Combinatorial methods in networks and communications

这项提议是我目前研究工作的继续，这项工作得到了NSERC发现基金的支持。网络和通信领域有很多与组合数学相关的研究课题，本文的主要目的是对这些领域中的一些重要课题进行研究。这一提议的一个显著特点是，组合方法是接近目的地的主要工具。我以前工作中的许多有趣和重要的结果表明，组合方法在这些领域是强大和有用的研究工具。然而，由于这项研究需要网络、通信和组合学方面的知识，所以现在没有足够的研究人员在这个方向上工作。大多数从事组合数学研究的研究人员从事数学工作，而不是从事网络和通信研究，而从事网络和通信研究的研究人员对组合数学并不熟悉。这项提议致力于通过研究网络和通信代码领域的几个重要主题，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。人们期待着提出新的理论和高效的协议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。在通信码方面，本方案重点研究了构造最优的二维光正交码，这是支持共享介质中多个用户同时使用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，这是保证传感器网络通信安全的重要步骤；构造传感器网络调度方案，用于有效地延长传感器网络的寿命。以及其他一些组合设计和相关编码。该提案还将进一步探讨这些组合主题。我相信这项研究将为现实世界的应用创造*重要的成果，并在组合数学和编码理论的基础理论方面取得成果。*

This proposal is a continuation of my current research work which is supported by an NSERC Discovery Grant. There are a lot of*research 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 most*important 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 to*prolong the lifetime of sensor networks effectively.There are several set systems with special properties, which are related to*various 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 create*important results for real world applications and results in fundamental theories in combinatorial mathematics and coding theory.***