Linear network coding explained

In computer networking, linear network coding is a program in which intermediate nodes transmit data from source nodes to sink nodes by means of linear combinations.

Linear network coding may be used to improve a network's throughput, efficiency, and scalability, as well as reducing attacks and eavesdropping. The nodes of a network take several packets and combine for transmission. This process may be used to attain the maximum possible information flow in a network.

It has been proven that, theoretically, linear coding is enough to achieve the upper bound in multicast problems with one source.^[1] However linear coding is not sufficient in general; even for more general versions of linearity such as convolutional coding and filter-bank coding.^[2] Finding optimal coding solutions for general network problems with arbitrary demands is a hard problem, which can be NP-hard^{[3] [4]} and even undecidable.^{[5] [6]}

Encoding and decoding

In a linear network coding problem, a group of nodes

P are involved in moving the data from S source nodes to K sink nodes. Each node generates new packets which are linear combinations of past received packets by multiplying them by coefficients chosen from a finite field, typically of size GF( 2 ^{s)} .

More formally, each node,

p _{k} with indegree, InDeg(p _{k)} = S , generates a message X _{k} from the linear combination of received messages \{M _{i\}} ^{S} ^{i =1} by the formula:X _{k} = \sum ^{S} _{i =1} g ^{i ⋅} _{k} M _{i} Where the values g ^{i} _{k} are coefficients selected from GF( 2 ^{s)} . Since operations are computed in a finite field, the generated message is of the same length as the original messages. Each node forwards the computed value X _{k} along with the coefficients, g ^{i} _{k} , used in the k ^{th} level, g ^{i} _{k} .

Sink nodes receive these network coded messages, and collect them in a matrix. The original messages can be recovered by performing Gaussian elimination on the matrix.^[7] In reduced row echelon form, decoded packets correspond to the rows of the form

e _{i=[0} ... 0 1 0 ... 0 ]

Background

l{G}=(V, E, C) . V is the set of nodes or vertices, E is the set of directed links (or edges), and C gives the capacity of each link of E . Let T(s, t) be the maximum possible throughput from node s to node t . By the max-flow min-cut theorem, T(s, t) is upper bounded by the minimum capacity of all cuts, which is the sum of the capacities of the edges on a cut, between these two nodes.

Karl Menger proved that there is always a set of edge-disjoint paths achieving the upper bound in a unicast scenario, known as the max-flow min-cut theorem. Later, the Ford–Fulkerson algorithm was proposed to find such paths in polynomial time. Then, Edmonds proved in the paper "Edge-Disjoint Branchings" the upper bound in the broadcast scenario is also achievable, and proposed a polynomial time algorithm.

However, the situation in the multicast scenario is more complicated, and in fact, such an upper bound can't be reached using traditional routing ideas. Ahlswede et al. proved that it can be achieved if additional computing tasks (incoming packets are combined into one or several outgoing packets) can be done in the intermediate nodes.^[8]

The Butterfly Network

The butterfly network^[8] is often used to illustrate how linear network coding can outperform routing. Two source nodes (at the top of the picture) have information A and B that must be transmitted to the two destination nodes (at the bottom). Each destination node wants to know both A and B. Each edge can carry only a single value (we can think of an edge transmitting a bit in each time slot).

If only routing were allowed, then the central link would be only able to carry A or B, but not both. Supposing we send A through the center; then the left destination would receive A twice and not know B at all. Sending B poses a similar problem for the right destination. We say that routing is insufficient because no routing scheme can transmit both A and B to both destinations simultaneously. Meanwhile, it takes four time slots in total for both destination nodes to know A and B.

Using a simple code, as shown, A and B can be transmitted to both destinations simultaneously by sending the sum of the symbols through the two relay nodes – encoding A and B using the formula "A+B". The left destination receives A and A + B, and can calculate B by subtracting the two values. Similarly, the right destination will receive B and A + B, and will also be able to determine both A and B. Therefore, with network coding, it takes only three time slots and improves the throughput.

Random Linear Network Coding

Random linear network coding^[9] (RLNC) is a simple yet powerful encoding scheme, which in broadcast transmission schemes allows close to optimal throughput using a decentralized algorithm. Nodes transmit random linear combinations of the packets they receive, with coefficients chosen randomly, with a uniform distribution from a Galois field. If the field size is sufficiently large, the probability that the receiver(s) will obtain linearly independent combinations (and therefore obtain innovative information) approaches 1. It should however be noted that, although random linear network coding has excellent throughput performance, if a receiver obtains an insufficient number of packets, it is extremely unlikely that they can recover any of the original packets. This can be addressed by sending additional random linear combinations until the receiver obtains the appropriate number of packets.

Operation and key parameters

There are three key parameters in RLNC. The first one is the generation size. In RLNC, the original data transmitted over the network is divided into packets. The source and intermediate nodes in the network can combine and recombine the set of original and coded packets. The original

M packets form a block, usually called a generation. The number of original packets combined and recombined together is the generation size. The second parameter is the packet size. Usually, the size of the original packets is fixed. In the case of unequally-sized packets, these can be zero-padded if they are shorter or split into multiple packets if they are longer. In practice, the packet size can be the size of the maximum transmission unit (MTU) of the underlying network protocol. For example, it can be around 1500 bytes in an Ethernet frame. The third key parameter is the Galois field used. In practice, the most commonly used Galois fields are binary extension fields. And the most commonly used sizes for the Galois fields are the binary field GF( 2 ) and the so-called binary-8 (GF( 2 ^{8)} ). In the binary field, each element is one bit long, while in the binary-8, it is one byte long. Since the packet size is usually larger than the field size, each packet is seen as a set of elements from the Galois field (usually referred to as symbols) appended together. The packets have a fixed amount of symbols (Galois field elements), and since all the operations are performed over Galois fields, then the size of the packets does not change with subsequent linear combinations.

