Maximization Network Throughput based on Maximal Flow for Single-Source Two-Destinations Multicast

Network coding (NC) and erasure coding (EC) share a common principle of encoding incoming data packets at network intermediate nodes so that destination nodes can reconstruct the original data packets using a sufficient number of encoded data packets collected at the destinations. While NC in general reduces the number of packets sent through the network, EC introduces redundancy into the packet streams to recover from lost packets. Many research papers in NC assume loss-free packet transmission, and to address this issue, end-to-end packet loss recovery through EC has been proposed. In this paper, we investigate hop-by-hop packet loss recovery through EC so as to avoid the accumulation of lost packets throughout the network using flow oriented EC. Specifically, we explore combined NC and EC at intermediate nodes in the networks to allow for improved packet loss recovery compared to end-to-end EC. Different implementations trading the packet processing complexity at the intermediate and destination nodes are considered. This paper first examines the effects of data loss in NC and then the improvements achievable with the proposed method are presented.

This paper studies joint scheduling and network coding in wireless multicast networks with independent sources. Designing a network coding solution for wireless networks involves scheduling interference-free transmissions and optimizing a performance measure for the predetermined scheduling sets, followed by constructing network codes for the specific solution. In such a design process, the results of prior steps need to provide enough information to the subsequent steps. In this paper, we formulate a linear optimization problem whose results can be used to design a coding solution. We build our work on previous works and present statistics that show the importance of incorporating unequal timeshares in designing network codes. In particular, our statistics show a throughput improvement of about 35% in maximum flow problems and energy savings between 13% and 30%, depending on the network size, in minimum energy problems. We also present the requirements of code construction algorithms for wireless networks that capture the broadcast property of these networks and can design proper codes when timeshares are unequal. In particular, the adaptation of a centralized network coding scheme for wireless networks is discussed. Overall, the work reported here provides a three-step solution to derive network codes that optimize a performance criterion of interest while also solving the scheduling problem in multihop wireless networks.

Network coding is a technology with great potentiality in improving wireless multi-hop network throughput. And some routings combined with network coding have been proposed for wireless multi-hop network. In the routings combined with network coding, network coding condition is used to find network coding opportunities, which is very important to the performance improving of routings combined with network coding. However, the network coding conditions defined by existing routings combined with network coding unilaterally focus on the growth of network coding opportunities, which results in the increasing of cost and delay in routing discovery. Moreover, the more flows participating network coding, the higher probability of decoding failure, which degrade the network coding gain. In this paper, low complexity network coding condition (LCNC) is proposed. LCNC only detects two-flows network coding opportunity, and ensures the destination make successful decoding. In addition, the actual network coding gain is designed through analysis of link quality. Network coding opportunity will be ignored in case the actual network coding gain is negative. Based on LCNC, a low complexity network coding aware routing (LNCR) is designed aiming wireless multi-hop network. Simulation results demonstrate that LNCR obtain a balance between network coding gain and routing discovery cost, and can obtain higher network throughput when the network load is high compared with the classical network coding aware routings.

Network coding has been proven to be an effective way to achieve the maximum flow capacity in a multicast network, which is bounded by the famous maximum-flow minimum-cut theorem. This technique is specially fit for some new types of network, e.g., ad-hoc, sensor network etc. In order to reduce the cost and complexity of network coding, rather than carrying out encoding at all the nodes along the routes of traffic flow, it is better to find out the nodes that need encoding, and perform the coding algorithm at these nodes only, so that the number of encoding nodes are as few as possible. Fragouli et al. (2004) presented a method to get the encoding nodes by subtree decomposition. In this paper, we take a random graph as the model of wireless ad-hoc multicast network, and apply a modified Ford-Fulkerson algorithm to obtain the maximum flow and encoding nodes in an undirected graph. Its correctness can be proven in theory. Furthermore, simulations are done in different conditions to get some meaningful results of this scheme. We also investigate the statistical properties of encoding nodes and maximum flow in ad-hoc multicast networks by random graph theory. We showed that the number of encoding nodes is approximately binomial-distributed, and as the size of the network tends to infinite, it is approximately a Poisson distribution. (8 pages)

