Linear network coding: Difference between revisions

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{{Short description|Computer Networking Program}}

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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 combination]]s.

Linear network coding may be used to improve a network's throughput, efficiency, and [[scalability]], as well as reducing attacks and eavesdropping. The [[Node (networking)|node]]s of a network take ''several'' packets and combine for transmission. This process may be used to attain the maximum possible [[information]] [[flow network|flow]] in a [[Network theory|network]].

It has been proven that, theoretically, [[linear code|linear coding]] is enough to achieve the upper bound in multicast problems with one source.<ref>S. Li, R. Yeung, and N. Cai, "Linear Network Coding"([http://pdos.lcs.mit.edu/decouto/papers/li03.pdf PDF]), in IEEE Transactions on Information Theory, Vol 49, No. 2, pp. 371–381, 2003</ref> However linear coding is not sufficient in general; even for more general versions of linearity such as [[convolutional coding]] and [[filter-bank coding]].<ref>R. Dougherty, [[Chris Freiling|C. Freiling]], and K. Zeger, "Insufficiency of Linear Coding in Network Information Flow" ([http://code.ucsd.edu/~zeger/publications/journals/DoFrZe05-IT-Insufficiency/DoFrZe05-IT-Insufficiency.pdf PDF]), in IEEE Transactions on Information Theory, Vol. 51, No. 8, pp. 2745-2759, August 2005 ( [http://code.ucsd.edu/~zeger/publications/journals/DoFrZe05-IT-Insufficiency/DoFrZe05-IT-Insufficiency-erratum.pdf erratum])</ref> Finding optimal coding solutions for general network problems with arbitrary demands is a hard problem, which can be [[NP-hard]]<ref name="lehman_nc">{{cite conference|last1=Rasala Lehman|first1=A.|title=Complexity classification of network information flow problems|last2=Lehman|first2=E.|conference=15th ACM-SIAM SODA|date=2004|pagepages=142-150142–150}}</ref><ref name="langberg_nc">{{cite journal|last1=Langberg|first1=M.|title=The encoding complexity of network coding|last2=Sprintson|first2=A.|last3=Bruck|first3=J.|journal=IEEE Transactions on Information Theory|date=2006|volume=52|issue=6|pagepages=2386-23972386–2397|doi=10.1109/TIT.2006.874434|bibcode=2006ITIT...52.2386L |s2cid=1414385 |url=https://resolver.caltech.edu/CaltechAUTHORS:LANieeetit06 }}</ref>

and even [[Undecidable problem|undecidable]].<ref name="li_nc">{{cite journal|last1=Li|first1=C. T.|title=Undecidability of Network Coding, Conditional Information Inequalities, and Conditional Independence Implication|journal=IEEE Transactions on Information Theory|date=2023|volume=69 |issue=6 |page=13493 |doi=10.1109/TIT.2023.3247570|arxiv=2205.11461 |bibcode=2023ITIT...69.3493L |s2cid=248986512 }}</ref><ref name="kuhne_matroid">{{cite journal|last1=Kühne|first1=L.|title=Representability of Matroids by c-Arrangements is Undecidable|last2=Yashfe|first2=G.|journal=[[Israel Journal of Mathematics]]|date=2022|volume=252 |pagepages=1-5395–147|doi=10.1007/s11856-022-2345-z|arxiv=1912.06123 |s2cid=209324252 }}</ref>

== Encoding and decoding ==

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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, inwith Intel Core i5 processors with [[Single instruction, multiple data|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.<ref>{{Cite book |last1=Sørensen |first1=Chres W. |last2=Paramanathan |first2=Achuthan |last3=Cabrera |first3=Juan A. |last4=Pedersen |first4=Morten V. |last5=Lucani |first5=Daniel E. |last6=Fitzek |first6=Frank H.P. |title=2016 IEEE Wireless Communications and Networking Conference |chapter=Leaner and meaner: Network coding in SIMD enabled commercial devices |date=April 2016 |chapter-url=https://www.researchgate.net/publication/314198052 |pages=1–6 |doi=10.1109/WCNC.2016.7565066|isbn=978-1-4673-9814-5 |s2cid=10468008 |archive-url=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 |archive-date=2022-04-08 }}</ref> Furthermore, today's algorithms can be vastly parallelizable, increasing the encoding and decoding goodput even further.<ref>{{Cite journal |last1=Wunderlich |first1=Simon |last2=Cabrera |first2=Juan A. |last3=Fitzek |first3=Frank H. P. |last4=Reisslein |first4=Martin |date=August 2017 |title=Network Coding in Heterogeneous Multicore IoT Nodes With DAG Scheduling of Parallel Matrix Block Operations |url=https://faculty.engineering.asu.edu/mre/wp-content/uploads/sites/31/2020/04/NCMC.pdf |journal=IEEE Internet of Things Journal |volume=4 |issue=4 |pages=917–933 |doi=10.1109/JIOT.2017.2703813 |bibcode=2017IITJ....4..917W |s2cid=30243498 |issn=2327-4662 |archive-url=https://web.archive.org/web/20220408140133/https://faculty.engineering.asu.edu/mre/wp-content/uploads/sites/31/2020/04/NCMC.pdf |archive-date=8 Apr 2022}}</ref>

'''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 <math>M</math> 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 <math>M * log_2(s) = 32</math> 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%.

[[File:LinDependenciesbinary.png|thumb|448x448px|Expected linearly dependent packets at different stages of transmission for a Galois field <math>GF(2)</math> and a generation size of 16 packets. At the beginning of the transmission, the linear dependencies are minimal. It is the last packet of the transmission that is more likely to be linearly dependent.]]

[[File:LinDependenciesbinaryvsg.png|thumb|445x445px|The expected number of linearly dependent packets per generation is practically independent of the generation size.]]

