Quantum Network Coding

Since quantum information is continuous, its handling is sometimes surprisingly harder than the classical counterpart. A typical example is cloning; making a copy of digital information is straightforward but it is not possible exactly for quantum information. The question in this paper is whether or not quantum network coding is possible. Its classical counterpart is another good example to show that digital information flow can be done much more efficiently than conventional (say, liquid) flow. Our answer to the question is similar to the case of cloning, namely, it is shown that quantum network coding is possible if approximation is allowed, by using a simple network model called Butterfly. In this network, there are two flow paths, s_1 to t_1 and s_2 to t_2, which shares a single bottleneck channel of capacity one. In the classical case, we can send two bits simultaneously, one for each path, in spite of the bottleneck. Our results for quantum network coding include: (i) We can send any quantum state |psi_1> from s_1 to t_1 and |psi_2> from s_2 to t_2 simultaneously with a fidelity strictly greater than 1/2. (ii) If one of |psi_1> and |psi_2> is classical, then the fidelity can be improved to 2/3. (iii) Similar improvement is also possible if |psi_1> and |psi_2> are restricted to only a finite number of (previously known) states. (iv) Several impossibility results including the general upper bound of the fidelity are also given.Comment: 27pages, 11figures. The 12page version will appear in 24th International Symposium on Theoretical Aspects of Computer Science (STACS 2007

Representations of the Multicast Network Problem

We approach the problem of linear network coding for multicast networks from different perspectives. We introduce the notion of the coding points of a network, which are edges of the network where messages combine and coding occurs. We give an integer linear program that leads to choices of paths through the network that minimize the number of coding points. We introduce the code graph of a network, a simplified directed graph that maintains the information essential to understanding the coding properties of the network. One of the main problems in network coding is to understand when the capacity of a multicast network is achieved with linear network coding over a finite field of size q. We explain how this problem can be interpreted in terms of rational points on certain algebraic varieties.Comment: 24 pages, 19 figure

Practical Network Coding in Sensor Networks: Quo Vadis?

Abstract. Network coding is a novel concept for improving network ca-pacity. This additional capacity may be used to increase throughput or reliability. Also in wireless networks, network coding has been proposed as a method for improving communication. We present our experience from two studies of applying network coding in realistic wireless sen-sor networks scenarios. As we show, network coding is not as useful in practical deployments as earlier theoretical work suggested. We discuss limitations and future opportunities for network coding in sensor net-works. 1 Network Coding in Wireless Sensor Networks Network Coding was introduced by Ahlswede et al. [1], proving that it can in-crease multicast capacity. Since then, it has been investigated in several different networked scenarios which demand different traffic characteristics. Most previous research has focused on theoretical aspects of applying network coding to sensor networks. There are, however, also more practical examples of applying networ

An Extended Network Coding Opportunity Discovery Scheme in Wireless Networks

Network coding is known as a promising approach to improve wireless network performance. How to discover the coding opportunity in relay nodes is really important for it. There are more coding chances, there are more times it can improve network throughput by network coding operation. In this paper, an extended network coding opportunity discovery scheme (ExCODE) is proposed, which is realized by appending the current node ID and all its 1-hop neighbors' IDs to the packet. ExCODE enables the next hop relay node to know which nodes else have already overheard the packet, so it can discover the potential coding opportunities as much as possible. ExCODE expands the region of discovering coding chance to n-hops, and have more opportunities to execute network coding operation in each relay node. At last, we implement ExCODE over the AODV protocol, and efficiency of the proposed mechanism is demonstrated with NS2 simulations, compared to the existing coding opportunity discovery scheme.Comment: 15 pages and 7 figure

Wireless Broadcast with Network Coding in Mobile Ad-Hoc Networks: DRAGONCAST

Network coding is a recently proposed method for transmitting data, which has been shown to have potential to improve wireless network performance. We study network coding for one specific case of multicast, broadcasting, from one source to all nodes of the network. We use network coding as a loss tolerant, energy-efficient, method for broadcast. Our emphasis is on mobile networks. Our contribution is the proposal of DRAGONCAST, a protocol to perform network coding in such a dynamically evolving environment. It is based on three building blocks: a method to permit real-time decoding of network coding, a method to adjust the network coding transmission rates, and a method for ensuring the termination of the broadcast. The performance and behavior of the method are explored experimentally by simulations; they illustrate the excellent performance of the protocol