Download - Network Coding: An Overview
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Network Coding: Network Coding: An OverviewAn Overview
Raymond W. YeungInstitute of Network Coding &Department of Information EngineeringThe Chinese University of Hong Kong (CUHK)
Presented at InnoAsia 2010
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Outline
• Introduction and Examples• Single-Source Network Coding• Recent Developments• Concluding Remarks
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A Network Coding Example
The Butterfly Network
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b1b2
b1b2b1b2
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b1
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b1 b2
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b1 b2
b1
b1
b2
b2b1+b2
b1+b2b1+b2
b1 b2
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A Network Coding Example
with Two Sources
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b2b1
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b1
b2b1
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b1 b2
b2b1
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b1 b2
b2b1
b1+b2
b1+b2
b1+b2
b1 b2
b2b1
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Satellite/Wireless Application
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Satellite/Wireless ApplicationA
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Satellite/Wireless ApplicationA
A
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Satellite/Wireless ApplicationA
A
B
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Satellite/Wireless ApplicationA
B A
B
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Satellite/Wireless ApplicationA
B A
B
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Satellite/Wireless ApplicationA
B A
BA
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Satellite/Wireless ApplicationA
B A
BA B
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Satellite/Wireless ApplicationA
B A
BA
A+B
B
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Satellite/Wireless Application
• NASA project proposal (2008)
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Satellite/Wireless Application
• NASA project proposal (2008)• Katti et al. (2006/2008) implemented on 802.11
at MAC layer (COPE)
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Satellite/Wireless Application
• NASA project proposal (2008)• Katti et al. (2006/2008) implemented on 802.11
at MAC layer (COPE)• Demos available at youtube: “network coding”
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Two Themes of Network Coding
• When there is 1 source to be multicast in a network, store-and-forward may fail to optimize bandwidth
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Two Themes of Network Coding
• When there is 1 source to be multicast in a network, store-and-forward may fail to optimize bandwidth
• When there are 2 or more independent sources to be transmitted in a network (even for unicast), store-and-forward may fail to optimize bandwidth
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Two Themes of Network Coding
• When there is 1 source to be multicast in a network, store-and-forward may fail to optimize bandwidth
• When there are 2 or more independent sources to be transmitted in a network (even for unicast), store-and-forward may fail to optimize bandwidth
• In short, Information is NOT a commodity!
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Single Source vs. Multiple Sources
• Single-source network coding– Explicit characterization by Max-flow Min-Cut
Theorem for information flow (graph-theoretic)– Numerous applications are emerging
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Single Source vs. Multiple Sources
• Single-source network coding– Explicit characterization by Max-flow Min-Cut
Theorem for information flow (graph-theoretic)– Numerous applications are emerging
• Multi-source network coding– Implicit characterization in terms of achievable
entropy functions (Yan, Yeung, Zhang, 2007)– Still at the stage of theoretical research
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Single-Source Network Coding
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Max-Flow Min-Cut: Commodity Flow
• Elias, Feinstein, and Shannon (1956)• Ford and Fulkerson (1956)
Maximum flow = Minimum cutMaximum flow = Minimum cut
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Max-Flow Min-Cut: Information Flow
tt11
tt22
ttmm
ss
kk
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Max-Flow Min-Cut: Information Flow
• Ahlswede, Cai, Li, and Yeung (1998/2000)
Rate = k is achievableRate = k is achievableby means of network codingby means of network coding
Rate = k is achievableRate = k is achievableby means of network codingby means of network coding
maxflow(s,tmaxflow(s,tii) ≥ k) ≥ k
for i = 1, 2, …, mfor i = 1, 2, …, m
maxflow(s,tmaxflow(s,tii) ≥ k) ≥ k
for i = 1, 2, …, mfor i = 1, 2, …, m
iffiff
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Linear Network Coding
• Linear network coding suffices– Vector space approach: Li, Yeung and Cai
(1999/2003)
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Linear Network Coding
• Linear network coding suffices– Vector space approach: Li, Yeung and Cai
(1999/2003)– Matrix approach: Koetter and Medard (2002/03)
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Linear Network Coding
• Linear network coding suffices– Vector space approach: Li, Yeung and Cai
(1999/2003)– Matrix approach: Koetter and Medard (2002/03)
• A sufficiently large finite field chosen as the base field
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Example: Butterfly Network
b1 b2
b1
b1
b2
b2b1+b2
b1+b2b1+b2
k = 2F = GF(2)k = 2F = GF(2)
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Random Linear Network Coding
• Ho, Koetter, Medard, Karger, Effros (2003/06)
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Random Linear Network Coding
• Ho, Koetter, Medard, Karger, Effros (2003/06)• Random coefficients for linear network coding
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Random Linear Network Coding
• Ho, Koetter, Medard, Karger, Effros (2003/06)• Random coefficients for linear network coding• Can decode w.p.≈ 1 provided that the base field
is sufficiently large
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Random Linear Network Coding
• Ho, Koetter, Medard, Karger, Effros (2003/06)• Random coefficients for linear network coding• Can decode w.p.≈ 1 provided that the base field
is sufficiently large• Enables network coding in unknown network
topologies
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Random Linear Network Coding
• Ho, Koetter, Medard, Karger, Effros (2003/06)• Random coefficients for linear network coding• Can decode w.p.≈ 1 provided that the base field
is sufficiently large• Enables network coding in unknown network
topologies• Subspace coding: Koetter and Kschischang
(2007/08)
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Recent Developments
