Research In Some Aspects Of Network Coding Thoery

In 2000,Ahlswede et al introduced the network information flow model,where it was assumed that all nodes are connected in the point-to-point manner and the links are noiseless.Based on the model, Ahlswede et al gave a deep investigation of the network capacity issue and introduced the concept of "network coding".In traditional data communication network, switch nodes forward received data without processing them. When network coding is used, a switch node encoding received data flow before sending them, and then the receiver nodes decoding received data and recover the source information. It is proved that network coding can improve network resource utilization and generally it is necessary to use network coding to achieve network capacity. Network coding theory is an important breakthrough in the field of network information theory in recent years, which rises great interest of researchers around the world.This work gives an investigation of some aspects of network coding theory. After a concise introduction to network coding's background, concept, and basic theory, our main work is as follows.Security of network coding. Security is an important aspect of research and design of modern network. In Chapter 3,we first introduce some auxiliary mathematical results which show the equivalence between linear independence and statistical independence in the context of network coding.Based on those results, we give a necessary and sufficient condition for security of linear network coding. To achieve information-theoretic security, it is generally necessary to add secret key information to randomize source information. We propose a lower bound of secret key information rate for network coding in a special multicast communication.Weak security of network coding.For security of system, it is necessary to add secret key information, which will decrease the communication efficiency of the system. In some cases, the information-theoretic security can be loosened to achieve higher transmission efficiency. In Chapter 4, we give two definitions of weak security criteria for network coding and give some examination. Network coding and network flow control.In modern network, flow control is an indispensable component for reliability and efficiency. Especially in packet network, flow control is needed to control congestion, improve throughput, reduce delay, and ensure fairness among different users.In Chapter 5,we discuss flow control issue for network coding based multicast.Following the network utility maximization framework, we give a hierarchical decomposition to the primal problem and a functionality allocation for network coding based multicast.With the decomposition approach, a distributed flow control algorithm is obtained.In Chapter 6, the contribution of this work is summarized.This work is supported by National Basic Research Program of China (973 Program) 2007CB310604 & 2009CB320401 and national key scientific and technological project of China 2008ZX03003-005.