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2009, Journal of Communications
Network coding is a promising generalization of routing which allows a network node to generate output messages by encoding its received messages to reduce the bandwidth consumption in the network. An important application where network coding offers unique advantages is the multicast network where a source node generates messages and multiple receivers collect the messages. Previous network coding schemes primarily considered encoding the messages in a single multicast session. In this paper, we consider the linear inter-session network coding for multicast. The basic idea is to divide the sessions into different groups and construct a linear network coding scheme for each group. To maximize the performance, we introduce two metrics: overlap ratio and overlap width, to measure the benefit that a system can achieve by inter-session network coding. The overlap ratio mainly characterizes the network bandwidth while the overlap width characterizes the system throughput. Our simulation results show that the proposed inter-session network coding scheme can achieve about ¿¼± higher throughput than intra-session network coding.
2008
In this paper, we study the contribution of network coding (NC) in improving the multicast capacity of random wireless ad hoc networks when nodes are endowed with multipacket transmission (MPT) and multi-packet reception (MPR) capabilities. We show that a per session throughput capacity of Θ`nT 3 (n)´, where n is the total number of nodes and T (n) is the communication range, can be achieved as a tight bound when each session contains a constant number of sinks. Surprisingly, an identical order capacity can be achieved when nodes have only MPR and MPT capabilities. This result proves that NC does not contribute to the order capacity of multicast traffic in wireless ad hoc networks when MPR and MPT are used in the network. The result is in sharp contrast to the general belief (conjecture) that NC improves the order capacity of multicast. Furthermore, if the communication range is selected to guarantee the connectivity in the network, i.e., T (n) ≥ Θ " p log n/n " , then the combination of MPR and MPT achieves a throughput capacity of Θ " log 3 2 n √ n « which provides an order capacity gain of Θ`log 2 n´compared to the point-to-point multicast capacity with the same number of destinations.
Proceedings of the 4th International ICST Conference on Wireless Internet, 2008
Multicasting is the delivery of common information to multiple receivers. It finds its application in multi-media broadcasts, group communication in social networks etc. The multicast traffic in networks can constitute a significant portion of the total traffic (e.g. 80% in military communications) and hence it is imperative that they are served efficiently. So far "single rate" multicasting, where all receivers receive the data at a common rate from the source has attracted most of the attention . Yet, single-rate multicasting may yield low utilization of the network resources when a subset of the receivers creates a bottleneck for the whole multicast group. Multirate multicasting is a strategy where the source is allowed to multicast its data to different destinations at different rates based on the condition of the network to them. Multirate multicasting allows users with better channels to achieve maximum performance.
IEEE Transactions on Vehicular Technology, 2015
We propose a network coding strategy for multicast applications called the simple network coding scheme, which takes network coding chances raised among adjacent nodes. The proposed scheme incorporates both intrasession and intersession network coding strategies and effectively improves multicast throughput. We characterize the capacity region of the proposed scheme and derive an optimal control algorithm for the proposed scheme. We perform a complexity analysis for the proposed control algorithm and provide some insights into its practical implementation. For a comparison, we also formulate the capacity region of conventional multicast schemes and provide performance evaluation using a linear programming solver. In empirical analyses, we investigate how the proposed scheme improves multicast throughput gains from various perspectives (i.e., the number of flows, the number of network coded packets, and split-multicast) and find out that most of the gains can be achieved by simple pairwise network coding with non-split-multicast. We observe dramatic throughput gains up to 75% beyond the conventional schemes on random topologies with ten nodes.
IEEE Transactions on Information Theory, 2000
We establish, for multiple multicast sessions with intra-session network coding, the capacity region of input rates for which the network remains stable in ergodically time-varying networks. Building on the back-pressure approach introduced by Tassiulas et al., we present dynamic algorithms for multicast routing, network coding, rate control, power allocation, and scheduling that achieves stability for rates within the capacity region. Decisions on routing, network coding, and scheduling between different sessions at a node are made locally at each node based on virtual queues for different sinks. For correlated sources, the sinks locally determine and control transmission rates across the sources. The proposed approach yields a completely distributed algorithm for wired networks. In the wireless case, scheduling and power control among different transmitters are centralized while routing, network coding, and scheduling between different sessions at a given node are distributed.