The sources and the intermediate nodes can combine any subset of the original and previously coded packets performing linear operations. To form a coded packet in RLNC, the original and previously coded packets are multiplied by randomly chosen coefficients and added together. Since each packet is just an appended set of Galois field elements, the operations of multiplication and addition are performed symbol-wise over each of the individual symbols of the packets, as shown in the picture from the example.

To preserve the statelessness of the code, the coding coefficients used to generate the coded packets are appended to the packets transmitted over the network. Therefore, each node in the network can see what coefficients were used to generate each coded packet. One novelty of linear network coding over traditional block codes is that it allows the recombination of previously coded packets into new and valid coded packets. This process is usually called recoding. After a recoding operation, the size of the appended coding coefficients does not change. Since all the operations are linear, the state of the recoded packet can be preserved by applying the same operations of addition and multiplication to the payload and the appended coding coefficients. In the following example, we will illustrate this process.

Any destination node must collect enough linearly independent coded packets to be able to reconstruct the original data. Each coded packet can be understood as a linear equation where the coefficients are known since they are appended to the packet. In these equations, each of the original

M packets is the unknown. To solve the linear system of equations, the destination needs at least M linearly independent equations (packets).

Example

In the figure, we can see an example of two packets linearly combined into a new coded packet. In the example, we have two packets, namely packet

f and packet e . The generation size of our example is two. We know this because each packet has two coding coefficients (C _{ij} ) appended. The appended coefficients can take any value from the Galois field. However, an original, uncoded data packet would have appended the coding coefficients [ 0 , 1 ] or [ 1 , 0 ] , which means that they are constructed by a linear combination of zero times one of the packets plus one time the other packet. Any coded packet would have appended other coefficients. In our example, packet f for instance has appended the coefficients [C _{11} ,C _{12} ] . Since network coding can be applied at any layter of the communication protocol, these packets can have a header from the other layers, which is ignored in the network coding operations.

Now, lets assume that the network node wants to produce a new coded packet combining packet

f and packet e . In RLNC, it will randomly choose two coding coefficients, d _{1} and d _{2} in the example. The node will multiply each symbol of packet f by d _{1} , and each symbol of packet e by d _{2} . Then, it will add the results symbol-wise to produce the new coded data. It will perform the same operations of multiplication and addition to the coding coefficients of the coded packets.

Misconceptions

Linear network coding is still a relatively new subject. However, the topic has been vastly researched over the last twenty years. Nevertheless, there are still some misconceptions that are no longer valid:

Decoding computational complexity: Network coding decoders have been improved over the years. Nowadays, the algorithms are highly efficient and parallelizable. In 2016, with Intel Core i5 processors with SIMD instructions enabled, the decoding goodput of network coding was 750 MB/s for a generation size of 16 packets and 250 MB/s for a generation size of 64 packets.^[10] Furthermore, today's algorithms can be vastly parallelizable, increasing the encoding and decoding goodput even further.^[11]

Transmission Overhead: It is usually thought that the transmission overhead of network coding is high due to the need to append the coding coefficients to each coded packet. In reality, this overhead is negligible in most applications. The overhead due to coding coefficients can be computed as follows. Each packet has appended

M coding coefficients. The size of each coefficient is the number of bits needed to represent one element of the Galois field. In practice, most network coding applications use a generation size of no more than 32 packets per generation and Galois fields of 256 elements (binary-8). With these numbers, each packet needs M * log _{2(s)} = 32 bytes of appended overhead. If each packet is 1500 bytes long (i.e. the Ethernet MTU), then 32 bytes represent an overhead of only 2%.Overhead due to linear dependencies: Since the coding coefficients are chosen randomly in RLNC, there is a chance that some transmitted coded packets are not beneficial to the destination because they are formed using a linearly dependent combination of packets. However, this overhead is negligible in most applications. The linear dependencies depend on the Galois fields' size and are practically independent of the generation size used. We can illustrate this with the following example. Let us assume we are using a Galois field of q elements and a generation size of M packets. If the destination has not received any coded packet, we say it has M degrees of freedom, and then almost any coded packet will be useful and innovative. In fact, only the zero-packet (only zeroes in the coding coefficients) will be non-innovative. The probability of generating the zero-packet is equal to the probability of each of the M coding coefficient to be equal to the zero-element of the Galois field. I.e., the probability of a non-innovative packet is of (1)/(q ^{M}) . With each successive innovative transmission, it can be shown that the exponent of the probability of a non innovative packet is reduced by one. When the destination has received M -1 innovative packets (i.e., it needs only one more packet to fully decode the data). Then the probability of a non innovative packet is of (1)/(q) . We can use this knowledge to calculate the expected number of linearly dependent packets per generation. In the worst-case scenario, when the Galois field used contains only two elements (q =2 ), the expected number of linearly dependent packets per generation is of 1.6 extra packets. If our generation size if of 32 or 64 packets, this represents an overhead of 5% or 2.5%, respectively. If we use the binary-8 field (q =256 ), then the expected number of linearly dependent packets per generation is practically zero. Since it is the last packets the major contributor to the overhead due to linear dependencies, there are RLNC-based protocols such as tunable sparse network coding^[12] that exploit this knowledge. These protocols introduce sparsity (zero-elements) in the coding coefficients at the beginning of the transmission to reduce the decoding complexity, and reduce the sparsity at the end of the transmission to reduce the overhead due to linear dependencies.

