Combinatorial methods in networks and communications

点击翻译按钮获取中文摘要

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.***