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Network Coding NC is a relatively recent subset of network information theory that has led to great advancements in the optimization of network throughput.
- Information Theory and Network Coding
- Network coding : fundamentals and applications
- Information Theory and Network Coding
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Information Theory and Network Coding
Network Coding NC is a relatively recent subset of network information theory that has led to great advancements in the optimization of network throughput. It involves performing operations other than mere forwarding and replication at the nodes that constitute a network. In this paper, we seek to review the developments in this field and examine the impact this has had on wireless networks, in terms of both the improvements it has made and its resulting application to various categories within wireless networking.
We look at the theory behind NC, the various NC schemes that have been proposed and utilized over the years, the emergence of applying NC at the physical layer of networks, and various selected applications of NC in wireless networks. This paper seeks to explore the concept of network coding NC , a relatively new subset of information theory, specifically within the domain of wireless networks.
Prior to the seminal paper [Ahlswede00] describing this field, the transmission of data through a network was merely viewed as a commodity flow, which is an exchange of commodities without the ability to process the commodities themselves [Bassoli13]. Network coding changed that, suggesting that operations more complicated than simple replication and transmission of data packets could be performed at the nodes that make up a given network. This lead to rapid advancements and spurred the use of new mathematical tools, in fields such as algebra, matroid theory, geometry, graph theory, combinatorics and optimization theory among others [Bassoli13].
While NC is a complicated topic to discuss without significant mathematical background, this paper is aimed towards a more casual audience and thus we will take steps to reduce the complexity of the mathematical theory discussed, while striving to still capture the various nuances within. In this introduction, we aim to give a succinct description of what NC entails, and in so doing shed light on the various characteristics defining this technology.
In order to achieve this, we provide some background regarding NC and its underlying theory in this section, discuss popular coding schemes currently in use in Section II and briefly analyze physical layer-based network coding in Section III, focusing on physical network coding PNC since it is most used in wireless networks. We then look more closely at various applications of NC in wireless networks in Section IV, challenges faced by these applications in Section V and then conclude with a summary of the information we have obtained.
Network coding is a networking technique where operations, which in practice tend to be algebraic algorithms, are performed on data as it passes through the nodes within a network. While in theory any manner of algorithm could be performed on the data at a node, current NC algorithms tend to be concerned with accumulating the various transmissions that pass through a given node.
In traditional routing networks, packets are simply cached and then forwarded to the next node downstream in the network. As such, if a routing node receives two packets from two distinct sources it will forward them sequentially, even if they are both addressed to the same destination, while queueing any others it may receive in the meantime.
This results in the node creating separate transmissions for each and every message being delivered, which results in a decrease in network efficiency. NC is used to mitigate this by merging relevant messages at the relay node, using a given encoding, then forwarding this accumulated result to the destination for decoding. In order for this to work, the destination node needs to be synchronized with the transmitting nodes, a constraint especially important when it comes to network coding done at the physical layer [Liew13] , which we shall discuss later on in Section III of this paper.
In [Ahlswede00] , which defined the beginning of NC research, a multicast session over a directed graph with lossless links was considered. The results of this paper are expressed as the max-flow min-cut theorem in network theory. Basically, if all receivers have the same min-cut from the source, then NC would allow all nodes to achieve the min-cut capacity simultaneously. This capacity would also correspond to the maximum flow rate that each receiver could get if it were the only receiving node in the network.
The simplest example that demonstrates the key idea and the benefits of NC in the multicast case is the butterfly network depicted in Figure 1. Each edge in this network can only carry a single message. Assuming we sent message A through the central link between nodes 3 and 4, then node 5 would receive message A twice and would never receive message B.
The same problem would occur at node 6 if we sent message B through the central link, with node 6 never receiving message A. We can immediately see here that routing would be insufficient to transmit both messages since no routing scheme can simultaneously transmit A and B to both sink nodes.
This is where the operation on data at relay nodes come into play; a simple linear code is demonstrated here, where A and B are encoded using their sum. From this simple example we can see that various other encoding techniques could be applied to a varying number of packets, in various network configurations.
These techniques could greatly increase the amount of information that could be transmitted in a single instance, thus significantly improving the throughput and power efficiency of networks that implement them. This result can also be applied to wireless networks with two simultaneous unicast connections as shown below:.
Figure 2: Modified wireless butterfly network [Magli13]. The modified wireless butterfly network shown in Figure 2 is different from the original butterfly network in the sense that packet transmissions can be transmitted from the source node to more than one node.
Thus, transmissions are represented using hyper-arcs, instead of arcs. We now have a brief and hopefully accessible overview of the theory behind, and the nature of network coding. In Section II we shall now look into some of the more popular coding schemes being utilized. The majority of the NC schemes in use nowadays have their basis in algebraic theory. Whereas earlier schemes, such as the traditional XOR-coding scheme and the Deterministic Linear Network Coding scheme were deterministic in nature, the more common schemes in use today are non-deterministic, meaning they are free from the constraint of having packet feedback information for every transmitted packet from all the receivers.