Applications

Over the years, multiple researchers and companies have integrated network coding solutions into their applications.^[13] We can list some of the applications of network coding in different areas:

• VoIP:^[14] The performance of streaming services such as VoIP over wireless mesh networks can be improved with network coding by reducing the network delay and jitter.
• Video^[15] and audio^[16] streaming and conferencing:^{[17] [18]} The performance of MPEG-4 traffic in terms of delay, packet loss, and jitter over wireless networks prone to packet erasures can be improved with RLNC. In the case of audio streaming over wireless mesh networks, the packet delivery ratio, latency, and jitter performance of the network can be significantly increased when using RLNC instead of packet forwarding-based protocols such as simplified multicast forwarding and partial dominant pruning. The performance improvements of network coding for video conferencing are not only theoretical. In 2016, the authors of built a real-world testbed of 15 wireless Android devices to evaluate the feasibility of network-coding-based video conference systems. Their results showed large improvements in packet delivery ratio and overall user experience, especially over poor quality links compared to multicasting technologies based on packet forwarding.
• Software-defined wide area networks (SD-WAN):^{[19] [20] [21] [22]} Large industrial IoT wireless networks can benefit from network coding. Researchers showed that network coding and its channel bundling capabilities improved the performance of SD-WANs with a large number of nodes with multiple cellular connections. Nowadays, companies such as Barracuda are employing RLNC-based solutions due to their advantages in low latency, small footprint on computing devices, and low overhead.
• Channel bundling:^[23] Due to the statelessness characteristics of RLNC, it can be used to efficiently perform channel bundling, i.e., the transmission of information through multiple network interfaces. Since the coded packets are randomly generated, and the state of the code traverses the network together with the coded packets, a source can achieve bundling without much planning just by sending coded packets through all its network interfaces. The destination can decode the information once enough coded packets arrive, irrespectively of the network interface. A video demonstrating the channel bundling capabilities of RLNC is available at.
• 5G private networks:^{[24] [25]} RLNC can be integrated into the 5G NR standard to improve the performance of video delivery over 5G systems. In 2018, a demo presented at the Consumer Electronics Show demonstrated a practical deployment of RLNC with NFV and SDN technologies to improve video quality against packet loss due to congestion at the core network.
• Remote collaboration.^[26]
• Augmented reality remote support and training.^[27]
• Remote vehicle driving applications.^{[28] [29] [30] [31]}
• Connected cars networks.^{[32] [33]}
• Gaming applications such as low latency streaming and multiplayer connectivity.^{[34] [35] [36]}
• Healthcare applications.^{[37] [38] [39]}
• Industry 4.0.^{[40] [41] [42]}
• Satellite networks.^[43]
• Agricultural sensor fields.^{[44] [45]}
• In-flight entertainment networks.^[46]
• Major security and firmware updates for mobile product families.^{[47] [48]}
• Smart city infrastructure.^[49]
• Information-centric networking and named data networking.:^[50] Linear network coding can improve the network efficiency of information-centric networking solutions by exploiting the multi-source multi-cast nature of such systems. It has been shown, that RLNC can be integrated into distributed content delivery networks such as IPFS to increase data availability while reducing storage resources.^[51]
• Alternative to forward error correction and automatic repeat requests in traditional and wireless networks with packet loss, such as Coded TCP^[52] and Multi-user ARQ^[53]
• Protection against network attacks such as snooping, eavesdropping, replay, or data corruption.^{[54] [55]}
• Digital file distribution and P2P file sharing, e.g. Avalanche filesystem from Microsoft
• Distributed storage^{[56] [57]}
• Throughput increase in wireless mesh networks, e.g.: COPE,^[58] CORE,^[59] Coding-aware routing,^[60] and B.A.T.M.A.N.^[61]
• Buffer and delay reduction in spatial sensor networks: Spatial buffer multiplexing^[62]
• Wireless broadcast: RLNC can reduce the number of packet transmission for a single-hop wireless multicast network, and hence improve network bandwidth^[63]
• Distributed file sharing^[64]
• Low-complexity video streaming to mobile device^[65]
• Device-to-device extensions^{[66] [67] [68] [69] [70]}

See also

• Secret sharing protocol
• Homomorphic signatures for network coding
• Triangular network coding

References

• Fragouli, C.; Le Boudec, J. & Widmer, J. "Network coding: An instant primer" in Computer Communication Review, 2006. https://doi.org/10.1145/1111322.1111337
• Ali Farzamnia, Sharifah K. Syed-Yusof, Norsheila Fisa "Multicasting Multiple Description Coding Using p-Cycle Network Coding", KSII Transactions on Internet and Information Systems, Vol 7, No 12, 2013.

