On the Capacity Bounds of Undirected Networks

In this work we improve on the bounds presented by Li&Li for network coding gain in the undirected case. A tightened bound for the undirected multicast problem with three terminals is derived. An interesting result shows that with fractional routing, routing throughput can achieve at least 75% of the coding throughput. A tighter bound for the general multicast problem with any number of terminals shows that coding gain is strictly less than 2. Our derived bound depends on the number of terminals in the multicast network and approaches 2 for arbitrarily large number of terminals.Comment: 5 pages, 5 figures, ISIT 2007 conferenc

Path Gain Algebraic Formulation for the Scalar Linear Network Coding Problem

In the algebraic view, the solution to a network coding problem is seen as a variety specified by a system of polynomial equations typically derived by using edge-to-edge gains as variables. The output from each sink is equated to its demand to obtain polynomial equations. In this work, we propose a method to derive the polynomial equations using source-to-sink path gains as the variables. In the path gain formulation, we show that linear and quadratic equations suffice; therefore, network coding becomes equivalent to a system of polynomial equations of maximum degree 2. We present algorithms for generating the equations in the path gains and for converting path gain solutions to edge-to-edge gain solutions. Because of the low degree, simplification is readily possible for the system of equations obtained using path gains. Using small-sized network coding problems, we show that the path gain approach results in simpler equations and determines solvability of the problem in certain cases. On a larger network (with 87 nodes and 161 edges), we show how the path gain approach continues to provide deterministic solutions to some network coding problems.Comment: 12 pages, 6 figures. Accepted for publication in IEEE Transactions on Information Theory (May 2010

On Average Throughput Benefits and Alphabet Size in Network Coding

We examine the throughput benefits that network coding offers with respect to the average through- put achievable by routing, where the average throughput refers to the average of the rates that the indi- vidual receivers experience. We relate these benefits to the integrality gap of a standard LP formulation for the directed Steiner tree problem. We describe families of configurations over which network coding at most doubles the average throughput, and analyze a class of directed graph configurations with N receivers where network coding offers benefits proportional to √N. We also discuss other throughput measures in networks, and show how in certain classes of networks, the average throughput can be achieved uniformly by all receivers by employing vector routing and channel coding. Finally, we show configurations where use of randomized coding may require an alphabet size exponentially larger than the minimum alphabet size required

An implementation of a reliable broadcast scheme for 802.11 using network coding

Forward Error Correction and retransmission are two approaches used to reliably broadcast data in a network with poor quality of service. Taking some assumptions, it has been suggested that a retransmission based reliable broadcasting scheme using network coding should in theory provide an increase in bandwidth efficiency by combining packets as they are retransmitted. In this thesis, we remove those assumptions by providing two algorithms to implement the previously proposed scheme. These two algorithms differ in a way that allows them to compare the tradeoffs between two different methods of packet loss notification. We test these two algorithms over several parameters and provide insights into the cause of their performance attributes

Optimizing Network Coding Algorithms for Multiple Applications.

Deviating from the archaic communication approach of treating information as a fluid moving through pipes, the concepts of Network Coding (NC) suggest that optimal throughput of a multicast network can be achieved by processing information at individual network nodes. However, existing challenges to harness the advantages of NC concepts for practical applications have prevented the development of NC into an effective solution to increase the performance of practical communication networks. In response, the research work presented in this thesis proposes cross-layer NC solutions to increase the network throughput of data multicast as well as video quality of video multicast applications. First, three algorithms are presented to improve the throughput of NC enabled networks by minimizing the NC coefficient vector overhead, optimizing the NC redundancy allocation and improving the robustness of NC against bursty packet losses. Considering the fact that majority of network traffic occupies video, rest of the proposed NC algorithms are content-aware and are optimized for both data and video multicast applications. A set of content and network-aware optimization algorithms, which allocate redundancies for NC considering content properties as well as the network status, are proposed to efficiently multicast data and video across content delivery networks. Furthermore content and channel-aware joint channel and network coding algorithms are proposed to efficiently multicast data and video across wireless networks. Finally, the possibilities of performing joint source and network coding are explored to increase the robustness of high volume video multicast applications. Extensive simulation studies indicate significant improvements with the proposed algorithms to increase the network throughput and video quality over related state-of-the-art solutions. Hence, it is envisaged that the proposed algorithms will contribute to the advancement of data and video multicast protocols in the future communication networks

Design and Reliability Performance Evaluation of Network Coding Schemes for Lossy Wireless Networks

This thesis investigates lossy wireless networks, which are wireless communication networks consisting of lossy wireless links, where the packet transmission via a lossy wireless link is successful with a certain value of probability. In particular, this thesis analyses all-to-all broadcast in lossy wireless networks, where every node has a native packet to transmit to all other nodes in the network. A challenge of all-to-all broadcast in lossy wireless networks is the reliability, which is defined as the probability that every node in the network successfully obtains a copy of the native packets of all other nodes. In this thesis, two novel network coding schemes are proposed, which are the neighbour network coding scheme and the random neighbour network coding scheme. In the two proposed network coding schemes, a node may perform a bit-wise exclusive or (XOR) operation to combine the native packet of itself and the native packet of its neighbour, called the coding neighbour, into an XOR coded packet. The reliability of all-to-all broadcast under both the proposed network coding schemes is investigated analytically using Markov chains. It is shown that the reliability of all-to-all broadcast can be improved considerably by employing the proposed network coding schemes, compared with non-coded networks with the same link conditions, i.e. same probabilities of successful packet transmission via wireless channels. Further, the proposed schemes take the link conditions of each node into account to maximise the reliability of a given network. To be more precise, the first scheme proposes the optimal coding neighbour selection method while the second scheme introduces a tuning parameter to control the probability that a node performs network coding at each transmission. The observation that channel condition can have a significant impact on the performance of network coding schemes is expected to be applicable to other network coding schemes for lossy wireless networks

Design and Reliability Performance Evaluation of Network Coding Schemes for Lossy Wireless Networks

This thesis investigates lossy wireless networks, which are wireless communication networks consisting of lossy wireless links, where the packet transmission via a lossy wireless link is successful with a certain value of probability. In particular, this thesis analyses all-to-all broadcast in lossy wireless networks, where every node has a native packet to transmit to all other nodes in the network. A challenge of all-to-all broadcast in lossy wireless networks is the reliability, which is defined as the probability that every node in the network successfully obtains a copy of the native packets of all other nodes. In this thesis, two novel network coding schemes are proposed, which are the neighbour network coding scheme and the random neighbour network coding scheme. In the two proposed network coding schemes, a node may perform a bit-wise exclusive or (XOR) operation to combine the native packet of itself and the native packet of its neighbour, called the coding neighbour, into an XOR coded packet. The reliability of all-to-all broadcast under both the proposed network coding schemes is investigated analytically using Markov chains. It is shown that the reliability of all-to-all broadcast can be improved considerably by employing the proposed network coding schemes, compared with non-coded networks with the same link conditions, i.e. same probabilities of successful packet transmission via wireless channels. Further, the proposed schemes take the link conditions of each node into account to maximise the reliability of a given network. To be more precise, the first scheme proposes the optimal coding neighbour selection method while the second scheme introduces a tuning parameter to control the probability that a node performs network coding at each transmission. The observation that channel condition can have a significant impact on the performance of network coding schemes is expected to be applicable to other network coding schemes for lossy wireless networks

高性能通信指向のネットワークコーディング

Tohoku University堀口 進課