network coding: an overview

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

Outline

• Introduction and Examples• Single-Source Network Coding• Recent Developments• Concluding Remarks

A Network Coding Example

The Butterfly Network

b1b2

b1b2b1b2

b1 b2

b1

b1

b2

b2b1+b2

b1+b2b1+b2

b1 b2

A Network Coding Example

with Two Sources

b1

b2b1

b1 b2

b2b1

b1 b2

b2b1

b1+b2

b1+b2

b1+b2

b1 b2

b2b1

Satellite/Wireless Application

Satellite/Wireless ApplicationA


A


A

B


B A

B


B A

BA


B A

BA B


B A

BA

A+B

B


• NASA project proposal (2008)


• NASA project proposal (2008)• Katti et al. (2006/2008) implemented on 802.11

at MAC layer (COPE)


• NASA project proposal (2008)• Katti et al. (2006/2008) implemented on 802.11

at MAC layer (COPE)• Demos available at youtube: “network coding”

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



• 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!

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

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

Single-Source Network Coding

Max-Flow Min-Cut: Commodity Flow

• Elias, Feinstein, and Shannon (1956)• Ford and Fulkerson (1956)

Maximum flow = Minimum cutMaximum flow = Minimum cut

Max-Flow Min-Cut: Information Flow

tt11

tt22

ttmm

ss

kk

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

Linear Network Coding

• Linear network coding suffices– Vector space approach: Li, Yeung and Cai

(1999/2003)



(1999/2003)– Matrix approach: Koetter and Medard (2002/03)



(1999/2003)– Matrix approach: Koetter and Medard (2002/03)

• A sufficiently large finite field chosen as the base field

Example: Butterfly Network

b1 b2

b1

b1

b2

b2b1+b2

b1+b2b1+b2

k = 2F = GF(2)k = 2F = GF(2)

Random Linear Network Coding

• Ho, Koetter, Medard, Karger, Effros (2003/06)


• Ho, Koetter, Medard, Karger, Effros (2003/06)• Random coefficients for 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



is sufficiently large• Enables network coding in unknown network

topologies



is sufficiently large• Enables network coding in unknown network

topologies• Subspace coding: Koetter and Kschischang

(2007/08)

Recent Developments

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)

Major Research Projects

• USA: IT-MANET, CB-MANET (DARPA)• Europe: N-CRAVE (European Commission)• Hong Kong: Institute of Network Coding (HK

Government)

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

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

Network Coding RoadmapNetwork Coding RoadmapChannel coding theoryChannel coding theory

Computer networksComputer networks


Switching theorySwitching theory

Network codingNetwork codingModern theoryModern theory

of communicationof communication

Network Coding RoadmapNetwork Coding RoadmapChannel coding theoryChannel coding theory

Computer networksComputer networks


Switching theorySwitching theory

Network codingNetwork codingModern theoryModern theory

of communicationof communication

““Signal” NCSignal” NC Improved wirelessImproved wireless

communicationscommunications

Network Error Correction

• Cai and Yeung (2002/2006)


• Cai and Yeung (2002/2006)• Use network coding for 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


• 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

Secure Network Coding

• Cai and Yeung (2002/2007)


• Cai and Yeung (2002/2007)• Uses network coding against wiretapping


• Cai and Yeung (2002/2007)• Uses network coding against wiretapping• Subsumes secret sharing in cryptography


• Cai and Yeung (2002/2007)• Uses network coding against wiretapping• Subsumes secret sharing in cryptography• Information-theoretic bounds achievable for

some important special cases

Signal-Level Network Coding

• Allows wireless signals to add up physically


• Allows wireless signals to add up physically• Can further improve the efficiency of wireless

network coding



network coding• Physical-Layer NC: Zhang, Liew, and Lam (2006)



network coding• Physical-Layer NC: Zhang, Liew, and Lam (2006)• Analog NC: Katti, Gollakota, and Katabi (2007)

Illustration of PNC/ANC

Illustration of PNC/ANCA B

Illustration of PNC/ANCA

A+B

B


A+B

B

PNCPNC- Estimates A+B- Estimates A+B


A+B

B

PNCPNC- Estimates A+B- Estimates A+B

ANCANC- Amplify and forward- Amplify and forward

Concluding Remarks

• 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





• A new information infrastructure for transmission, storage, security, etc, is underway

• Network coding will continue to interact with different fields of research

Thank you

network coding: an overview

Documents

network codingmaxflows

emergingsingle source

matrix approach

information flowahlswede

independent sources

butterfly networkk

mac layer copedemos

commodity flowelias