External links

• Network Coding Homepage
• A network coding bibliography
• Raymond W. Yeung, Information Theory and Network Coding, Springer 2008, http://iest2.ie.cuhk.edu.hk/~whyeung/book2/
• Raymond W. Yeung et al., Network Coding Theory, now Publishers, 2005, http://iest2.ie.cuhk.edu.hk/~whyeung/netcode/monograph.html
• Christina Fragouli et al., Network Coding: An Instant Primer, ACM SIGCOMM 2006, http://infoscience.epfl.ch/getfile.py?mode=best&recid=58339.
• Avalanche Filesystem, http://research.microsoft.com/en-us/projects/avalanche/default.aspx
• Random Network Coding, https://web.archive.org/web/20060618083034/http://www.mit.edu/~medard/coding1.htm
• Digital Fountain Codes, http://www.icsi.berkeley.edu/~luby/
• Coding-Aware Routing, https://web.archive.org/web/20081011124616/http://arena.cse.sc.edu/papers/rocx.secon06.pdf
• MIT offers a course: Introduction to Network Coding
• Network coding: Networking's next revolution?
• Coding-aware protocol design for wireless networks: http://scholarcommons.sc.edu/etd/230/

Notes and References

1. S. Li, R. Yeung, and N. Cai, "Linear Network Coding"(PDF), in IEEE Transactions on Information Theory, Vol 49, No. 2, pp. 371–381, 2003
2. R. Dougherty, C. Freiling, and K. Zeger, "Insufficiency of Linear Coding in Network Information Flow" (PDF), in IEEE Transactions on Information Theory, Vol. 51, No. 8, pp. 2745-2759, August 2005 (erratum)
3. Rasala Lehman. A.. Complexity classification of network information flow problems. Lehman. E.. 15th ACM-SIAM SODA. 2004. 142–150.
4. Langberg. M.. The encoding complexity of network coding. Sprintson. A.. Bruck. J.. IEEE Transactions on Information Theory. 2006. 52. 6. 2386–2397. 10.1109/TIT.2006.874434. 1414385 .
5. Li. C. T.. Undecidability of Network Coding, Conditional Information Inequalities, and Conditional Independence Implication. IEEE Transactions on Information Theory. 2023. 69 . 6 . 1 . 10.1109/TIT.2023.3247570. 2205.11461 . 248986512 .
6. Kühne. L.. Representability of Matroids by c-Arrangements is Undecidable. Yashfe. G.. Israel Journal of Mathematics. 2022. 252 . 95–147. 10.1007/s11856-022-2345-z. 1912.06123 . 209324252 .
7. .
8. Rudolf. Ahlswede. Rudolf Ahlswede. N. Cai . S.-Y. R. Li . R. W. Yeung . Network Information Flow. IEEE Transactions on Information Theory. 1204–1216. 2000. 10.1109/18.850663. 46. 4. 10.1.1.722.1409.
9. T. Ho, R. Koetter, M. Médard, D. R. Karger and M. Effros, "The Benefits of Coding over Routing in a Randomized Setting" in 2003 IEEE International Symposium on Information Theory.
10. Book: Sørensen . Chres W. . Paramanathan . Achuthan . Cabrera . Juan A. . Pedersen . Morten V. . Lucani . Daniel E. . Fitzek . Frank H.P. . 2016 IEEE Wireless Communications and Networking Conference . Leaner and meaner: Network coding in SIMD enabled commercial devices . April 2016 . https://www.researchgate.net/publication/314198052 . 1–6 . 10.1109/WCNC.2016.7565066. 978-1-4673-9814-5 . 10468008 . https://web.archive.org/web/20220408093330/https://www.researchgate.net/profile/Chres-Sorensen/publication/314198052_Leaner_and_Meaner_Network_Coding_in_SIMD_Enabled_Commercial_Devices/links/5a008b894585159634bafaa8/Leaner-and-Meaner-Network-Coding-in-SIMD-Enabled-Commercial-Devices.pdf . 2022-04-08 .
11. Wunderlich . Simon . Cabrera . Juan A. . Fitzek . Frank H. P. . Reisslein . Martin . August 2017 . Network Coding in Heterogeneous Multicore IoT Nodes With DAG Scheduling of Parallel Matrix Block Operations . IEEE Internet of Things Journal . 4 . 4 . 917–933 . 10.1109/JIOT.2017.2703813 . 30243498 . 2327-4662 . https://web.archive.org/web/20220408140133/https://faculty.engineering.asu.edu/mre/wp-content/uploads/sites/31/2020/04/NCMC.pdf . 8 Apr 2022.
12. Book: Feizi . Soheil . Lucani . Daniel E. . Sørensen . Chres W. . Makhdoumi . Ali . Médard . Muriel . 2014 International Symposium on Network Coding (NetCod) . Tunable sparse network coding for multicast networks . June 2014 . https://ieeexplore.ieee.org/document/6892129 . 1–6 . 10.1109/NETCOD.2014.6892129. 978-1-4799-6217-4 . 18256950 .
13. Web site: Coding the Network: Next Generation Coding for Flexible Network Operation IEEE Communications Society . 2022-06-06 . www.comsoc.org.
14. Book: Lopetegui . I. . Carrasco . R.A. . Boussakta . S. . 2010 7th International Symposium on Communication Systems, Networks & Digital Signal Processing (CSNDSP 2010) . VoIP design and implementation with network coding schemes for wireless networks . July 2010 . https://ieeexplore.ieee.org/document/5580304 . Newcastle upon Tyne . IEEE . 857–861 . 10.1109/CSNDSP16145.2010.5580304 . 978-1-4244-8858-2. 1761089 .