Here, we shall once again utilize a network model for a general communication system that consists of source, network and sink nodes connected by channels that are potentially lossy. In RLNC, coded packets are random linear combinations of the original packets over a finite field of size q [Ostovari16]. Each coded packet is in the form:. A Galois field is any field that contains a finite number of elements. Linear independence is important in ensuring uniform distribution, thus reducing redundant information being forwarded to a given node.
The smaller the field size, however, the less complex the resulting system, which is especially advantageous in wireless networks [Magli13]. Instead of transmitting the original packets, the source node generates and transmits random-coded packets over the k packets.
In order to decode the coded packets and retrieve the original packets, the destination nodes need to receive k linearly independent coded packets. They can use Gaussian elimination to decode the coded packets [Ostovari16]. As powerful as this encoding scheme is, it does have its challenges, chief among them the fact that if a receiver gets an insufficient number of packets, it is extremely unlikely that it can recover any of the original packets. This is known as the index coding problem [Qureshi12].
This can be fixed by sending additional random linear combinations until the receiver receives the required number of packets. Other challenges include the high decoding computational complexity due to using the Gauss-Jordan elimination method and the high transmission overhead due adding large coefficient vectors to encoded blocks.
Linear Network Coding LNC computational complexity makes it unsuitable for practical use in devices that operate on battery power, such as mobile phones and wireless sensors. In order to intrinsically fix the problem with RLNC detailed above, where receivers that get an insufficient number of packets cannot recover the original packets, triangular network coding was proposed in [Qureshi12].
The triangular pattern based packet coding scheme is performed in two stages. Figure 3: Triangular Pattern [Qureshi12]. The decoding process is similar to the LNC decoding process, which involves Gaussian elimination. However in this case, it is simplified since the coded packets are in a triangular pattern and as such the receiver only needs to perform back-substitution, where each row is solved, from the last row to the first row.
This is far less computationally intense and gives triangular coding the bandwidth performance of LNC, while affording the computation cost of XOR coding [Qureshi12]. In ONC, the sensor nodes can snoop on all transmissions in their neighborhood and store the overheard data packets, whether they are intended for them or not [Shen12].
As such, the sensor nodes know the overheard and routed packets that each neighboring node possesses, and can perform network coding operations based on this information. Each node has its own queue of received uncoded packets p 1 ,p 2 , The node then dequeues the first packet, p 1 and, while making sure all of next hop recipients can immediately decode the resulting combination, steps through the queue to greedily add packets for combination [Shen12]. A recipient can immediately decode a combined packet if it knows all but one uncoded packet.
We are now familiar with some of the common coding schemes in use, and can now see that most of these are geared towards packet-based networks. In wireless networks however, there are significant gains to be made at layers beside the application layer, which is where the bulk of NC is done at present.
We shall hence look at physical layer network coding in Section III. Physical-layer network coding as a concept was proposed in for application in wireless networks [Liew13]. This simple idea lead to numerous advancements, with subsequent works by various researchers leading to many new results in the domains of wireless communication, wireless information theory, and wireless networking.
We shall attempt to give a brief overview of both the theory behind this concept and the implications of the results in the three fields listed above. Interference is often treated as a destructive phenomenon in wireless communication networks today. When multiple transmitters send radio waves to their respective receivers, a receiver may receive signals from its transmitter as well as from other transmitters at the same time. The radio waves from the other transmitters are often treated as interference that corrupts the intended signal, as a result of their overlapping.
In Wi-Fi networks, for example, when multiple nodes transmit together, packet collisions can occur leading to none of the packets being received correctly. PNC takes advantage of the fact that when multiple EM waves come together within the same physical space, they add together or superimpose, thus increasing in amplitude. TWRC is a three-node linear network in which two end nodes, nodes T 1 and T 2 , want to communicate via a relay node R.
This is illustrated in Figure 4 below:. There is no direct signal path between nodes T 1 and T 2. A real-world example of such a system is a satellite network in which nodes T 1 and T 2 are the ground stations, and the relay R is the satellite.
The half-duplex constraint is often imposed on wireless communication systems to ease engineering design [Liew13]. With the half-duplex constraint, a node cannot transmit and receive at the same time. This means that each packet from node T 1 to node T 2 and similarly, each packet from node T 2 to node T 1 must use up at least two time slots to reach its destination. Thus, the best possible packet exchange throughput is two packets for every two slots, one in each direction.
