In a network with capacity h for multicast, information Xh = (X1, X2, · · · , Xh) can be transmitted from a source node to sink nodes without error by a linear network code. Furthermore, secret information S r = (S 1, S 2, · · · , S r) can be transmitted securely against wiretappers by k-secure network coding for k ≤ h−r. In this case, no information of the secret leaks out even if an adversary...

We take a unified view of network coding and decentralized control. Precisely speaking, we consider both as linear time-invariant systems by appropriately restricting channels and coding schemes of network coding to be linear time-invariant, and the plant and controllers of decentralized control to be linear timeinvariant as well. First, we apply linear system theory to network coding. This giv...

Random linear network coding is a feasible encoding tool for network coding, specially for the non-coherent network, and its performance is important in theory and application. In this letter, we study the performance of random linear network coding for the well-known butterfly network by analyzing the failure probabilities. We determine the failure probabilities of random linear network coding...

Constant dimension codes are subsets of the finite Grassmann variety. The study of these codes is a central topic in random linear network coding theory. Orbit codes represent a subclass of constant dimension codes. They are defined as orbits of a subgroup of the general linear group on the Grassmannian. This paper gives a complete characterization of orbit codes that are generated by an irredu...

Linear network coding provides a new communication diagram to significantly increase the network capacity by allowing the relay nodes to encode the incoming messages. However, this communication diagram is fragile to communication errors and pollution attacks. How to combat errors while maintaining the network efficiency is a challenging research problem. In this dissertation, we study how to c...