15. Book: Shrimali . R. . Narmawala . Z. . 2012 Nirma University International Conference on Engineering (NUiCONE) . A survey on MPEG-4 streaming using network coding in wireless networks . December 2012 . https://ieeexplore.ieee.org/document/6493203 . 1–5 . 10.1109/NUICONE.2012.6493203. 978-1-4673-1719-1 . 7791774 .
16. Book: Saeed . Basil . Lung . Chung-Horng . Kunz . Thomas . Srinivasan . Anand . 2011 IFIP Wireless Days (WD) . Audio streaming for ad hoc wireless mesh networks using network coding . October 2011 . https://ieeexplore.ieee.org/document/6098167 . 1–5 . 10.1109/WD.2011.6098167. 978-1-4577-2028-4 . 8052927 .
17. Wang . Lei . Yang . Zhen . Xu . Lijie . Yang . Yuwang . July 2016 . NCVCS: Network-coding-based video conference system for mobile devices in multicast networks . Ad Hoc Networks . en . 45 . 13–21 . 10.1016/j.adhoc.2016.03.002.
18. Book: Wang . Hui . Chang . Ronald Y. . Kuo . C.-C. Jay . 2009 IEEE International Conference on Multimedia and Expo . Wireless Multi-party video conferencing with network coding . June 2009 . https://ieeexplore.ieee.org/document/5202786 . 1492–1495 . 10.1109/ICME.2009.5202786. 978-1-4244-4290-4 . 8234088 .
19. Book: Rachuri . Sri Pramodh . Ansari . Ahtisham Ali . Tandur . Deepaknath . Kherani . Arzad A. . Chouksey . Sameer . 2019 International Conference on contemporary Computing and Informatics (IC3I) . Network-Coded SD-WAN in Multi-Access Systems for Delay Control . December 2019 . https://ieeexplore.ieee.org/document/9055565 . Singapore, Singapore . IEEE . 32–37 . 10.1109/IC3I46837.2019.9055565 . 978-1-7281-5529-6. 215723197 .
20. Book: Ansari . Ahtisham Ali . Rachuri . Sri Pramodh . Kherani . Arzad A. . Tandur . Deepaknath . 2019 IEEE International Conference on Advanced Networks and Telecommunications Systems (ANTS) . An SD-WAN Controller for Delay Jitter Minimization in Coded Multi-access Systems . December 2019 . https://ieeexplore.ieee.org/document/9117981 . 1–6 . 10.1109/ANTS47819.2019.9117981 . 978-1-7281-3715-5 . 219853700.
21. Web site: Steinwurf's next-gen FECs aren't a choice for SD-WAN, they're an imperative. . 2022-06-06 . www.linkedin.com . en.
22. Web site: Barracuda Networks optimizes SD-WAN traffic with patented erasure correction technology from Steinwurf . 2022-06-06 . Steinwurf . en-GB.
23. Book: Pedersen . Morten V. . Lucani . Daniel E. . Fitzek . Frank H. P. . Sorensen . Chres W. . Badr . Arash S. . 2013 IEEE Information Theory Workshop (ITW) . Network coding designs suited for the real world: What works, what doesn't, what's promising . September 2013 . https://ieeexplore.ieee.org/document/6691231 . Sevilla . IEEE . 1–5 . 10.1109/ITW.2013.6691231 . 978-1-4799-1321-3. 286822 .
24. Vukobratovic . Dejan . Tassi . Andrea . Delic . Savo . Khirallah . Chadi . April 2018 . Random Linear Network Coding for 5G Mobile Video Delivery . Information . en . 9 . 4 . 72 . 1802.04873 . 10.3390/info9040072 . 2078-2489. free .
25. Book: Gabriel . Frank . Nguyen . Giang T. . Schmoll . Robert-Steve . Cabrera . Juan A. . Muehleisen . Maciej . Fitzek . Frank H.P. . 2018 15th IEEE Annual Consumer Communications & Networking Conference (CCNC) . Practical deployment of network coding for real-time applications in 5G networks . January 2018 . https://ieeexplore.ieee.org/document/8319320 . Las Vegas, NV . IEEE . 1–2 . 10.1109/CCNC.2018.8319320 . 978-1-5386-4790-5. 3982619 .
26. Magli . Enrico . Wang . Mea . Frossard . Pascal . Markopoulou . Athina . August 2013 . Network Coding Meets Multimedia: A Review . IEEE Transactions on Multimedia . 15 . 5 . 1195–1212 . 10.1109/TMM.2013.2241415 . 1211.4206 . 3200945 . 1520-9210.
27. Torres Vega . Maria . Liaskos . Christos . Abadal . Sergi . Papapetrou . Evangelos . Jain . Akshay . Mouhouche . Belkacem . Kalem . Gökhan . Ergüt . Salih . Mach . Marian . Sabol . Tomas . Cabellos-Aparicio . Albert . October 2020 . Immersive Interconnected Virtual and Augmented Reality: A 5G and IoT Perspective . Journal of Network and Systems Management . en . 28 . 4 . 796–826 . 10.1007/s10922-020-09545-w . 2117/330129 . 219589307 . 1064-7570. free .