'''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 <math>q</math> elements and a generation size of <math>M</math> packets. If the destination has not received any coded packet, we say it has <math>M</math> 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 <math>M</math> coding coefficient to be equal to the zero-element of the Galois field. I.e., the probability of a non-innovative packet is of <math>\frac{1}{q^M}</math>. 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 <math>M-1</math> 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 <math>\frac{1}{q}</math>. 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 (<math>q=2</math>), 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 (<math>q=256</math>), 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<ref>{{Cite book |last1=Feizi |first1=Soheil |last2=Lucani |first2=Daniel E. |last3=Sørensen |first3=Chres W. |last4=Makhdoumi |first4=Ali |last5=Médard |first5=Muriel |title=2014 International Symposium on Network Coding (Net ''Cod''NetCod) |chapter=Tunable sparse network coding for multicast networks |date=June 2014 |chapter-url=https://ieeexplore.ieee.org/document/6892129 |pages=1–6 |doi=10.1109/NETCOD.2014.6892129|isbn=978-1-4799-6217-4 |s2cid=18256950 }}</ref> 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 ==

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Over the years, multiple researchers and companies have integrated network coding solutions into their applications.<ref>{{Cite web |title=Coding the Network: Next Generation Coding for Flexible Network Operation {{!}} IEEE Communications Society |url=https://www.comsoc.org/publications/ctn/coding-network-next-generation-coding-flexible-network-operation |access-date=2022-06-06 |website=www.comsoc.org}}</ref> We can list some of the applications of network coding in different areas:

* [[Voice over IP|VoIP]]:<ref>{{Cite book |last1=Lopetegui |first1=I. |last2=Carrasco |first2=R.A. |last3=Boussakta |first3=S. |title=2010 7th International Symposium on Communication Systems, Networks & Digital Signal Processing (CSNDSP 2010) |chapter=VoIP design and implementation with network coding schemes for wireless networks |date=July 2010 |chapter-url=https://ieeexplore.ieee.org/document/5580304 |___location=Newcastle upon Tyne |publisher=IEEE |pages=857–861 |doi=10.1109/CSNDSP16145.2010.5580304 |isbn=978-1-4244-8858-2|s2cid=1761089 }}</ref> 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.{{citation needed|date=June 2022}}

* Video<ref name=":2">{{Cite book |last1=Shrimali |first1=R. |last2=Narmawala |first2=Z. |title=2012 Nirma University International Conference on Engineering (NUiCONE) |chapter=A survey on MPEG-4 streaming using network coding in wireless networks |date=December 2012 |chapter-url=https://ieeexplore.ieee.org/document/6493203 |pages=1–5 |doi=10.1109/NUICONE.2012.6493203|isbn=978-1-4673-1719-1 |s2cid=7791774 }}</ref> and audio<ref name=":3">{{Cite book |last1=Saeed |first1=Basil |last2=Lung |first2=Chung-Horng |last3=Kunz |first3=Thomas |last4=Srinivasan |first4=Anand |title=2011 IFIP Wireless Days (WD) |chapter=Audio streaming for ad hoc wireless mesh networks using network coding |date=October 2011 |chapter-url=https://ieeexplore.ieee.org/document/6098167 |pages=1–5 |doi=10.1109/WD.2011.6098167|isbn=978-1-4577-2028-4 |s2cid=8052927 }}</ref> streaming and conferencing:<ref name=":4">{{Cite journal |last1=Wang |first1=Lei |last2=Yang |first2=Zhen |last3=Xu |first3=Lijie |last4=Yang |first4=Yuwang |date=July 2016 |title=NCVCS: Network-coding-based video conference system for mobile devices in multicast networks |url=https://linkinghub.elsevier.com/retrieve/pii/S1570870516300713 |journal=Ad Hoc Networks |language=en |volume=45 |pages=13–21 |doi=10.1016/j.adhoc.2016.03.002|url-access=subscription }}</ref><ref>{{Cite book |last1=Wang |first1=Hui |last2=Chang |first2=Ronald Y. |last3=Kuo |first3=C.-C. Jay |title=2009 IEEE International Conference on Multimedia and Expo |chapter=Wireless Multi-party video conferencing with network coding |date=June 2009 |chapter-url=https://ieeexplore.ieee.org/document/5202786 |pages=1492–1495 |doi=10.1109/ICME.2009.5202786|isbn=978-1-4244-4290-4 |s2cid=8234088 }}</ref> 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.<ref name=":2" /> 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.<ref name=":3" /> The performance improvements of network coding for video conferencing are not only theoretical. In 2016, the authors of <ref name=":4" /> built a real-world testbed of 15 wireless [[Android (operating system)|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]]):<ref name=":5">{{Cite book |last1=Rachuri |first1=Sri Pramodh |last2=Ansari |first2=Ahtisham Ali |last3=Tandur |first3=Deepaknath |last4=Kherani |first4=Arzad A. |last5=Chouksey |first5=Sameer |title=2019 International Conference on contemporary Computing and Informatics (IC3I) |chapter=Network-Coded SD-WAN in Multi-Access Systems for Delay Control |date=December 2019 |chapter-url=https://ieeexplore.ieee.org/document/9055565 |___location=Singapore, Singapore |publisher=IEEE |pages=32–37 |doi=10.1109/IC3I46837.2019.9055565 |isbn=978-1-7281-5529-6|s2cid=215723197 }}</ref><ref>{{Cite book |last1=Ansari |first1=Ahtisham Ali |last2=Rachuri |first2=Sri Pramodh |last3=Kherani |first3=Arzad A. |last4=Tandur |first4=Deepaknath |title=2019 IEEE International Conference on Advanced Networks and Telecommunications Systems (ANTS) |chapter=An SD-WAN Controller for Delay Jitter Minimization in Coded Multi-access Systems |date=December 2019 |chapter-url=https://ieeexplore.ieee.org/document/9117981 |pages=1–6 |doi=10.1109/ANTS47819.2019.9117981 |isbn=978-1-7281-3715-5 |s2cid=219853700}}</ref><ref name=":6">{{Cite web |title=Steinwurf's next-gen FECs aren't a choice for SD-WAN, they're an imperative. |url=https://www.linkedin.com/pulse/steinwurfs-next-gen-fecs-arent-choice-sd-wan-theyre-videb%C3%A6k-pedersen |access-date=2022-06-06 |website=www.linkedin.com |language=en}}</ref><ref name=":7">{{Cite web |title=Barracuda Networks optimizes SD-WAN traffic with patented erasure correction technology from Steinwurf |url=https://www.steinwurf.com/blog/barracuda-networks |access-date=2022-06-06 |website=Steinwurf |language=en-GB}}</ref> Large industrial [[Internet of things|IoT]] wireless networks can benefit from network coding. Researchers showed<ref name=":5" /> 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 Networks|Barracuda]] are employing RLNC-based solutions due to their advantages in low latency, small footprint on computing devices, and low overhead.<ref name=":6" /><ref name=":7" />