Network Coding (NC) has witnessed a tremendous upsurge in interest and activities in recent years, both in academia and industry. Indeed, since the pioneering publication of Ahlswede et al. in 2000, NC has rapidly emerged as a major research area in information theory due to its wide applicability to communication through real networks. The many contributions available in the literature to date, ranging from purely theoretical studies on fundamental limits to practical experimentations in real–world environments, offer a clear evidence that the shift in paradigm envisaged by NC might revolutionize the way we manage, operate, and understand the organization of networks. However, the principle of NC is not without its limitations. Initial studies on NC were mainly focused on lossless channels, which, however, might have limited applicability to a wireless context. As a matter of fact, in practical wireless environments, NC might be very susceptible to transmission errors caused by noise, fading, or interference. In particular, the algebraic operations accomplished by the intermediate nodes of the network introduce some packet dependencies in a way that the injection of even a single erroneous packet has the potential to corrupt every packet received by the destination nodes. Motivated by this consideration, recent research efforts have been devoted to the design of robust NC, with the main goal to circumvent the critical limitations of the NC paradigm in practical operating environments. In this paper, we aim at providing an overview of the most important and notable research directions in this emerging field.

This paper considers the interplay between rate adaptation and inter-session network coding gains in wireless mesh or ad hoc networks. Inter-session network coding opportunities at relay nodes depend on packets being overheard by surrounding nodes ? The more packets nodes overhear, the more opportunities relays have to combine packets, resulting in a potential increase in network throughput. Thus, by adapting its transmission rate, a node can increase the range over which its packets are overheard, enabling additional opportunities for coding and increased overall throughput. This paper considers inter-session coding, restricted to a single relay (bottleneck) node, or star network topology. Even for such simple topologies the optimal joint rate adaptation and network coding policy is known to be NP-hard. Optimal rate vector selection is a combinatorial optimization problem, which is NP-hard, and finding optimal coding scheme turns out to be a clique partitioning problem which is also NP-hard. So, we provide heuristics to find a suboptimal rate vector and coding scheme. Additionally, we provide a linear programming formulation for network coding when only pairwise intersession coding is allowed. We evaluate the averaged throughput in two different scenarios, in which relays have different access opportunities, giving some intuition on the impact of rate adaptation in lightly and heavily loaded systems. The gains of joint rate adaptation and network coding are marginal when the relay has a higher access opportunity than other nodes, or when the MAC operates ideally it ranges from 9% to 19% as compared to a network without network coding and 4% over a network using regular network coding. While, when the relay has equal access opportunity as other source nodes, which is more typical of todays MAC protocols under heavy loads, the gain ranges from 40% to 62% as compared to the standard relaying case and is upto around 20% as compared to a network with regular pairwise network coding. This can further be increased to a gain of 40% to 120% by replacing pairwise coding with sub-optimal general network coding scheme.

Network coding is a promising enhancement of routing to improve network throughput and provide high reliability. It allows a node to generate output messages by encoding its received messages. Peer-to-peer networks are a perfect place to apply network coding due to two reasons: the topology of a peer-to-peer network is constructed arbitrarily, thus it is easy to tailor the topology to facilitate network coding; the nodes in a peer-to-peer network are end hosts which can perform more complex operations such as decoding and encoding than simply storing and forwarding messages. In this paper, we propose a scheme to apply network coding to peer-to-peer file sharing which employs a peer-to-peer network to distribute files resided in a web server or a file server. The scheme exploits a special type of network topology called combination network. It was proved that combination networks can achieve unbounded network coding gain measured by the ratio of network throughput with network coding to that without network coding. Our scheme encodes a file into multiple messages and divides peers into multiple groups with each group responsible for relaying one of the messages. The encoding scheme is designed to satisfy the property that any subset of the messages can be used to decode the original file as long as the size of the subset is sufficiently large. To meet this requirement, we first define a deterministic linear network coding scheme which satisfies the desired property, then we connect peers in the same group to flood the corresponding message, and connect peers in different groups to distribute messages for decoding. Moreover, the scheme can be readily extended to support link heterogeneity and topology awareness to further improve system performance in terms of throughput, reliability and link stress. Our simulation results show that the new scheme can achieve 15%–20% higher throughput than another peer-to-peer multicast system, Narada, which does not employ network coding. In addition, it achieves good reliability and robustness to link failure or churn.

