We describe a mathematical structure which corresponds to the eigenstates of a density operator. For an unknown density operator, we propose an estimating procedure which uses successive ＂yes/no＂ measurements to scan the Bloch sphere and approximately yields the eigenstates. This result is based on the quantum method of types and implies a relationship between the typical subspace and the Young frame.
We investigate the error detection ability of intermedi- ate nodes of zig-zag network with small downstream link. We show that the error detection capability of zig-zag networks in the presence of z malicious edges and 2z-1 limited links from node B to node u. Also, at last we analyze a family of networks, which shows that the upper bound of network is smaller than the bound we expected, indicating that Singleton bound is not the tightest bound in the particular condition of network. According to this result, we design corresponding encode and decode strategy to reach the bound we propose in this paper.
Combinatorial networks are widely applied in many practical scenarios. In this paper, we compute the closed-form probability expressions of successful decoding at a sink and at all sinks in the multicast scenario, in which one source sends messages to k destinations through m relays using random linear network coding over a Galois field. The formulation at a （all） sink（s） represents the impact of major parameters, i.e., the size of field, the number of relays （and sinks） and provides theoretical groundings to numerical results in the literature. Such condition maps to the receivers＇ capability to decode the original information and its mathematical characterization is helpful to design the coding. In addition, numerical results show that, under a fixed exact decoding probability, the required field size can be minimized.
Existing solutions against wiretapping attacks for network coding either bring significant bandwidth overhead or incur a high computational complexity.In order to reduce the security overhead of the existing solutions for securing network coding,a novel securing network coding paradigm is presented relying on two coding models:intra-generation coding and inter-generation coding.The basic idea to secure network coding using intra-generation coding is to limit the encryption operations for each generation,and then subject the scrambled and the remaining original source vectors to a linear transformation.This method is then generalized seamlessly using inter-generation coding by further exploiting the algebraic structure of network coding.We show that the proposed schemes have properties of low-complexity security,little bandwidth consumption,and high efficiency in integrating with the existing security techniques effectively.
LIU GuangjunLIU BinyueLIU XimengLI FangGUO Wangmei
A tag encoding authentication scheme for network coding proposed by Wu et al was claimed to defend pollution attacks efficiently. However, we find that the scheme easily incurs multi-generation pollution attacks, where an adversary may be able to recover the main secret key of the source with high probability during multi-generation transmitting, and the scheme also cannot resist against inter-generation pollution attacks. Using a dynamic source secret key technology that the key can be updated with the change of generation identifier, an improved scheme is then presented, which can counteract these security defects without any efficiency compromise.
Existing works for securing network coding against wiretapping either incur high coding complexity or bring large bandwidth overhead. For exploiting the lightweight security mechanism for resource-constrained networks, an efficient secure coding scheme is proposed in conjunction with the inherent mix- ing characteristic of network coding. The key idea is to minimize the randomizing operations to the entire plaintext data. The pro- posed scheme is shown to have properties of lightweight security complexity and lower communication overhead compared with the existing traditional solutions, and can be easy in implementation and combination with classical cryptography techniques.
We study the construction of minimum bandwidth regenerating code with combinatorial design. At first, a method of constructing minimum storage regenerating （MBR） codes is presented, which can tolerate only one-node failure. Then, we give examples to explain the code. Finally, we discuss the case of repairing multiple nodes, and analyze the performance with an example.
We consider the problem of characterizing network capacity in the presence of adversarial errors on network links,focusing in particular on the effect of small downstream links,where the downstream link is the directed link of feedback links across the cut of network.In this paper,we present a family of zigzag networks where the inner bound and the outer bound coincide.We also establish tight condition for this family of zig-zag network,and develop encoding scheme and detection and decoding strategy.