* Channel bundling:<ref name=":8">{{Cite book |last1=Pedersen |first1=Morten V. |last2=Lucani |first2=Daniel E. |last3=Fitzek |first3=Frank H. P. |last4=Sorensen |first4=Chres W. |last5=Badr |first5=Arash S. |title=2013 IEEE Information Theory Workshop (ITW) |chapter=Network coding designs suited for the real world: What works, what doesn't, what's promising |date=September 2013 |chapter-url=https://ieeexplore.ieee.org/document/6691231 |___location=Sevilla |publisher=IEEE |pages=1–5 |doi=10.1109/ITW.2013.6691231 |isbn=978-1-4799-1321-3|s2cid=286822 }}</ref> 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.<ref name=":8" /> 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.<ref>{{Citation |title=Channel Bundling Using Random Linear Network Coding | date=22 September 2013 |url=https://www.youtube.com/watch?v=mTBRdU8Rc-0 |language=en |access-date=2022-06-06}}</ref>

* [[5G]] private networks:<ref name=":9">{{Cite journal |last1=Vukobratovic |first1=Dejan |last2=Tassi |first2=Andrea |last3=Delic |first3=Savo |last4=Khirallah |first4=Chadi |date=April 2018 |title=Random Linear Network Coding for 5G Mobile Video Delivery |journal=Information |language=en |volume=9 |issue=4 |pages=72 |arxiv=1802.04873 |doi=10.3390/info9040072 |issn=2078-2489|doi-access=free }}</ref><ref name=":10">{{Cite book |last1=Gabriel |first1=Frank |last2=Nguyen |first2=Giang T. |last3=Schmoll |first3=Robert-Steve |last4=Cabrera |first4=Juan A. |last5=Muehleisen |first5=Maciej |last6=Fitzek |first6=Frank H.P. |title=2018 15th IEEE Annual Consumer Communications & Networking Conference (CCNC) |chapter=Practical deployment of network coding for real-time applications in 5G networks |date=January 2018 |chapter-url=https://ieeexplore.ieee.org/document/8319320 |___location=Las Vegas, NV |publisher=IEEE |pages=1–2 |doi=10.1109/CCNC.2018.8319320 |isbn=978-1-5386-4790-5|s2cid=3982619 }}</ref> RLNC can be integrated into the [[5G NR]] standard to improve the performance of video delivery over 5G systems.<ref name=":9" /> In 2018, a demo presented at the [[Consumer Electronics Show]] demonstrated a practical deployment of RLNC with [[Network function virtualization|NFV]] and [[Software-defined networking|SDN]] technologies to improve video quality against packet loss due to congestion at the core network.<ref name=":10" />

* Remote collaboration.<ref>{{Cite journal |last1=Magli |first1=Enrico |last2=Wang |first2=Mea |last3=Frossard |first3=Pascal |last4=Markopoulou |first4=Athina |date=August 2013 |title=Network Coding Meets Multimedia: A Review |url=https://ieeexplore.ieee.org/document/6416071 |journal=IEEE Transactions on Multimedia |volume=15 |issue=5 |pages=1195–1212 |doi=10.1109/TMM.2013.2241415 |arxiv=1211.4206 |bibcode=2013ITMm...15.1195M |s2cid=3200945 |issn=1520-9210}}</ref>

* [[Augmented reality]] remote support and training.<ref>{{Cite journal |last1=Torres Vega |first1=Maria |last2=Liaskos |first2=Christos |last3=Abadal |first3=Sergi |last4=Papapetrou |first4=Evangelos |last5=Jain |first5=Akshay |last6=Mouhouche |first6=Belkacem |last7=Kalem |first7=Gökhan |last8=Ergüt |first8=Salih |last9=Mach |first9=Marian |last10=Sabol |first10=Tomas |last11=Cabellos-Aparicio |first11=Albert |date=October 2020 |title=Immersive Interconnected Virtual and Augmented Reality: A 5G and IoT Perspective |url=https://link.springer.com/10.1007/s10922-020-09545-w |journal=Journal of Network and Systems Management |language=en |volume=28 |issue=4 |pages=796–826 |doi=10.1007/s10922-020-09545-w |hdl=2117/330129 |s2cid=219589307 |issn=1064-7570|hdl-access=free }}</ref>