2007
Abstract Multicast is an important communication paradigm, also a problem well known for its difficulty (NP-completeness) to achieve certain optimization goals, such as minimum network delay. Recent advances in network coding has shed a new light onto this problem. In network coding, forwarding nodes can perform arbitrary operations on data received, other than forwarding or replicating, to enhance throughput of a multicast session.
In recent years, network coding has become one of the most interesting fields and has attracted considerable attention from both industry and academia. The idea of network coding is based on the concept of allowing intermediate nodes to encode and combine incoming packets instead of only copy and forward them. This approach, by augmenting the multicast and broadcast efficiency of multi-hop wireless networks, increases the capacity of the network and improves its throughput and robustness. While a wide variety of papers described applications of network coding in different types of networks such as delay tolerant networks, peer to peer networks and wireless sensor networks, the detailed practical implementation of network coding has not been noted in most papers. Since applying network coding in real scenarios requires an acceptable understanding of mathematics and algebra, especially linear equations, reduced row echelon matrices, field and its operations, this paper provides a comprehensive guidance for the implementation of almost all required concepts in network coding. The paper explains the implementation details of network coding in real scenarios and describes the effect of the field size on network coding.
Computer Communications, 2019
This paper presents a Network Coding Assisted Multicast Least Cost Anypath Routing (NC-MLCAR) scheme for packet transmission over a multi-hop wireless network. Our objective is to transmit packets efficiently from the source node to the destination set with the help of a selected forwarder set to reduce the expected number of transmissions for efficient network capacity usage. The forwarder set is selected using the earlier Multicast Least Cost Anypath Routing (MLCAR) algorithm. Network coded packets are then transmitted by allocating traffic efficiently between the nodes of the forwarder set while ensuring that each destination receives all the packets. Simulation results are presented for the cases when the packets receptions over different links are considered to be (i) independent and (ii) correlated. The extensive simulation results presented in the paper are compared with the corresponding MLCAR approach and other network coding schemes employed for multicasting like MORE and Pacifier. It is observed that the proposed NC-MLCAR scheme significantly reduces the expected number of overall transmissions in the network, for both independent links and correlated links, when compared to the existing multicasting schemes. Complexity analysis of NC-MLCAR is also presented.
IEEE Access
In this article, a new multicast protocol is introduced at the session layer, which is based on network coding and is called the Network Coding Datagram Protocol (NCDP). The NCDP protocol is specifically designed for content delivery systems that utilize multicast data transmission from multiple sources. The development of the NCDP packet and its operational logic takes into consideration the variability of the protocols used in conjunction with it, as well as the packet header processing algorithms for routing nodes-coders. Additionally, a virtual laboratory bench is proposed to facilitate research on the operation of the protocol. The article also includes the results of testing the NCDP protocol in networks with butterfly and diamond topologies, with a comparison between simple sequential multicast transmission and network coding transmission.
2004
Abstract Optimal data routing in a network can be often understood as a multicommodity flow problem. Given a network and a set of commodities, ie, a set of source-destination pairs, one tries to achieve certain optimization goal, such as minimum delay, maximum throughput, while maintaining certain fairness among all commodities. The constraints of such optimization problems are usually network link capacity and traffic demand of each commodity.
International Teletraffic Congress, 2012
Network coding has been shown to be the solution that allows to reach the theoretical maximum throughput in a capacitated telecommunication network [1]. It has also been shown to be a very appealing and practical alternative to routing-based approaches to send traffic from sources (servers) to terminals (clients) for many different applications. However, the initial theoretical claim of throughput benefit remains relatively unclear, mainly because the multicast throughput maximization problem is difficult to solve (it is closely related to the fractional Steiner tree packing problem which is NP-hard). In this paper, we show that these optimization problems are still tractable even for instances with a significant size (up to 50 nodes and 300 edges). We also propose and solve the multicast maximum throughput problem with an additional constraint on the number of multicast trees. We apply our algorithms on large sets of randomly generated instances, mainly based on bidirected graphs, because they are the most relevant to model fixed telecommunication infrastructures. The main result of our intensive experimental study is that, in practice, network coding does not increase throughput compared to traditional multicast. Instances showing a throughput gain can only be generated somewhat artificially by imposing some structure or trying to maximize the throughput gap. However, when we limit the number of multicast trees, then, most of the times, very significant throughput gaps appeared. Since management constraints often impose on network administrators a very limited use of multicast trees, network coding appears clearly as a very nice alternative for delivering content to customers.
