction, minor, series and parallel connection and 2-sum. Utilizing these results, we characterize two classes of matroidal entropy functions, i.e., those induced by regular matroids and matroids with the same p-characteristic set as uniform matroid U_{2,4}. As the support of characterizing random vector of a matroidal entropy function, i.e., the set of rows of the corresponding VOA is equivalent to the code book of an almost affine code, they can be applied to solve coding problems in secret sharing, network coding, index coding and locally repairable code.
主讲人简介
陈琦，西安电子科技大学副教授。2014年毕业于香港中文大学，获博士学位，之后留校从事博士后研究至2017年。2015年9月-2016年1月，他同时也是美国Drexel大学博士后。他于2018年加入西安电子科技大学空天地一体化国家重点实验室以及通信工程学院。他是中国电子学会2018年信息论学术年会最佳报告奖获得者。他的研究兴趣为信息论及其相关领域，特别是信息不等式及熵区域的刻画问题。