* Remote vehicle driving applications.<ref>{{Cite book |last1=De Jonckere |first1=Olivier |last2=Chorin |first2=Jean |last3=Feldmann |first3=Marius |title=2017 6th International Conference on Space Mission Challenges for Information Technology (SMC-IT) |chapter=Simulation Environment for Network Coding Research in Ring Road Networks |date=September 2017 |chapter-url=https://ieeexplore.ieee.org/document/8227552 |___location=Alcala de Henares |publisher=IEEE |pages=128–131 |doi=10.1109/SMC-IT.2017.29 |isbn=978-1-5386-3462-2|s2cid=6180560 }}</ref><ref>{{Cite journal |last1=Jamil |first1=Farhan |last2=Javaid |first2=Anam |last3=Umer |first3=Tariq |last4=Rehmani |first4=Mubashir Husain |date=November 2017 |title=A comprehensive survey of network coding in vehicular ad-hoc networks |url=http://link.springer.com/10.1007/s11276-016-1294-z |journal=Wireless Networks |language=en |volume=23 |issue=8 |pages=2395–2414 |doi=10.1007/s11276-016-1294-z |s2cid=13624914 |issn=1022-0038|url-access=subscription }}</ref><ref>{{Cite journal |last1=Park |first1=Joon-Sang |last2=Lee |first2=Uichin |last3=Gerla |first3=Mario |date=May 2010 |title=Vehicular communications: emergency video streams and network coding |journal=Journal of Internet Services and Applications |language=en |volume=1 |issue=1 |pages=57–68 |doi=10.1007/s13174-010-0006-7 |s2cid=2143201 |issn=1867-4828|doi-access=free }}</ref><ref>{{cite arXiv |last1=Noor-A-Rahim |first1=Md |last2=Liu |first2=Zilong |last3=Lee |first3=Haeyoung |last4=Khyam |first4=M. Omar |last5=He |first5=Jianhua |last6=Pesch |first6=Dirk |last7=Moessner |first7=Klaus |last8=Saad |first8=Walid |last9=Poor |first9=H. Vincent |date=2022-05-01 |title=6G for Vehicle-to-Everything (V2X) Communications: Enabling Technologies, Challenges, and Opportunities |class=cs.IT |eprint=2012.07753}}</ref>

* [[Connected cars]] networks.<ref>{{Cite book |last1=Achour |first1=Imen |last2=Bejaoui |first2=Tarek |last3=Busson |first3=Anthony |last4=Tabbane |first4=Sami |title=2017 IEEE International Conference on Communications Workshops (ICC Workshops) |chapter=Network Coding scheme behavior in a Vehicle-to-Vehicle safety message dissemination |date=October 2017 |chapter-url=https://ieeexplore.ieee.org/document/7962697 |___location=Paris, France |publisher=IEEE |pages=441–446 |doi=10.1109/ICCW.2017.7962697 |isbn=978-1-5090-1525-2|s2cid=22423560 }}</ref><ref>{{Cite journal |last1=Wang |first1=Shujuan |last2=Lu |first2=Shuguang |last3=Zhang |first3=Qian |date=April 2019 |title=Instantly decodable network coding–assisted data dissemination for prioritized services in vehicular ad hoc networks |journal=International Journal of Distributed Sensor Networks |language=en |volume=15 |issue=4 |pages=155014771984213 |doi=10.1177/1550147719842137 |s2cid=145983739 |issn=1550-1477|doi-access=free }}</ref>

* Gaming applications such as low latency streaming and multiplayer connectivity.<ref>{{cite arXiv |last1=Dammak |first1=Marwa |last2=Andriyanova |first2=Iryna |last3=Boujelben |first3=Yassine |last4=Sellami |first4=Noura |date=2018-03-29 |title=Routing and Network Coding over a Cyclic Network for Online Video Gaming |class=cs.IT |eprint=1803.11102 }}</ref><ref>{{Cite journalbook |last1=Lajtha |first1=Balázs |last2=Biczók |first2=Gergely |last3=Szabó |first3=Róbert |title=Networked Services and Applications - Engineering, Control and Management |chapter=Enabling P2P Gaming with Network Coding |date=2010 |editor-last=Aagesen |editor-first=Finn Arve |editor2-last=Knapskog |editor2-first=Svein Johan |title=Enabling P2P Gaming with Network Coding |journal=Networked Services and Applications - Engineering, Control and Management |series=Lecture Notes in Computer Science |volume=6164 |language=en |___location=Berlin, Heidelberg |publisher=Springer |pages=76–86 |doi=10.1007/978-3-642-13971-0_8 |isbn=978-3-642-13971-0|doi-access=free }}</ref><ref>{{Cite thesis |title=Network coding application for online games platformes |url=https://tel.archives-ouvertes.fr/tel-02284091 |publisher=Université de Cergy Pontoise ; École nationale d'ingénieurs de Sfax (Tunisie) |date=2018-11-20 |degree=phdthesis |language=en |first=Marwa |last=Dammak}}</ref><ref>{{Citation |last1=Lajtha |first1=Balázs |title=Enabling P2P Gaming with Network Coding |date=2010 |work=Networked Services and Applications - Engineering, Control and Management |volume=6164 |pages=76–86 |editor-last=Aagesen |editor-first=Finn Arve |place=Berlin, Heidelberg |publisher=Springer Berlin Heidelberg |doi=10.1007/978-3-642-13971-0_8 |isbn=978-3-642-13970-3 |last2=Biczók |first2=Gergely |last3=Szabó |first3=Róbert |series=Lecture Notes in Computer Science |editor2-last=Knapskog |editor2-first=Svein Johan|doi-access=free }}</ref>