28. Book: De Jonckere . Olivier . Chorin . Jean . Feldmann . Marius . 2017 6th International Conference on Space Mission Challenges for Information Technology (SMC-IT) . Simulation Environment for Network Coding Research in Ring Road Networks . September 2017 . https://ieeexplore.ieee.org/document/8227552 . Alcala de Henares . IEEE . 128–131 . 10.1109/SMC-IT.2017.29 . 978-1-5386-3462-2. 6180560 .
29. Jamil . Farhan . Javaid . Anam . Umer . Tariq . Rehmani . Mubashir Husain . November 2017 . A comprehensive survey of network coding in vehicular ad-hoc networks . Wireless Networks . en . 23 . 8 . 2395–2414 . 10.1007/s11276-016-1294-z . 13624914 . 1022-0038.
30. Park . Joon-Sang . Lee . Uichin . Gerla . Mario . May 2010 . Vehicular communications: emergency video streams and network coding . Journal of Internet Services and Applications . en . 1 . 1 . 57–68 . 10.1007/s13174-010-0006-7 . 2143201 . 1867-4828. free .
31. Noor-A-Rahim . Md . Liu . Zilong . Lee . Haeyoung . Khyam . M. Omar . He . Jianhua . Pesch . Dirk . Moessner . Klaus . Saad . Walid . Poor . H. Vincent . 2022-05-01 . 6G for Vehicle-to-Everything (V2X) Communications: Enabling Technologies, Challenges, and Opportunities . cs.IT . 2012.07753.
32. Book: Achour . Imen . Bejaoui . Tarek . Busson . Anthony . Tabbane . Sami . 2017 IEEE International Conference on Communications Workshops (ICC Workshops) . Network Coding scheme behavior in a Vehicle-to-Vehicle safety message dissemination . October 2017 . https://ieeexplore.ieee.org/document/7962697 . Paris, France . IEEE . 441–446 . 10.1109/ICCW.2017.7962697 . 978-1-5090-1525-2. 22423560 .
33. Wang . Shujuan . Lu . Shuguang . Zhang . Qian . April 2019 . Instantly decodable network coding–assisted data dissemination for prioritized services in vehicular ad hoc networks . International Journal of Distributed Sensor Networks . en . 15 . 4 . 155014771984213 . 10.1177/1550147719842137 . 145983739 . 1550-1477. free .
34. Dammak . Marwa . Andriyanova . Iryna . Boujelben . Yassine . Sellami . Noura . 2018-03-29 . Routing and Network Coding over a Cyclic Network for Online Video Gaming . cs.IT . 1803.11102 .
35. Book: Lajtha . Balázs . Biczók . Gergely . Szabó . Róbert . Networked Services and Applications - Engineering, Control and Management . Enabling P2P Gaming with Network Coding . 2010 . Aagesen . Finn Arve . Knapskog . Svein Johan . Lecture Notes in Computer Science . 6164 . en . Berlin, Heidelberg . Springer . 76–86 . 10.1007/978-3-642-13971-0_8 . 978-3-642-13971-0. free .
36. Network coding application for online games platformes . Université de Cergy Pontoise; École nationale d'ingénieurs de Sfax (Tunisie) . 2018-11-20 . phdthesis . en . Marwa . Dammak.
37. Book: Sensor networks for sustainable development . 2014 . Mohammad . Ilyas . Sami S. . Alwakeel . Mohammed M. . Alwakeel . el-Hadi M. . Aggoune . 978-1-4665-8207-1 . Boca Raton, FL . Exploiting Network Coding for Smart Healthcare . 10.1201/b17124-13 . 881429695 . https://www.taylorfrancis.com/chapters/edit/10.1201/b17124-13/exploiting-network-coding-smart-healthcare-elli-kartsakli-angelos-antonopoulos-christos-verikoukis.
38. Kartsakli . Elli . Antonopoulos . Angelos . Alonso . Luis . Verikoukis . Christos . 2014-03-10 . A Cloud-Assisted Random Linear Network Coding Medium Access Control Protocol for Healthcare Applications . Sensors . en . 14 . 3 . 4806–4830 . 10.3390/s140304806 . 1424-8220 . 4003969 . 24618727. 2014Senso..14.4806K . free .
39. Book: Taparugssanagorn . Attaphongse . Ono . Fumie . Kohno . Ryuji . 2010 IEEE 21st International Symposium on Personal, Indoor and Mobile Radio Communications Workshops . Network coding for non-invasive Wireless Body Area Networks . September 2010 . https://ieeexplore.ieee.org/document/5670413 . 134–138 . 10.1109/PIMRCW.2010.5670413. 978-1-4244-9117-9 . 25872472 .
40. Book: Peralta . Goiuri . Iglesias-Urkia . Markel . Barcelo . Marc . Gomez . Raul . Moran . Adrian . Bilbao . Josu . 2017 IEEE International Workshop of Electronics, Control, Measurement, Signals and their Application to Mechatronics (ECMSM) . Fog computing based efficient IoT scheme for the Industry 4.0 . May 2017 . https://ieeexplore.ieee.org/document/7945879 . Donostia, San Sebastian, Spain . IEEE . 1–6 . 10.1109/ECMSM.2017.7945879 . 978-1-5090-5582-1. 37985560 .
41. Peralta . Goiuri . Garrido . Pablo . Bilbao . Josu . Agüero . Ramón . Crespo . Pedro . 2019-04-08 . On the Combination of Multi-Cloud and Network Coding for Cost-Efficient Storage in Industrial Applications . Sensors . en . 19 . 7 . 1673 . 10.3390/s19071673 . 1424-8220 . 6479523 . 30965629. 2019Senso..19.1673P . free .
