Combinatorial methods in networks and communications

网络和通信中的组合方法

• 批准号: RGPIN-2016-05610
• 负责人: Wei, Ruizhong
• 金额: $ 1.6万
• 依托单位: Lakehead University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=634978
• 关键词: Combinatorial; methods; networks; communications

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.

该提案是我当前研究工作的延续，该研究工作得到了 NSERC 发现补助金的支持。网络和通信领域有很多研究课题都与组合数学相关。本提案的主要目的是对这些领域的一些重要课题进行研究。该提案的显着特征之一是组合方法是接近目的地的主要工具。 我之前的工作的许多有趣且重要的结果表明，组合方法是这些领域强大且有用的研究工具。然而，由于这项研究需要网络、通信和组合学方面的知识，因此目前没有足够的研究人员在这个方向上工作。大多数涉及组合学的研究人员都从事数学工作，而不是网络和通信领域，而从事网络和通信领域的研究人员并不熟悉组合学。该提案致力于通过研究这些领域的几个重要主题并培训该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。博士后和硕士生将参与这项研究。预计将提出新的理论和有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。关于通信代码，该提案重点关注几个主题，包括构建最佳的二维光学正交码（这是支持共享媒体中多个同时用户的最重要技术之一，以增加光纤的传输容量）、构建传感器网络密钥分配方案（这是确保传感器网络通信安全的重要一步）以及构建可用于延长传感器寿命的传感器网络调度方案 有一些具有特殊性质的集合系统，涉及网络、网络安全和通信编码中的各种问题，例如循环和半循环设计、超简单循环设计、置换数组以及其他一些组合设计和相关代码。该提案也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。