* Healthcare applications.<ref>{{Cite book |url=https://www.worldcat.org/oclc/881429695 |title=Sensor networks for sustainable development |date=2014 |first1=Mohammad |last1=Ilyas |first2=Sami S. |last2=Alwakeel |first3=Mohammed M. |last3=Alwakeel |first4=el-Hadi M. |last4=Aggoune |isbn=978-1-4665-8207-1 |___location=Boca Raton, FL |chapter=Exploiting Network Coding for Smart Healthcare |doi=10.1201/b17124-13 |oclc=881429695 |chapter-url=https://www.taylorfrancis.com/chapters/edit/10.1201/b17124-13/exploiting-network-coding-smart-healthcare-elli-kartsakli-angelos-antonopoulos-christos-verikoukis}}</ref><ref>{{Cite journal |last1=Kartsakli |first1=Elli |last2=Antonopoulos |first2=Angelos |last3=Alonso |first3=Luis |last4=Verikoukis |first4=Christos |date=2014-03-10 |title=A Cloud-Assisted Random Linear Network Coding Medium Access Control Protocol for Healthcare Applications |journal=Sensors |language=en |volume=14 |issue=3 |pages=4806–4830 |doi=10.3390/s140304806 |issn=1424-8220 |pmc=4003969 |pmid=24618727|bibcode=2014Senso..14.4806K |doi-access=free }}</ref><ref>{{Cite book |last1=Taparugssanagorn |first1=Attaphongse |last2=Ono |first2=Fumie |last3=Kohno |first3=Ryuji |title=2010 IEEE 21st International Symposium on Personal, Indoor and Mobile Radio Communications Workshops |chapter=Network coding for non-invasive Wireless Body Area Networks |date=September 2010 |chapter-url=https://ieeexplore.ieee.org/document/5670413 |pages=134–138 |doi=10.1109/PIMRCW.2010.5670413|isbn=978-1-4244-9117-9 |s2cid=25872472 }}</ref>

* [[Fourth Industrial Revolution|Industry 4.0]].<ref>{{Cite book |last1=Peralta |first1=Goiuri |last2=Iglesias-Urkia |first2=Markel |last3=Barcelo |first3=Marc |last4=Gomez |first4=Raul |last5=Moran |first5=Adrian |last6=Bilbao |first6=Josu |title=2017 IEEE International Workshop of Electronics, Control, Measurement, Signals and their Application to Mechatronics (ECMSM) |chapter=Fog computing based efficient IoT scheme for the Industry 4.0 |date=May 2017 |chapter-url=https://ieeexplore.ieee.org/document/7945879 |___location=Donostia, San Sebastian, Spain |publisher=IEEE |pages=1–6 |doi=10.1109/ECMSM.2017.7945879 |isbn=978-1-5090-5582-1|s2cid=37985560 }}</ref><ref>{{Cite journal |last1=Peralta |first1=Goiuri |last2=Garrido |first2=Pablo |last3=Bilbao |first3=Josu |last4=Agüero |first4=Ramón |last5=Crespo |first5=Pedro |date=2019-04-08 |title=On the Combination of Multi-Cloud and Network Coding for Cost-Efficient Storage in Industrial Applications |journal=Sensors |language=en |volume=19 |issue=7 |pages=1673 |doi=10.3390/s19071673 |issn=1424-8220 |pmc=6479523 |pmid=30965629|bibcode=2019Senso..19.1673P |doi-access=free }}</ref><ref>{{Cite journalbook |last1=Zverev |first1=Mihail |last2=Agüero |first2=Ramón |last3=Garrido |first3=Pablo |last4=Bilbao |first4=Josu |datetitle=2019-10-22Proceedings of the 9th International Conference on the Internet of Things |titlechapter=Network Coding for IIoT Multi-Cloud Environments |date=2019-10-22 |chapter-url=https://doi.org/10.1145/3365871.3365903 |journal=Proceedings of the 9th International Conference on the Internet of Things |series=IoT 2019 |___location=New York, NY, USA |publisher=Association for Computing Machinery |pages=1–4 |doi=10.1145/3365871.3365903 |isbn=978-1-4503-7207-7|s2cid=207940281 }}</ref>

* Satellite networks.<ref>{{Cite web |title=DLR - Institute of Communications and Navigation - NEXT - Network Coding Satellite Experiment |url=https://www.dlr.de/kn/en/desktopdefault.aspx/tabid-12748/22264_read-26607/ |access-date=2022-06-06 |website=www.dlr.de}}</ref>

* Agricultural sensor fields.<ref>{{Cite journalbook |last1=Hsu |first1=Hsiao-Tzu |last2=Wang |first2=Tzu-Ming |last3=Kuo |first3=Yuan-Cheng |datetitle=Proceedings of the 2018 2nd International Conference on Education and E-11-05Learning |titlechapter=Implementation of Agricultural Monitoring System Based Onon Thethe Internet of Things |date=2018-11-05 |chapter-url=https://doi.org/10.1145/3291078.3291098 |journal=Proceedings of the 2018 2nd International Conference on Education and E-Learning |series=ICEEL 2018 |___location=New York, NY, USA |publisher=Association for Computing Machinery |pages=212–216 |doi=10.1145/3291078.3291098 |isbn=978-1-4503-6577-2|s2cid=59337140 }}</ref><ref>{{Cite journal |last1=Syed |first1=Abid Husain |last2=Ali |first2=Syed Zakir |date=2021-08-11 |title=Towards Transforming Agriculture for Challenges of 21st Century by Optimizing Resources Using IOT, Fuzzy Logic and Network Coding |url=https://www.preprints.org/manuscript/202108.0262/v1 |doi=10.20944/preprints202108.0262.v1|s2cid=238723260 }}</ref><ref>{{Cite journal |last1=Camilli |first1=Alberto |last2=Cugnasca |first2=Carlos E. |last3=Saraiva |first3=Antonio M. |last4=Hirakawa |first4=André R. |last5=Corrêa |first5=Pedro L. P. |date=2007-08-01 |title=From wireless sensors to field mapping: Anatomy of an application for precision agriculture |url=https://www.sciencedirect.com/science/article/pii/S0168169907000610 |journal=Computers and Electronics in Agriculture |series=Precision Agriculture in Latin America |language=en |volume=58 |issue=1 |pages=25–36 |doi=10.1016/j.compag.2007.01.019 |bibcode=2007CEAgr..58...25C |issn=0168-1699|url-access=subscription }}</ref>