Nowadays, wireless networks are employed for many applications, but they face some problems such as power source limitation and collision due to common media. These problems decrease the network throughput and increase the power consumption. Fading is another important characteristic of wireless channels, which degrades the network performance. On the contrary, network coding is a useful method that can be applied to increase throughput. We extend the network coding model from two nodes with one relay to four nodes with the same relay over Rayleigh fading channels. Each side of the relay consists of two neighbouring nodes, which relaying nodes are not needed between them. In this paper, we propose a new method that uses priority property for decoding so that high or low priority for a node means that the node will XOR received data from relay node and its own data or data received from its neighbour, respectively. Also, decoding procedure includes two stages in which one of the neighbour nodes in each side has high priority and the other one has low priority. Then, network performance and the effects of Rayleigh fading on network coding over double‐link channels are studied under power‐constant and channel‐inversion schemes. By solving optimisation problems called Double‐Link Network Coding Constant Power and Double‐Link Network Coding Channel Inversion, we obtain optimum network throughput. The results show that the proposed method increases network throughput and decreases power consumption by reducing number of time slots in comparison with the simple method. Copyright © 2013 John Wiley & Sons, Ltd.

Network coding has shown the promise of significant throughput improvement. In this paper, we study the network throughput using network coding and explore how the maximum throughput can be achieved in a two-way relay wireless network. Unlike previous studies, we consider a more general network with arbitrary structure of overhearing status between receivers and transmitters. To efficiently utilize the coding opportunities, we invent the concept of network coding cliques (NCCs), upon which a formal analysis on the network throughput using network coding is elaborated. In particular, we derive the closed-form expression of the network throughput under certain traffic load in a slotted ALOHA network with basic medium access control. Furthermore, the maximum throughput as well as optimal medium access probability at each node is studied under various network settings. Our theoretical findings have been validated by simulation as well. © 2014 IEEE.

This paper proposes a cooperative relay transmission exploiting a concatenated structure composed of a simple exclusive OR (XOR) network code and channel codes. A main contribution of this paper is to clarify the joint network-and-channel coding combined with an iterative decoding is effective in providing highly reliable wireless communications even in the case where distances from one destination node to two source nodes are not the same in the case of triangular topology network. In this case, it is subject to imbalanced signal powers at the destination node, resulting in imbalanced link quality. In this paper, we focus on an analogy between the triangular topology network and a quaternary PSK (QPSK) symbol with a rectangular shape, i.e., imbalanced the in-phase and quadrature-phase (I-Q). After demonstrating that the rectangular QPSK has a potential to detect signals with high accuracy by iterative decoding, a configuration of the cooperative relay to be proposed in this paper is revealed. Computer simulation confirms that both the rectangular QPSK and the cooperation are effective to solve the imbalanced problem.

For a special class of three unicast sessions, in which the maximum flow from each sender to each receiver is the same positive integer k, a network coding approach is proposed. A multigeneration mixed strategy, in which (2 × n + 1) consecutive generations are taken as a mixed set, is adopted. The precoding strategy is adopted at the senders, random linear network coding technology is adopted at intermediate nodes to transmit data, and interference alignment technology is used at the receivers to eliminate some interference information. The proposed approach can construct a network coding data transmission scheme, in which the transmission rate vector of the senders is [(n + 1) × k/(2 × n + 1), n × k/(2 × n + 1), n × k/(2 × n + 1)]. The feasibility of the proposed approach is mathematically deduced and proven, and the simulation results verify the conclusions of the theoretical analysis.

