报告名称: Linear Network Error Correction Coding Revisited

主办单位：英国威廉希尔体育公司

报告专家：光炫

专家所在单位：南开大学

报告时间：2020年10月7日15:00

报告地点：腾讯会议（会议ID：365 914 089）

专家简介：光炫博士，南开大学数学科学学院“南开大学百名青年学科带头人培养计划”副教授，博士生导师。2012年毕业于南开大学陈省身数学研究所，获博士学位，导师为符方伟教授。2011年1月至2012年8月在美国南加州大学从事联合培养博士，导师为张箴教授。2015年11月至2018年11月在香港中文大学网络编码研究所从事研究工作，导师为杨伟豪教授。研究方向为信息论、编码理论与密码学；目前的研究兴趣为网络编码、网络函数计算、网络信息论。光炫博士近年来完成一部学术专著Linear Network Error Correction Coding，由德国Springer出版社出版发行；发表学术论文40余篇，其中在IEEE Trans. Inf. Theory上发表论文6篇；在IEEE J. Sel. Areas Commun.和IEEE Trans. Commun.上发表论文各1篇。研究成果获多个国内外会议的最佳论文奖。

报告摘要：We consider linear network error correction (LNEC) coding when errors may occur on the edges of a communication network of which the topology is known. In this talk, we first revisit and explore the framework of LNEC coding, and then unify two well-known LNEC coding approaches. Furthermore, by developing a graph-theoretic approach to the framework of LNEC coding, we obtain a significantly enhanced characterization of the capability of an LNEC code. In LNEC coding, LNEC maximum distance separable (MDS) codes are a type of most important optimal codes. However, the minimum required field size for the existence of LNEC MDS codes is an open problem not only of theoretical interest but also of practical importance, because it is closely related to the implementation of such coding schemes in terms of computational complexity and storage requirement. By applying the graph-theoretic approach, we obtain an improved lower bound on the required field size. The improvement over the existing results is in general significant. The improved lower bound thus obtained, which depends only on the network topology and a given LNEC capability, is graph-theoretical and is not given in a form which is readily computable. Toward computing the lower bound efficiently, we develop an efficient approach. With this, a polynomial-time algorithm is devised for computing the lower bound. This is a joint work with Dr. Raymond W. Yeung.

邀请人：郑大彬