* In-flight enterteinmententertainment networks.<ref>{{Cite patent|number=US8401021B2|title=Systems and methods for prioritizing wireless communication of aircraft|gdate=2013-03-19|invent1=Buga|invent2=Trent|inventor1-first=Wladyslaw Jan|inventor2-first=Tracy Raymond|url=https://patents.google.com/patent/US8401021B2/en}}</ref>

* Major security and firmware updates for mobile product families.<ref>{{Cite book |last1=Tonyali |first1=Samet |last2=Akkaya |first2=Kemal |last3=Saputro |first3=Nico |last4=Cheng |first4=Xiuzhen |author4-link= Xiuzhen Cheng |title=2017 26th International Conference on Computer Communication and Networks (ICCCN) |chapter=An Attribute & Network Coding-Based Secure Multicast Protocol for Firmware Updates in Smart Grid AMI Networks |date=July 2017 |chapter-url=https://ieeexplore.ieee.org/document/8038415 |___location=Vancouver, BC, Canada |publisher=IEEE |pages=1–9 |doi=10.1109/ICCCN.2017.8038415 |isbn=978-1-5090-2991-4|s2cid=25131878 }}</ref><ref>{{Cite journalbook |last1=Jalil |first1=Syed Qaisar |last2=Chalup |first2=Stephan |last3=Rehmani |first3=Mubashir Husain |title=Smart Grid and Internet of Things |chapter=A Smart Meter Firmware Update Strategy Through Network Coding for AMI Network |date=2019 |editor-last=Pathan |editor-first=Al-Sakib Khan |editor2-last=Fadlullah |editor2-first=Zubair Md. |editor3-last=Guerroumi |editor3-first=Mohamed |title=A Smart Meter Firmware Update Strategy Through Network Coding for AMI Network |chapter-url=https://link.springer.com/chapter/10.1007/978-3-030-05928-6_7 |journal=Smart Grid and Internet of Things |series=Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering |volume=256 |language=en |___location=Cham |publisher=Springer International Publishing |pages=68–77 |doi=10.1007/978-3-030-05928-6_7 |isbn=978-3-030-05928-6|s2cid=59561476 }}</ref>

* [[Smart city]] infrastructure.<ref>{{Cite book |last1=Kumar |first1=Vaibhav |last2=Cardiff |first2=Barry |last3=Flanagan |first3=Mark F. |title=2017 IEEE 28th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC) |chapter=Physical-layer network coding with multiple antennas: An enabling technology for smart cities |date=October 2017 |chapter-url=https://ieeexplore.ieee.org/document/8292785 |___location=Montreal, QC |publisher=IEEE |pages=1–6 |doi=10.1109/PIMRC.2017.8292785 |hdl=10197/11114 |isbn=978-1-5386-3529-2|s2cid=748535 |hdl-access=free }}</ref><ref>{{Citation |last1=Darif |first1=Anouar |title=Network Coding for Energy Optimization of SWIMAC in Smart Cities Using WSN Based on IR-UWB |date=2020 |url=http://link.springer.com/10.1007/978-3-030-37629-1_48 |work=Innovations in Smart Cities Applications Edition 3 |pages=663–674 |editor-last=Ben Ahmed |editor-first=Mohamed |place=Cham |publisher=Springer International Publishing |language=en |doi=10.1007/978-3-030-37629-1_48 |isbn=978-3-030-37628-4 |access-date=2022-06-06 |last2=Chaibi |first2=Hasna |last3=Saadane |first3=Rachid |series=Lecture Notes in Intelligent Transportation and Infrastructure |s2cid=214486109 |editor2-last=Boudhir |editor2-first=Anouar Abdelhakim |editor3-last=Santos |editor3-first=Domingos |editor4-last=El Aroussi |editor4-first=Mohamed|url-access=subscription }}</ref>

* [[Information-centric networking]] and [[named data networking]].:<ref name="Bilal, Muhammad 2019 1376–1385">{{cite journal |author=Bilal, Muhammad |display-authors=etal |year=2019 |title=Network-Coding Approach for Information-Centric Networking |journal=IEEE Systems Journal |volume=13 |issue=2 |pages=1376–1385 |arxiv=1808.00348 |bibcode=2019ISysJ..13.1376B |doi=10.1109/JSYST.2018.2862913 |s2cid=51894197}}</ref> Linear network coding can improve the network efficiency of information-centric networking solutions by exploiting the multi-source multi-cast nature of such systems.<ref name="Bilal, Muhammad 2019 1376–1385" /> It has been shown, that RLNC can be integrated into distributed content delivery networks such as [[InterPlanetary File System|IPFS]] to increase data availability while reducing storage resources.<ref>{{Cite book |last1=Zimmermann |first1=Sandra |last2=Rischke |first2=Justus |last3=Cabrera |first3=Juan A. |last4=Fitzek |first4=Frank H. P. |title=GLOBECOM 2020 - 2020 IEEE Global Communications Conference |chapter=Journey to MARS: Interplanetary Coding for relieving CDNS |date=December 2020 |chapter-url=https://ieeexplore.ieee.org/document/9322478 |___location=Taipei, Taiwan |publisher=IEEE |pages=1–6 |doi=10.1109/GLOBECOM42002.2020.9322478 |isbn=978-1-7281-8298-8|s2cid=231725197 }}</ref>