42. Book: Zverev . Mihail . Agüero . Ramón . Garrido . Pablo . Bilbao . Josu . Proceedings of the 9th International Conference on the Internet of Things . Network Coding for IIoT Multi-Cloud Environments . 2019-10-22 . https://doi.org/10.1145/3365871.3365903 . IoT 2019 . New York, NY, USA . Association for Computing Machinery . 1–4 . 10.1145/3365871.3365903 . 978-1-4503-7207-7. 207940281 .
43. Web site: DLR - Institute of Communications and Navigation - NEXT - Network Coding Satellite Experiment . 2022-06-06 . www.dlr.de.
44. Book: Hsu . Hsiao-Tzu . Wang . Tzu-Ming . Kuo . Yuan-Cheng . Proceedings of the 2018 2nd International Conference on Education and E-Learning . Implementation of Agricultural Monitoring System Based on the Internet of Things . 2018-11-05 . https://doi.org/10.1145/3291078.3291098 . ICEEL 2018 . New York, NY, USA . Association for Computing Machinery . 212–216 . 10.1145/3291078.3291098 . 978-1-4503-6577-2. 59337140 .
45. Camilli . Alberto . Cugnasca . Carlos E. . Saraiva . Antonio M. . Hirakawa . André R. . Corrêa . Pedro L. P. . 2007-08-01 . From wireless sensors to field mapping: Anatomy of an application for precision agriculture . Computers and Electronics in Agriculture . Precision Agriculture in Latin America . en . 58 . 1 . 25–36 . 10.1016/j.compag.2007.01.019 . 0168-1699.
46. US8401021B2. Systems and methods for prioritizing wireless communication of aircraft. 2013-03-19. Buga. Trent. Wladyslaw Jan. Tracy Raymond.
47. Book: Tonyali . Samet . Akkaya . Kemal . Saputro . Nico . Cheng . Xiuzhen . Xiuzhen Cheng . 2017 26th International Conference on Computer Communication and Networks (ICCCN) . An Attribute & Network Coding-Based Secure Multicast Protocol for Firmware Updates in Smart Grid AMI Networks . July 2017 . https://ieeexplore.ieee.org/document/8038415 . Vancouver, BC, Canada . IEEE . 1–9 . 10.1109/ICCCN.2017.8038415 . 978-1-5090-2991-4. 25131878 .
48. Book: Jalil . Syed Qaisar . Chalup . Stephan . Rehmani . Mubashir Husain . Smart Grid and Internet of Things . A Smart Meter Firmware Update Strategy Through Network Coding for AMI Network . 2019 . Pathan . Al-Sakib Khan . Fadlullah . Zubair Md. . Guerroumi . Mohamed . https://link.springer.com/chapter/10.1007/978-3-030-05928-6_7 . Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering . 256 . en . Cham . Springer International Publishing . 68–77 . 10.1007/978-3-030-05928-6_7 . 978-3-030-05928-6. 59561476 .
49. Book: Kumar . Vaibhav . Cardiff . Barry . Flanagan . Mark F. . 2017 IEEE 28th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC) . Physical-layer network coding with multiple antennas: An enabling technology for smart cities . October 2017 . https://ieeexplore.ieee.org/document/8292785 . Montreal, QC . IEEE . 1–6 . 10.1109/PIMRC.2017.8292785 . 10197/11114 . 978-1-5386-3529-2. 748535 . free .
50. Bilal, Muhammad . etal . 2019 . Network-Coding Approach for Information-Centric Networking . IEEE Systems Journal . 13 . 2 . 1376–1385 . 1808.00348 . 2019ISysJ..13.1376B . 10.1109/JSYST.2018.2862913 . 51894197.
51. Book: Zimmermann . Sandra . Rischke . Justus . Cabrera . Juan A. . Fitzek . Frank H. P. . GLOBECOM 2020 - 2020 IEEE Global Communications Conference . Journey to MARS: Interplanetary Coding for relieving CDNS . December 2020 . https://ieeexplore.ieee.org/document/9322478 . Taipei, Taiwan . IEEE . 1–6 . 10.1109/GLOBECOM42002.2020.9322478 . 978-1-7281-8298-8. 231725197 .
52. 1212.2291. Kim. Minji. Network Coded TCP (CTCP). cs.NI. 2012.
53. Book: Larsson . P. . Johansson . N. . 2006 IEEE 63rd Vehicular Technology Conference . Multi-User ARQ . 2006 . https://ieeexplore.ieee.org/document/1683207 . Melbourne, Australia . IEEE . 4 . 2052–2057 . 10.1109/VETECS.2006.1683207. 0-7803-9392-9 . 38823300 .
54. Web site: Welcome to Network Coding Security - Secure Network Coding . 26 March 2022 . securenetworkcoding.wikidot.com.
55. Yu . Zhen . Wei . Yawen . Ramkumar . Bhuvaneswari . Guan . Yong . An efficient signature-based scheme for securing network coding against pollution attacks . https://scholar.archive.org/work/keidxnnwaffnrouhg25c5l3ybi . 10.1109/INFOCOM.2008.199 . 1409–1417 . IEEE . INFOCOM 2008. 27th IEEE International Conference on Computer Communications, Joint Conference of the IEEE Computer and Communications Societies, 13–18 April 2008, Phoenix, AZ, USA . 2008.