A Wireless Mesh Network (WMN) is a multi-hop network that gains the benefits of low deployment cost, fast access speed, expanded service coverage and large network capacity. However, the multi-hop communication in WMNs limits the throughput capacity due to increased number of packet transmissions. As a result, network coding is a recently emerged paradigm that can enhance the throughput capacity (i.e. network throughput) by minimizing the quantity of network workload and at the same time it ensures the data transfer among all the users. Further, with network coding the transmission effectiveness of a node can be improved by encoding (combining) several packets collectively and verifies whether the coding strategies is satisfied or not. Subsequently, if the coding strategies are satisfied then it transmits only the resultant encoded packet to the desired destination. In other words, network coding can improve the network throughput in WMNs by minimizing the transmission counts needed to transfer several packets to the destination. It should be noted that, while employing network coding in WMNs there are several challenges that should be compensated such as (i) identifying packets that can be combined (encoded) collectively and (ii) integrating the coding strategies in routing protocols. In this paper, we proposed a new mesh routing protocol that integrates network-coding called as Network Coding Aware Routing (Net-CART) protocol. Therefore, to enjoy the whole benefit of network coding a Net-CART protocol uses the innovative routing metric called Code-Aware and Load-Aware Routing Metric. Additionally, to identify numerous ‘coding structures’ and to support number of ‘packet encodings’ an improved set of coding strategies known as Enhanced Universal Coding Strategies is also proposed. The proposed Net-CART protocol comprising an improved set of coding strategies and a new routing-metric considers both the coding-opportunities and “network workload”. The simulation study carried out in wide forms of network configurations showed that Net-CART gives more fairness performances than other protocols.

With the advancement in network coding, the congestion avoidance problems in TCP are now being explored from the perspective of a network coding paradigm. Some of the challenges in incorporating network coding along with TCP are the complexity involved in implementation, added redundancy in the network, and added latency due to packet processing. Several methods have been proposed to intelligently combine packets of opposite flows, and/or use two different types of network coding to improve the throughput of the network. However, very few papers have focussed on the effect of redundancy introduced due to network coding and the corresponding effect of the number of packets combined, also known as generation size. Also, none of the previous papers have presented an optimizing model demonstrating the effect of inherent redundancy introduced by network coding for multiple flows in TCP. This paper proposes a simple mathematical framework for optimizing the sending rate for TCP with network coding and the generation size at the sources for multiple flows. The analysis enforces the idea that an adaptive generation size sensitive to losses prevents undesirable packet drops in the network.

Network coding has been as a new coding paradigm that can significantly improve the throughput performance of a wireless multi-hop network. However, most previous studies either assume a fixed transmission power or do not take the impact of transmission power/rate to the network coding into consideration. Since in many scenarios, the selection of the transmission power/rate has big impact on network coding gains due to the fact the reception and overhearing probability, spatial reuse are both rely on transmission power/rate. Therefore, how to achieve high network throughput by appropriate selection of transmit power level and its corresponding packet transmit rate, network coding gain (if any) via localized network operations has been a critical issue in distributed multihop wireless networks, or alternatively, what is the best trade-off between the space-time resource (level of spatial reuse and transmission time) and the network coding gain? In this paper, our goal is to achieve the best trade-off between transmission power/rate and coding gains. Aiming at this, we propose a decentralized network coding aware power and rate control mechanism to enable each node to adjust its transmit power and data rate such that the network coding gains and the network throughput is maximized. Simulation results show that the proposed mechanism yields higher performance in network throughput as compared with existing work.

Analysis and scheduling of practical network coding in OFDMA relay networks