* Alternative to [[forward error correction]] and [[automatic repeat request]]s in traditional and wireless networks with packet loss, such as [[Coded TCP]]<ref>{{Cite arXiv |eprint = 1212.2291|last1 = Kim|first1 = Minji|title = Network Coded TCP (CTCP)|class = cs.NI|year = 2012}}</ref> and [[Multi-user ARQ]]<ref>{{Cite book |last1=Larsson |first1=P. |last2=Johansson |first2=N. |title=2006 IEEE 63rd Vehicular Technology Conference |chapter=Multi-User ARQ |date=2006 |chapter-url=https://ieeexplore.ieee.org/document/1683207 |___location=Melbourne, Australia |publisher=IEEE |volume=4 |pages=2052–2057 |doi=10.1109/VETECS.2006.1683207|isbn=0-7803-9392-9 |s2cid=38823300 }}</ref>

* Protection against network attacks such as snooping, eavesdropping, replay, or data corruption.<ref>{{Cite web |title=Welcome to Network Coding Security - Secure Network Coding |url=http://securenetworkcoding.wikidot.com/ |url-status=live |access-date=26 March 2022 |website=securenetworkcoding.wikidot.com}}</ref><ref>http://home.eng.iastate.edu/~yuzhen/publications/ZhenYu_INFOCOM_2008.pdf{{deadcite linkconference
|date=December 2017last1 |bot=InternetArchiveBot Yu |fix-attempted=yes }}<nowiki/>{{Deadfirst1 link|date=March 2022}}</ref>Zhen

| last2 = Wei | first2 = Yawen

| last3 = Ramkumar | first3 = Bhuvaneswari

| last4 = Guan | first4 = Yong

| contribution = An efficient signature-based scheme for securing network coding against pollution attacks

| contribution-url = https://scholar.archive.org/work/keidxnnwaffnrouhg25c5l3ybi

| doi = 10.1109/INFOCOM.2008.199

| pages = 1409–1417

| publisher = IEEE

| title = 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

| year = 2008| isbn = 978-1-4244-2026-1

}}</ref>

* Digital file distribution and P2P file sharing, e.g. [[Avalanche filesystem]] from Microsoft

* Distributed storage<ref name="Bilal, Muhammad 2019 1376–1385" /><ref>{{Cite web |last1=Acedański |first1=Szymon |last2=Deb |first2=Supratim |last3=Médard |first3=Muriel |last4=Koetter |first4=Ralf |title=How Good is Random Linear Coding Based Distributed Networked Storage? |url=http://web.mit.edu/~medard/www/page2/mpapers/netcod2005_accek.pdf |url-status=live |access-date=26 March 2022 |website=web.mit.edu}}</ref><ref>{{Cite arXiv |eprint = cs/0702015|last1 = Dimakis|first1 = Alexandros|title = Network Coding for Distributed Storage Systems|year = 2007}}</ref>

* Throughput increase in wireless mesh networks, e.g.: [[COPE (network coding)|COPE]],<ref name=":0">{{Cite journalbook |last1=Katti |first1=Sachin |last2=Rahul |first2=Hariharan |last3=Hu |first3=Wenjun |last4=Katabi |first4=Dina |last5=Médard |first5=Muriel |last6=Crowcroft |first6=Jon |datetitle=Proceedings of the 2006-08-11 conference on Applications, technologies, architectures, and protocols for computer communications |titlechapter=XORs in the air: practical wireless network coding|date=2006-08-11 |chapter-url=http://nms.csail.mit.edu/~sachin/papers/copesc.pdf |journal=Proceedings of the 2006 Conference on Applications, Technologies, Architectures, and Protocols for Computer Communications |series=SIGCOMM '06 |___location=New York, NY, USA |publisher=Association for Computing Machinery |pages=243–254 |doi=10.1145/1159913.1159942 |isbn=978-1-59593-308-9 |s2cid=207160426}}</ref> [[CORE (network coding)|CORE]],<ref>{{cite book | doi = 10.1109/VTCSpring.2013.6692495 | pages=1–6 | year=2013 | last1=Krigslund | first1=Jeppe | last2=Hansen | first2=Jonas | last3=Hundeboll | first3=Martin | last4=Lucani | first4=Daniel E. | last5=Fitzek | first5=Frank H. P. | title=2013 IEEE 77th Vehicular Technology Conference (VTC Spring) | chapter=CORE: COPE with MORE in Wireless Meshed Networks | isbn=978-1-4673-6337-2 | s2cid=1319567 }}</ref> [[Coding-aware routing]],<ref>{{Cite book |last1=Sengupta |first1=S. |last2=Rayanchu |first2=S. |last3=Banerjee |first3=S. |title=IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications |chapter=An Analysis of Wireless Network Coding for Unicast Sessions: The Case for Coding-Aware Routing |date=May 2007 |chapter-url=https://ieeexplore.ieee.org/document/4215706 |pages=1028–1036 |doi=10.1109/INFCOM.2007.124|isbn=978-1-4244-1047-7 |s2cid=3056111 }}</ref> and [[B.A.T.M.A.N.]]<ref>{{Cite web |title=NetworkCoding - batman-adv - Open Mesh |url=http://www.open-mesh.org/projects/batman-adv/wiki/NetworkCoding |url-status=live |archive-url=https://web.archive.org/web/20210512133041/https://www.open-mesh.org/projects/batman-adv/wiki/NetworkCoding |archive-date=12 May 2021 |website=www.open-mesh.org |accessdate=2015-10-28}}</ref>