We see that the use of natural network coding, through taking advantage of superimposition of waves could indeed be a major breakthrough. It is however subject to certain challenges we shall look at in the next subsection. PNC achieves this doubling of the TWRC throughput by reducing the needed time slots for the exchange of one packet from four to two [Lu12]. Unfortunately, PNC is yet to be in widespread use in wireless networks, since in a general multi-hop network, MAC-layer and network-layer issues will take on an increasingly important role, particularly with regard to the management of complexity when there are many simultaneous flows in the network [Huo16].
One of the key issues in PNC is how to deal with the asynchronies between the signals transmitted simultaneously by the two end nodes [Lu12]. Symbols transmitted by the two end nodes could potentially arrive at the receiver with symbol misalignment as well as relative carrier-phase offset.
This could result in significant penalties to performance. Reliability of transmission is also one of the challenges that face PNC. Channel coding is typically used to solve this issue, and its application to PNC is the subject of research today. With this in mind, PNC is the future of NC in wireless networks and thus it is important we understand it. Having given this overview, we shall now look at some of the applications that have been realised using NC in wireless networks in the next section.
It is unlikely that incorporating network coding at the physical layer will be practical in the near future, for a variety of reasons detailed in [Huo16]. It is however quite feasible to build network coding into overlay networks [Magli13]. In overlay networks, nodes are applications running in computers and edges are the transport-level connections between computers. Overlay networks can be infrastructure-based, as shown by content distribution networks like Akamai.
They can also be ad-hoc or peer-to-peer P2P networks of end hosts temporarily linked together to perform a particular communication task, for example file download, live broadcast, media on demand, instant messaging, conferencing, or gaming [Vukobratovic14].
Network coding : fundamentals and applications
The current rate of growth in computer network usage is a problematic issue motivates the inspiration to investigate less conventional solutions, similar to Network Coding NC which has attracted a lot of attention lately, to improve the bandwidth utilization and latency in computer networks. The objective of this paper is to show that the usage of Network coding is possible on enhancing the execution of Kurdistan Academic Network Backbone KANB to associate the primary ten urban communities in Kurdistan Region that almost contains a greater part of academic institutions. The proposed model applies peer to peer P2P multicasting on KANB, which does not require any centralized knowledge about the topology of the network. The Random Linear Network Coding RLNC has been utilized for its superior properties to address the problems of delay, throughput and lake of security associated with store-and-forward based classical networks. Simulation results point out the advantages of using network coding over the classical store and forward technique in term of improving the throughput gain and latency reduction. Hawler city the capital and greatest city in Kurdistan Region have been chosen as a source node while Slemani city has been elected as a sink, node. Thus, Network coding is applied at intermediate nodes.
Network coding is a relatively new cross-disciplined research area. It involves the areas of coding theorem, information theory, graph theory and networking. New applications of network coding have been emerging substantially for the recent years in the area of wireless communications, internetworking, content distribution, security, storage etc. The basic idea of network coding is to allow nodes in a network to compute functions of their incoming information messages before transmitting them further. Thus it is more general than routing which is currently the dominant network information transfer paradigm. It turns out that the use of network coding can provably improve network throughput and robustness.
PDF | Network coding is an elegant and novel technique introduced A companion issue deals primarily with applications of network coding.
Information Theory and Network Coding
Network coding is an elegant and novel technique introduced at the turn of the millennium to improve network throughput and performance. It is expected to be a critical technology for networks of the future. This tutorial addresses the first most natural questions one would ask about this new technique: how network coding works and what are its benefits, how network codes are designed and how much it costs to deploy networks implementing such codes, and finally, whether there are methods to deal with cycles and delay that are present in all real networks. A companion issue deals primarily with applications of network coding. Network Coding Fundamentals reviews the basic techniques with emphasis on multicasting over error free links.
Network coding is a field of information and coding theory and is a method of attaining maximum information flow in a network. This book is an ideal introduction for the communications and network engineer, working in research and development, who needs an intuitive introduction to network coding and to the increased performance and reliability it offers in many applications. This book is an ideal introduction for the research and development communications and network engineer who needs an intuitive introduction to the theory and wishes to understand the increased performance and reliability it offers over a number of applications.
Download the man7. The following courses are all available for onsite delivery, and in some cases are scheduled as public courses. Tailored versions of the above courses are also available for courses delivered onsite.
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For a long time, store-and-forward had been the transport mode in network communications. In other words, information had been regarded as a commodity that only needs to be routed through the network, possibly with replication at the intermediate nodes. Under the paradigm of network coding, information can be processed within the network for the purpose of transmission. It was demonstrated that compared with store-and-forward, the network throughput can generally be increased by employing network coding. Since then, network coding has made significant impact on different branches of information science. The impact of network coding has gone as far as mathematics, physics, and biology. This expository work aims to be an introduction to this fast-growing subject with a detailed discussion of the basic theoretical results.
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Network Coding Fundamentals
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