56. Web site: Acedański . Szymon . Deb . Supratim . Médard . Muriel . Koetter . Ralf . How Good is Random Linear Coding Based Distributed Networked Storage? . 26 March 2022 . web.mit.edu.
57. cs/0702015. Dimakis. Alexandros. Network Coding for Distributed Storage Systems. 2007.
58. Book: Katti . Sachin . Rahul . Hariharan . Hu . Wenjun . Katabi . Dina . Médard . Muriel . Crowcroft . Jon . Proceedings of the 2006 conference on Applications, technologies, architectures, and protocols for computer communications . XORs in the air . 2006-08-11 . http://nms.csail.mit.edu/~sachin/papers/copesc.pdf . SIGCOMM '06 . New York, NY, USA . Association for Computing Machinery . 243–254 . 10.1145/1159913.1159942 . 978-1-59593-308-9 . 207160426.
59. Book: 10.1109/VTCSpring.2013.6692495 . 1–6 . 2013 . Krigslund . Jeppe . Hansen . Jonas . Hundeboll . Martin . Lucani . Daniel E. . Fitzek . Frank H. P. . 2013 IEEE 77th Vehicular Technology Conference (VTC Spring) . CORE: COPE with MORE in Wireless Meshed Networks . 978-1-4673-6337-2 . 1319567 .
60. Book: Sengupta . S. . Rayanchu . S. . Banerjee . S. . IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications . An Analysis of Wireless Network Coding for Unicast Sessions: The Case for Coding-Aware Routing . May 2007 . https://ieeexplore.ieee.org/document/4215706 . 1028–1036 . 10.1109/INFCOM.2007.124. 978-1-4244-1047-7 . 3056111 .
61. Web site: NetworkCoding - batman-adv - Open Mesh . live . https://web.archive.org/web/20210512133041/https://www.open-mesh.org/projects/batman-adv/wiki/NetworkCoding . 12 May 2021 . www.open-mesh.org . 2015-10-28.
62. Book: Bhadra . S. . Shakkottai . S. . Proceedings IEEE INFOCOM 2006. 25TH IEEE International Conference on Computer Communications . Looking at Large Networks: Coding vs. Queueing . April 2006 . https://ieeexplore.ieee.org/document/4146919/;jsessionid=Vf_H7NM8pJZkcL5tUwrvGHQd45FXGbWGEGG9OyMg__IVxRlWxF8t!-1723551334 . 1–12 . 10.1109/INFOCOM.2006.266. 1-4244-0221-2 . 730706 .
63. 10.1109/TVT.2008.927729. Wireless Broadcast Using Network Coding. IEEE Transactions on Vehicular Technology. 58. 2. 914–925. 2009. Dong Nguyen. Tuan Tran. Thinh Nguyen. Bose. B.. 10.1.1.321.1962. 16989586.
64. Firooz . Mohammad Hamed . Roy . Sumit . 24 March 2012 . Data Dissemination in Wireless Networks with Network Coding . IEEE Communications Letters . 17 . 5 . 944–947 . 10.1109/LCOMM.2013.031313.121994 . 1203.5395 . 13576 . 1089-7798.
65. Fiandrotti . Attilio . Bioglio . Valerio . Grangetto . Marco . Gaeta . Rossano . Magli . Enrico . 11 October 2013 . Band Codes for Energy-Efficient Network Coding With Application to P2P Mobile Streaming . IEEE Transactions on Multimedia . 16 . 2 . 521–532 . 10.1109/TMM.2013.2285518 . 1309.0316 . 10548996 . 1941-0077.
66. Book: Wu . Yue . Liu . Wuling . Wang . Siyi . Guo . Weisi . Chu . Xiaoli . 2015 IEEE International Conference on Communications (ICC) . Network coding in device-to-device (D2D) communications underlaying cellular networks . June 2015 . https://ieeexplore.ieee.org/document/7248631 . 2072–2077 . 10.1109/ICC.2015.7248631. 978-1-4673-6432-4 . 19637201 .
67. Book: Zhao . Yulei . Li . Yong . Ge . Ning . 2015 IEEE Global Communications Conference (GLOBECOM) . Physical Layer Network Coding Aided Two-Way Device-to-Device Communication Underlaying Cellular Networks . December 2015 . https://ieeexplore.ieee.org/document/7417590 . 1–6 . 10.1109/GLOCOM.2015.7417590. 978-1-4799-5952-5 .
68. Book: Abrardo . Andrea . Fodor . Gábor . Tola . Besmir . 2015 IEEE 16th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC) . Network coding schemes for Device-to-Device communications based relaying for cellular coverage extension . 2015 . http://www.diva-portal.org/smash/get/diva2:795210/FULLTEXT01.pdf . 670–674 . 10.1109/SPAWC.2015.7227122. 978-1-4799-1931-4 . 9591953 .
69. Gao . Chuhan . Li . Yong . Zhao . Yulei . Chen . Sheng . October 2017 . A Two-Level Game Theory Approach for Joint Relay Selection and Resource Allocation in Network Coding Assisted D2D Communications . IEEE Transactions on Mobile Computing . 16 . 10 . 2697–2711 . 10.1109/TMC.2016.2642190 . 22233426 . 1558-0660.
70. Zhou . Ting . Xu . Bin . Xu . Tianheng . Hu . Honglin . Xiong . Lei . 1 February 2015 . User-specific link adaptation scheme for device-to-device network coding multicast . IET Communications . 9 . 3 . 367–374 . 10.1049/iet-com.2014.0323 . 27108894 . 1751-8636. free .