* Buffer and delay reduction in spatial sensor networks: [[Spatial buffer multiplexing]]<ref>{{Cite book |last1=Bhadra |first1=S. |last2=Shakkottai |first2=S. |title=Proceedings IEEE INFOCOM 2006. 25TH IEEE International Conference on Computer Communications |chapter=Looking at Large Networks: Coding vs. Queueing |date=April 2006 |chapter-url=https://ieeexplore.ieee.org/document/4146919/;jsessionid=Vf_H7NM8pJZkcL5tUwrvGHQd45FXGbWGEGG9OyMg__IVxRlWxF8t!-1723551334 |pages=1–12 |doi=10.1109/INFOCOM.2006.266|isbn=1-4244-0221-2 |s2cid=730706 }}</ref>

* Wireless broadcast:<ref name=":11" /> RLNC can reduce the number of packet transmission for a single-hop wireless multicast network, and hence improve network bandwidth<ref name=":11">{{Cite journal | doi=10.1109/TVT.2008.927729| title=Wireless Broadcast Using Network Coding| journal=IEEE Transactions on Vehicular Technology| volume=58| issue=2| pages=914–925| year=2009| last1=Dong Nguyen| last2=Tuan Tran| last3=Thinh Nguyen| last4=Bose| first4=B.| bibcode=2009ITVT...58..914N|citeseerx = 10.1.1.321.1962| s2cid=16989586}}</ref>

* Distributed file sharing<ref>{{Cite journal |last1=Firooz |first1=Mohammad Hamed |last2=Roy |first2=Sumit |date=24 March 2012 |title=Data Dissemination in Wireless Networks with Network Coding |journal=IEEE Communications Letters |volume=17 |issue=5 |pages=944–947 |doi=10.1109/LCOMM.2013.031313.121994 |arxiv=1203.5395 |s2cid=13576 |issn=1089-7798}}</ref>

* Low-complexity video streaming to mobile device<ref>{{Cite journal |last1=Fiandrotti |first1=Attilio |last2=Bioglio |first2=Valerio |last3=Grangetto |first3=Marco |last4=Gaeta |first4=Rossano |last5=Magli |first5=Enrico |date=11 October 2013 |title=Band Codes for Energy-Efficient Network Coding With Application to P2P Mobile Streaming |url=https://ieeexplore.ieee.org/document/6630050 |journal=IEEE Transactions on Multimedia |volume=16 |issue=2 |pages=521–532 |doi=10.1109/TMM.2013.2285518 |arxiv=1309.0316 |s2cid=10548996 |issn=1941-0077}}</ref>

* [[Device-to-device]] extensions<ref>{{Cite book |last1=Wu |first1=Yue |last2=Liu |first2=Wuling |last3=Wang |first3=Siyi |last4=Guo |first4=Weisi |last5=Chu |first5=Xiaoli |title=2015 IEEE International Conference on Communications (ICC) |chapter=Network coding in device-to-device (D2D) communications underlaying cellular networks |date=June 2015 |chapter-url=https://ieeexplore.ieee.org/document/7248631 |pages=2072–2077 |doi=10.1109/ICC.2015.7248631|isbn=978-1-4673-6432-4 |s2cid=19637201 }}</ref><ref>{{Cite book |last1=Zhao |first1=Yulei |last2=Li |first2=Yong |last3=Ge |first3=Ning |title=2015 IEEE Global Communications Conference (GLOBECOM) |chapter=Physical Layer Network Coding Aided Two-Way Device-to-Device Communication Underlaying Cellular Networks |date=December 2015 |chapter-url=https://ieeexplore.ieee.org/document/7417590 |pages=1–6 |doi=10.1109/GLOCOM.2015.7417590|isbn=978-1-4799-5952-5 }}</ref><ref>{{Cite book |last1=Abrardo |first1=Andrea |last2=Fodor |first2=Gábor |last3=Tola |first3=Besmir |title=2015 IEEE 16th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC) |chapter=Network coding schemes for Device-to-Device communications based relaying for cellular coverage extension |date=2015 |chapter-url=http://www.diva-portal.org/smash/get/diva2:795210/FULLTEXT01.pdf |pages=670–674 |doi=10.1109/SPAWC.2015.7227122|isbn=978-1-4799-1931-4 |s2cid=9591953 |url=http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-160505 }}</ref><ref>{{Cite journal |last1=Gao |first1=Chuhan |last2=Li |first2=Yong |last3=Zhao |first3=Yulei |last4=Chen |first4=Sheng |date=October 2017 |title=A Two-Level Game Theory Approach for Joint Relay Selection and Resource Allocation in Network Coding Assisted D2D Communications |url=https://eprints.soton.ac.uk/414039/1/NC_D2D.pdf |journal=IEEE Transactions on Mobile Computing |volume=16 |issue=10 |pages=2697–2711 |doi=10.1109/TMC.2016.2642190 |bibcode=2017ITMC...16.2697G |s2cid=22233426 |issn=1558-0660}}</ref><ref>{{Cite journal |last1=Zhou |first1=Ting |last2=Xu |first2=Bin |last3=Xu |first3=Tianheng |last4=Hu |first4=Honglin |last5=Xiong |first5=Lei |date=1 February 2015 |title=User‐specificUser-specific link adaptation scheme for device‐to‐devicedevice-to-device network coding multicast |url=https://ietresearch.onlinelibrary.wiley.com/doi/full/10.1049/iet-com.2014.0323 |journal=IET Communications |volume=9 |issue=3 |pages=367–374 |doi=10.1049/iet-com.2014.0323 |s2cid=27108894 |issn=1751-8636|doi-access=free }}</ref>

== See also ==