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Publications & Conferences• ~ 2,500 citations (Google Scholar)• ~ 1,000 citations for past 12 months• 4 books• ~ 8 special journal issues related to NC• ~ 8 journal & conference paper awards • 2 annual conferences: NetCod (since 2005), WiNC (since
2008)
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Major Research Projects
• USA: IT-MANET, CB-MANET (DARPA)• Europe: N-CRAVE (European Commission)• Hong Kong: Institute of Network Coding (HK
Government)
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Major Research Projects
• USA: IT-MANET, CB-MANET (DARPA)• Europe: N-CRAVE (European Commission)• Hong Kong: Institute of Network Coding (HK
Government)– Funded for 8 years– Conduct research in different aspects of NC– Train postdocs and PhDs– Protyping and implemention
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Information Information
theorytheory
Computer Computer
networksnetworks
SwitchingSwitching
theorytheory
Wireless Wireless
networksnetworks
ChannelChannel
codingcoding
ComputerComputer
sciencescience
CryptographyCryptography
OptimizationOptimization
theorytheory
Quantum Quantum
information information
theorytheory
GrapGraphh
theortheoryy
Game Game
theorytheory
Matroid Matroid
theorytheory Data Data
storagestorage
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Network Coding RoadmapNetwork Coding RoadmapChannel coding theoryChannel coding theory
Computer networksComputer networks
CryptographyCryptography
Switching theorySwitching theory
Network codingNetwork codingModern theoryModern theory
of communicationof communication
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Network Coding RoadmapNetwork Coding RoadmapChannel coding theoryChannel coding theory
Computer networksComputer networks
CryptographyCryptography
Switching theorySwitching theory
Network codingNetwork codingModern theoryModern theory
of communicationof communication
““Signal” NCSignal” NC Improved wirelessImproved wireless
communicationscommunications
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Network Error Correction
• Cai and Yeung (2002/2006)
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Network Error Correction
• Cai and Yeung (2002/2006)• Use network coding for error correction
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Network Error Correction
• Cai and Yeung (2002/2006)• Use network coding for error correction• Generalizes classical algebraic coding to
networks:– Bounds: Hamming, Gilbert-Varshamov, Singleton– Network Singleton bound achievable
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Network Error Correction
• Cai and Yeung (2002/2006)• Use network coding for error correction• Generalizes classical algebraic coding to
networks:– Bounds: Hamming, Gilbert-Varshamov, Singleton– Network Singleton bound achievable
• Can correct random errors and neutralize malicious nodes
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Secure Network Coding
• Cai and Yeung (2002/2007)
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Secure Network Coding
• Cai and Yeung (2002/2007)• Uses network coding against wiretapping
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Secure Network Coding
• Cai and Yeung (2002/2007)• Uses network coding against wiretapping• Subsumes secret sharing in cryptography
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Secure Network Coding
• Cai and Yeung (2002/2007)• Uses network coding against wiretapping• Subsumes secret sharing in cryptography• Information-theoretic bounds achievable for
some important special cases
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Signal-Level Network Coding
• Allows wireless signals to add up physically
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Signal-Level Network Coding
• Allows wireless signals to add up physically• Can further improve the efficiency of wireless
network coding
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Signal-Level Network Coding
• Allows wireless signals to add up physically• Can further improve the efficiency of wireless
network coding• Physical-Layer NC: Zhang, Liew, and Lam (2006)
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Signal-Level Network Coding
• Allows wireless signals to add up physically• Can further improve the efficiency of wireless
network coding• Physical-Layer NC: Zhang, Liew, and Lam (2006)• Analog NC: Katti, Gollakota, and Katabi (2007)
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Illustration of PNC/ANC
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Illustration of PNC/ANCA B
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Illustration of PNC/ANCA
A+B
B
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Illustration of PNC/ANCA
A+B
B
PNCPNC- Estimates A+B- Estimates A+B
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Illustration of PNC/ANCA
A+B
B
PNCPNC- Estimates A+B- Estimates A+B
ANCANC- Amplify and forward- Amplify and forward
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Concluding Remarks
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• For decades, network communication has been based on point-to-point solutions + routing
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• For decades, network communication has been based on point-to-point solutions + routing
• Network coding fundamentally changes the concept of network communications
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• For decades, network communication has been based on point-to-point solutions + routing
• Network coding fundamentally changes the concept of network communications
• Can apply to any communication system that can be modeled as a network
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• For decades, network communication has been based on point-to-point solutions + routing
• Network coding fundamentally changes the concept of network communications
• Can apply to any communication system that can be modeled as a network
• Researchers are investigating and re-investigating different aspects of network communications
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• For decades, network communication has been based on point-to-point solutions + routing
• Network coding fundamentally changes the concept of network communications
• Can apply to any communication system that can be modeled as a network
• Researchers are investigating and re-investigating different aspects of network communications
• A new information infrastructure for transmission, storage, security, etc, is underway
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• For decades, network communication has been based on point-to-point solutions + routing
• Network coding fundamentally changes the concept of network communications
• Can apply to any communication system that can be modeled as a network
• Researchers are investigating and re-investigating different aspects of network communications
• A new information infrastructure for transmission, storage, security, etc, is underway
• Network coding will continue to interact with different fields of research
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Thank you