1. 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

2. Outline Introduction and Examples Single-Source Network Coding
Recent Developments
Concluding Remarks

3. A Network Coding Example
The Butterfly Network

4. b1b2
b1b2
b1b2 4

5. b1 5

6. b1 b2 6

7. b1 b2 b1 b2 b1 b2 b1
b1+b2 b2
b1+b2
b1+b2 7

8. A Network Coding Example
with Two Sources

9. b1 b2

10. b1 b1 b2

11. b1 b2 b1 b2

12. b1 b2 b1 b2
b1+b2 b1 b2 b1 b2
b1+b2
b1+b2

13. Satellite/Wireless Application

14. Satellite/Wireless Application

15. Satellite/Wireless Application

16. Satellite/Wireless ApplicationB A A

17. Satellite/Wireless ApplicationB A A B

18. Satellite/Wireless ApplicationB A A B

19. Satellite/Wireless ApplicationB A A A B

20. Satellite/Wireless ApplicationB A B A A B

21. Satellite/Wireless ApplicationB A B A A B
A+B

22. Satellite/Wireless Application
NASA project proposal (2008)

23. Satellite/Wireless Application
NASA project proposal (2008)
Katti et al. (2006/2008) implemented on at MAC layer (COPE)

24. Satellite/Wireless Application
NASA project proposal (2008)
Katti et al. (2006/2008) implemented on at MAC layer (COPE)
Demos available at youtube: “network coding”

25. Two Themes of Network Coding
When there is 1 source to be multicast in a network, store-and-forward may fail to optimize bandwidth

26. 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

27. 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!

28. 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

29. 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

30. Single-Source Network Coding

31. Max-Flow Min-Cut: Commodity Flow
Elias, Feinstein, and Shannon (1956)
Ford and Fulkerson (1956)
Maximum flow = Minimum cut

32. Max-Flow Min-Cut: Information Flows k t1 tm t2

33. 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

34. Linear Network Coding Linear network coding suffices
Vector space approach: Li, Yeung and Cai (1999/2003)

35. Linear Network Coding Linear network coding suffices
Vector space approach: Li, Yeung and Cai (1999/2003)
Matrix approach: Koetter and Medard (2002/03)

36. 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

37. Example: Butterfly Network
b1+b2
k = 2
F = GF(2)

38. Random Linear Network Coding
Ho, Koetter, Medard, Karger, Effros (2003/06)

39. Random Linear Network Coding
Ho, Koetter, Medard, Karger, Effros (2003/06)
Random coefficients for linear network coding

40. 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

41. 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

42. 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)

43. Recent Developments

44. 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)

45. Major Research Projects
USA: IT-MANET, CB-MANET (DARPA)
Europe: N-CRAVE (European Commission)
Hong Kong: Institute of Network Coding (HK Government)

46. 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

47. 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.

48. 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.

49. 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.

50. Network Error Correction
Cai and Yeung (2002/2006)

51. Network Error Correction
Cai and Yeung (2002/2006)
Use network coding for error correction

52. 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

53. 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

54. Secure Network Coding
Cai and Yeung (2002/2007)

55. Secure Network Coding Cai and Yeung (2002/2007)
Uses network coding against wiretapping

56. Secure Network Coding Cai and Yeung (2002/2007)
Uses network coding against wiretapping
Subsumes secret sharing in cryptography

57. 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

58. Signal-Level Network Coding
Allows wireless signals to add up physically

59. Signal-Level Network Coding
Allows wireless signals to add up physically
Can further improve the efficiency of wireless network coding

60. 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)

61. 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)

62. Illustration of PNC/ANC

63. Illustration of PNC/ANCB A

64. Illustration of PNC/ANC
A+B B

65. Illustration of PNC/ANC
- Estimates A+B A
A+B B

66. Illustration of PNC/ANC
- Estimates A+B
ANC
- Amplify and forward A
A+B B

67. Concluding Remarks

68. For decades, network communication has been based on
For decades, network communication has been based on point-to-point solutions + routing

69. 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

70. 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

71. 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

72. 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

73. 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

74. Thank you