Here, we characterize the throughput of a broad cast network with receivers using rate less codes with block size. We characterize the system throughput asymptotically. Specifically, we explicitly show how the throughput behaves for different values of the coding block size as a function. We are able to provide a lower bound on the maximum achievable throughput. Using simulations, we show the tightness of the bound with respect to system parameters and find that its performance is significantly better than the previously known lower bounds. The packets are not decidable if any deviation is occurred.
2007
Abstract—In this paper, the problem of transmitting two symbols from two sources to multiple destinations using network coding is considered for general directed acyclic graphs. When all destination nodes are interested in both symbols, the feasibility of this problem is characterized by the classic min-cut maxflow theorem. This work focuses on the scenarios in which each destination is interested in one source symbol.
KSII Transactions on Internet and Information Systems
This work proposes a model to solve the problem of Network Coding over a one-session multicast network. The model is based on a system of restrictions that defines the packet flows received in the sink nodes as functions of the outgoing flows from the source node. A multicast network graph is used to derive a directed labeled line graph (DLLG). The successive powers of the DLLG adjacency matrix to the convergence in the null matrix permits the construction of the jump matrix Source-Sinks. In its reduced form, this shows the dependency of the incoming flows in the sink nodes as a function of the outgoing flows in the source node. The emerging packets for each outgoing link from the source node are marked with a tag that is a linear combination of variables that corresponds to powers of two. Restrictions are built based on the dependence of the outgoing and incoming flows and the packet tags as variables. The linear independence of the incoming flows to the sink nodes is mandatory. The method is novel because the solution is independent of the Galois field size where the packet contents are defined.
2009
Multi-resolution codes enable multicast at different rates to different receivers, a setup that is often desirable for graphics or video streaming. We propose a simple, distributed, two-stage message passing algorithm to generate network codes for single-source multicast of multi-resolution codes. The goal of this pushback algorithm is to maximize the total rate achieved by all receivers, while guaranteeing decodability of the base layer at each receiver. By conducting pushback and code assignment stages, this algorithm takes advantage of inter-layer as well as intra-layer coding. Numerical simulations show that in terms of total rate achieved, the pushback algorithm outperforms routing and intra-layer coding schemes, even with field sizes as small as 2 10 (10 bits). In addition, the performance gap widens as the number of receivers and the number of nodes in the network increases. We also observe that naïve inter-layer coding schemes may perform worse than intra-layer schemes under certain network conditions.
MILCOM 2007 - IEEE Military Communications Conference, 2007
This paper investigates the interaction between network coding and link-layer transmission rate diversity in multihop wireless networks. By appropriately mixing data packets at intermediate nodes, network coding allows a single multicast flow to achieve higher throughput to a set of receivers. Broadcast applications can also exploit link-layer rate diversity, whereby individual nodes can transmit at faster rates at the expense of corresponding smaller coverage area. We first demonstrate how combining rate-diversity with network coding can provide a larger capacity for data dissemination of a single multicast flow, and how consideration of rate diversity is critical for maximizing system throughput. We also study the impact of both network coding and rate diversity on the dissemination latency for a class of quasi real-time applications, where the freshness of disseminated data is important. Our results provide evidence that network coding may lead to a latency-vs-throughput tradeoff in wireless environments, and that it is thus necessary to adapt the degree of network coding to ensure conformance to both throughput and latency objectives. There is an increasing interest in understanding the potential performance gains accruing from the use of network coding in multi-hop wireless environments. In particular, many military battlefield scenarios exhibit two characteristics that appear to motivate the use of network coding: a) the reliance on bandwidth-constrained, ad-hoc wireless links (e.g. using MANETs formed by vehicle-mounted radios in urban insurgencies) and b) the need to disseminate information (e.g., maps, mission commands) to multiple recipients. The initial results on the power of network coding NC, such as the original demonstration in [1] of how in-network mixing of packets by intermediate nodes helps to achieve a communication capacity that is not achievable solely through routing, were obtained for the case of a lossless, wireline network. More recently, several groups have investigated the potential performance gains realized by network coding for both
2012 Proceedings of IEEE Southeastcon, 2012
Traditional method of solving group communications problem is by placing a super source with unlimited bandwidth to all sources. In this paper, we show that this method cannot guarantee the fairness within different sources for routing. Also in certain scenarios, the method can lead to wrong conclusion of network achieving higher throughput than it can actually deliver. Two algorithms are presented, one for routing and one for network coding to guarantee that each source has the same fairness and get the sub-optimal throughput for group communications in undirected networks. The throughputs achieved using either of these algorithms (one for routing only and one for network coding) are much better than any current widely-used IP multicast protocols. Between the two proposed algorithms, the algorithm for network coding can have throughput benefit in some scenarios but not always. Here, we show through simulation that network coding does not have constant throughput benefit in undirected networks in group communications scenario with the consideration of fairness within different sources.
