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Network Coding: An Overview
Raymond W. Yeung Institute of Network Coding & Department of Information Engineering The 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 b1b2 b1b2 4
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b1 5
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b1 b2 6
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b1 b2 b1 b2 b1 b2 b1 b1+b2 b2 b1+b2 b1+b2 7
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A Network Coding Example
with Two Sources
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b1 b2
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b1 b1 b2
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b1 b2 b1 b2
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b1 b2 b1 b2 b1+b2 b1 b2 b1 b2 b1+b2 b1+b2
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Satellite/Wireless Application
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Satellite/Wireless Application
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Satellite/Wireless Application
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Satellite/Wireless Application
B A A
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Satellite/Wireless Application
B A A B
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Satellite/Wireless Application
B A A B
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Satellite/Wireless Application
B A A A B
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Satellite/Wireless Application
B A B A A B
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Satellite/Wireless Application
B A B A A B A+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 at MAC layer (COPE)
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Satellite/Wireless Application
NASA project proposal (2008) Katti et al. (2006/2008) implemented on 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 cut
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Max-Flow Min-Cut: Information Flow
s k t1 tm t2
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Max-Flow Min-Cut: Information Flow
Ahlswede, Cai, Li, and Yeung (1998/2000) Rate = k is achievable by means of network coding iff maxflow(s,ti) ≥ k for i = 1, 2, …, m
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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 k = 2 F = 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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These fields are shown on the right hand side.
Information theory Quantum information theory Channel coding Graph theory Wireless networks Optimization theory Computer networks Game theory Switching theory Matroid theory Data storage Cryptography Computer science It is therefore not surprising that Network Coding has made tremendous impact on many fields in information science. These fields are shown on the right hand side. The impact of Network Coding goes as far as mathematics, physics and biology. In this AOE proposal, we will focus on fields that are related to information science.
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Network Coding Roadmap
Channel coding theory Computer networks Network coding Modern theory of communication Switching theory Cryptography Ever since the inception of Network Coding, we have been obtaining seminal results that start most of the important branches in the field. Specifically, we are in the process of integrating the classical fields of channel coding theory, computer networks, switching theory, and cryptography into a modern theory of communication under the framework of Network Coding. We are also in the process of further developing the theory of Network Coding at the signal level in order to exploit the potential of Network Coding in wireless communications.
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Network Coding Roadmap
Channel coding theory Computer networks Network coding Modern theory of communication Switching theory Cryptography “Signal” NC Improved wireless communications Ever since the inception of Network Coding, we have been obtaining seminal results that start most of the important branches in the field. Specifically, we are in the process of integrating the classical fields of channel coding theory, computer networks, switching theory, and cryptography into a modern theory of communication under the framework of Network Coding. We are also in the process of further developing the theory of Network Coding at the signal level in order to exploit the potential of Network Coding in wireless communications.
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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/ANC
B A
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Illustration of PNC/ANC
A+B B
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Illustration of PNC/ANC
- Estimates A+B A A+B B
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Illustration of PNC/ANC
- Estimates A+B ANC - Amplify and forward A A+B B
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Concluding Remarks
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For decades, network communication has been based on
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
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
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
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
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
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
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