Simplified random network codes for multicast networks

Thesis (M. Eng. and S.B.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.Includes bibliographical references (p. 43).Network coding is a method of data transmission across a network which involves coding at intermediate nodes. Network coding is particularly attractive for multicast. Building on the work done on random linear network codes, we develop a constrained, simplified code construction suitable for multicast in wireless networks. We analyze bounds on sufficient code size and code success probability via an algebraic framework for network coding. We also present simulation results that compare generalized random network codes with our code construction. Issues unique to the simplified code are explored and a relaxation of the code to improve code performance is discussed.by Anna H. Lee.M.Eng.and S.B

On achievable rates for multicast in the presence of side information

We investigate the network source coding rate region for networks with multiple sources and multicast demands in the presence of side information, generalizing earlier results on multicast rate regions without side information. When side information is present only at the terminal nodes, we show that the rate region is precisely characterized by the cut-set bounds and that random linear coding suffices to achieve the optimal performance. When side information is present at a non-terminal node, we present an achievable region. Finally, we apply these results to obtain an inner bound on the rate region for networks with general source-demand structures

Classifying Networks For Network Coding

Network coding is a relatively recent development in the realm of maximizing information transfer in communications and computer networks. Traditional networks operate by simply storing and forwarding data along. Network coding, however, allows intermediate network nodes to combine data using arithmetic operations. In many instances, this can lead to more efficient use of network resources. Since there is a significant throughput input in some networks, some studies have been done on what kinds of networks will benefit from coding. A coding advantage is defined as a situation where a network coded graph has a lower cost to send given information per unit time session than the same un-coded graph. It has been proven that for two simple single-sender-single-receiver communication sessions that a graph must have one of two special graph-theoretic structures called the butterfly and grail in order to yield a coding advantage. We decided to focus our efforts on a different traffic scenario: a multicast session with a single sender and multiple receivers. Through our research we proved that a multicast-version of the butterfly network structure is needed within a single session multicast with two sinks and one source in order to gain a coding advantage. We also performed a simulation-based study in order to study the structures of multicast sessions with a larger number of receivers. The study involved the random generation of networks using several graph generation techniques. We also considered a variety of different edge-weighting constraints. Given a particular graph with set edge weights, the coding advantage problem was modeled as a linear program and run through the simulator to determine if a coding advantage was gained. Based on visual inspection of these results, it appears that variations of the multicast butterfly are ultimately the dominant structure allowing for a coding advantage. We also found that many types of random networks only very rarely resulted in a coding advantage. Only the graphs generated using the rectangular grid method showed a coding advantage, with a coding advantage percentage of 0.005% for 4 sinks in a 30 node network, with the coding advantage percentage going up as the number of sinks within the network increased

Evolutionary Approaches to Minimizing Network Coding Resources

We wish to minimize the resources used for network coding while achieving the desired throughput in a multicast scenario. We employ evolutionary approaches, based on a genetic algorithm, that avoid the computational complexity that makes the problem NP-hard. Our experiments show great improvements over the sub-optimal solutions of prior methods. Our new algorithms improve over our previously proposed algorithm in three ways. First, whereas the previous algorithm can be applied only to acyclic networks, our new method works also with networks with cycles. Second, we enrich the set of components used in the genetic algorithm, which improves the performance. Third, we develop a novel distributed framework. Combining distributed random network coding with our distributed optimization yields a network coding protocol where the resources used for coding are optimized in the setup phase by running our evolutionary algorithm at each node of the network. We demonstrate the effectiveness of our approach by carrying out simulations on a number of different sets of network topologies.Comment: 9 pages, 6 figures, accepted to the 26th Annual IEEE Conference on Computer Communications (INFOCOM 2007

On distributed scheduling in wireless networks exploiting broadcast and network coding

In this paper, we consider cross-layer optimization in wireless networks with wireless broadcast advantage, focusing on the problem of distributed scheduling of broadcast links. The wireless broadcast advantage is most useful in multicast scenarios. As such, we include network coding in our design to exploit the throughput gain brought in by network coding for multicasting. We derive a subgradient algorithm for joint rate control, network coding and scheduling, which however requires centralized link scheduling. Under the primary interference model, link scheduling problem is equivalent to a maximum weighted hypergraph matching problem that is NP-complete. To solve the scheduling problem distributedly, locally greedy and randomized approximation algorithms are proposed and shown to have bounded worst-case performance. With random network coding, we obtain a fully distributed cross-layer design. Numerical results show promising throughput gain using the proposed algorithms, and surprisingly, in some cases even with less complexity than cross-layer design without broadcast advantage