2011 IEEE International Conference on Communications (ICC), 2011
This paper addresses the problem of inter-session network coding to maximize throughput for multiple communication sessions in wireless networks. We introduce virtual multicast connections which can extract packets from original sessions and code them together. Random linear network codes can be used for these virtual multicasts. The problem can be stated as a flowbased convex optimization problem with side constraints. The proposed formulation provides a rate region which is at least as large as the region without inter-session network coding. We show the benefits of our technique for several scenarios by means of simulation.
2012
In today's practical networks, end-to-end information delivery is performed by routing. Network coding generalizes routing by allowing a node to generate output data by mixing (i.e., computing certain functions of) its received data. Network coding techniques are used to find the minimum cost in given network. In wire line network, solving for the optimal coding subgraphs in network coding is equivalent to finding the optimal routing scheme in a multi-commodity flow problem. Multicast is an important factor for the communication in wireless network. This problem is also known as NP-complete. This paper focuses on the solution for the above problem and provides the analytical framework as well as distributed algorithm in multicast session. A set of node based distributed algorithm are designed at sources node and virtual at intermediate node. Keyword-Network coding, multi-commodity flow problem, distributed algorithm, wireless networks.
IEEE Transactions on Communications, 2000
Intra-session network coding has been shown to offer significant gains in terms of achievable throughput and delay in settings where one source multicasts data to several clients. In this paper, we consider a more general scenario where multiple sources transmit data to sets of clients and study the benefits of inter-session network coding, when network nodes have the opportunity to combine packets from different sources. In particular, we propose a novel framework for optimal rate allocation in inter-session network coding systems. We formulate the problem as the minimization of the average decoding delay in the client population and solve it with a gradient-based stochastic algorithm. Our optimized inter-session network coding solution is evaluated in different network topologies and compared with basic intra-session network coding solutions. Our results show the benefits of proper coding decisions and effective rate allocation for lowering the decoding delay when the network is used by concurrent multicast sessions.
2012 9th International Conference on Fuzzy Systems and Knowledge Discovery, 2012
The encoding complexity of network coding for single multicast networks has been intensively studied from several aspects: e.g., the time complexity, the required number of encoding links, and the required field size for a linear code solution. However, these issues as well as the solvability are less understood for networks with multiple multicast sessions. Recently, Wang and Shroff showed that the solvability of networks with two unit-rate multicast sessions (2-URMS) can be decided in polynomial time . In this paper, we prove that for the 2-URMS networks: 1) the solvability can be determined with time O(|E|); 2) a solution can be constructed with time O(|E|); 3) an optimal solution can be obtained in polynomial time; 4) the number of encoding links required to achieve a solution is upper-bounded by max{3, 2N -2}; and 5) the field size required to achieve a linear solution is upper-bounded by max{2, ⌊ 2N -7/4 + 1/2⌋}, where |E| is the number of links and N is the number of sinks of the underlying network. Both bounds are shown to be tight.
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