Combinatorial methods in networks and communications

这项建议是我目前的研究工作的延续，这项工作得到了NSERC发现资助的支持。在网络和通信领域有很多与组合数学相关的研究课题，本课题的主要目的是对这些领域中的一些重要课题进行研究.这一建议的一个显著特点是，组合方法是接近目的地的主要工具。 许多有趣的和重要的结果，我以前的工作表明，组合方法是强大的和有用的研究工具，在这些领域。然而，由于网络，通信和组合学的知识需要在这项研究中，没有足够的研究人员现在在这个方向上工作。大多数参与组合学的研究人员都在数学领域工作，而不是在网络和通信领域工作，而网络和通信领域的研究人员对组合学并不熟悉。该提案致力于通过调查这些领域的几个重要课题并通过培训这一领域的高素质年轻研究人员来促进网络和通信代码中的组合方法。博士后研究员和硕士研究生将参与这项研究。人们期待着新的理论和有效的协议将被提出来解决这些领域的重要问题。组合数学理论也将得到进一步发展。在通信编码方面，该提案集中于几个主题，包括构造最佳二维光正交码，这是支持多个同时用户在共享介质中以增加光纤传输容量的最重要技术之一，构造传感器网络密钥分配方案，这是安全传感器网络通信的重要步骤，有几个集合系统具有特殊的性质，它们与网络、网络安全和通信编码中的各种问题有关，如循环和半循环设计，超简单循环设计，置换阵列以及一些其他组合设计和相关代码。本提案也将进一步探讨这些组合主题。我相信这项研究将为真实的世界应用提供重要的结果，并在组合数学和编码理论的基础理论中产生结果。

This proposal is a continuation of my current research work which is supported by an NSERC Discovery Grant. There are a lot ofresearch topics in network and communication, which are related to combinatorial mathematics.The main purpose of this proposal is to do research on some important topics in these areas. One of the distinctive characteristics of this proposal is that combinatorial methods are the main tools to approach the destination. Many interesting and important results of my previous work show that combinatorial methods are powerful and useful research tools in these areas. However, since knowledge in networks, communication and combinatorics are required in this research, not enough researchers are now working in this direction. Most researchers involved in combinatorics are working in mathematics but not in networks and communications, while researchers working in networks and communications are not familiar with combinatorics. This proposal is dedicated to promoting combinatorial methods in networks and communication codes by investigating several important topics in these fields and by training highly qualified young researchers in this area. Post-doctoral fellows and master students will be involved in this research. It is expected that new theories and efficient protocols will be proposed to solve important problems in these fields. And theories of combinatorial mathematics will be further developed as well. Regarding communication codes, this proposal focuses on several topics including constructing optimal 2-dimensional optical orthogonal codes which is one of the mostimportant techniques supporting many simultaneous users in shared media so as to increase the transmission capacity of an optical fibre, constructing sensor network key distribution schemes which is an important step to secure sensor network communications, and constructing sensor network schedule schemes which can be used toprolong the lifetime of sensor networks effectively.There are several set systems with special properties, which are related tovarious problems in network, network security and communication codes, such as cyclic and semi-cyclic designs, super-simple cyclic designs, permutation arrays, and some other combinatorial designs and related codes. This proposal will further explore these combinatorial topics as well. I believe the research will createimportant results for real world applications and results in fundamental theories in combinatorial mathematics and coding theory.