Comex Task1

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Network Information Theory and CodingComex - Task 1

Jean-Claude Belfiore

Telecom ParisTech

September 13, 2012

cole Polytechnique


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Tools

Outline

1 Tools

2 Networks

3 Distributed computing and/or Network Coding

4 Security in Networks

5 Teams

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Tools

Information Theory & Coding

Information TheoryGives fundamental limits, essentially Achievable Rates for a reliable communication.Now,

Multi-Agent, Networking

Context ofnon reliableWireless links: outage behavior, ...

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Tools

Information Theory & Coding

Information TheoryGives fundamental limits, essentially Achievable Rates for a reliable communication.Now,

Multi-Agent, Networking

Context ofnon reliableWireless links: outage behavior, ...

CodingHow to achieve the fundamental limits given by Information Theory.

Network Coding(both linear and non linear)

Lattice Codingto address linear superposition of signals (PHY layer)

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Networks

Outline

1 Tools

2 Networks



5 Teams

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Networks

In-Network Computation

Computation of a function

Some nodes could compute a function of their inputs, either at the packet level or at the

signal level for distributed computation.

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Networks

In-Network Computation

Computation of a function

Some nodes could compute a function of their inputs, either at the packet level or at the

signal level for distributed computation.

Network Coding

Both at the packet level and at the signal level

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Networks

From Network Coding ...

A, B

A, B A, B

Figure: The butterfly network

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Networks


XA XB

A, B

A, B A, B


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Networks


XA

XA

XA

XB

XB

XB

A, B

A, B A, B


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Networks


XA

XA

XA

XB

XB

XB

A, B

XA

XB

A, B A, B


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Networks


XA

XA

XA

XB

XB

XB

XA XB

A, B

XA

XB

A, B A, B


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Networks

... to Wireless Network Coding

Br.

Rel. Rel.

Rel.

MAC

Int. Int.

Br.

Figure: Wireless Network

Br: Broadcast

Rel. Relay

MAC Multiple Access

Int. Interference

Problems

Wireless networks suffer frombroadcasting and superposi-tion properties from the wirelessmedium, interference, S N R s, fad-

ings, ...

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Networks

Network Information Theory and Stochastic Geometry

Capacity of a network

The capacityof a wireless network depends on the location of the nodes. Based on thisspatial point of view, Stochastic Geometry can be used for the analysis of large-scale S elf

O rganized N etworks in order to model and quantifyinterference, outage probability, ...

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Networks

Network Information Theory and Stochastic Geometry

Capacity of a network

The capacityof a wireless network depends on the location of the nodes. Based on thisspatial point of view, Stochastic Geometry can be used for the analysis of large-scale S elf

O rganized N etworks in order to model and quantifyinterference, outage probability, ...

Information Theory and Stochastic Geometry

Develop a framework combining Information Theoryand Stochastic Geometryin orderto investigate fundamental limits on information flow.

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Distributed computing and/or Network Coding

Outline

1 Tools

2 Networks



5 Teams

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Network Coding

Network Coding PerformancesIncrease data rates

Minimize energy consumption

Respect the quality of service required by the application layer

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Network Coding




Towards Wireless Network Coding

Network coding is done at the Networklayer. For wireless networks (no graph represen-tation), network coding at the PHYlayer should be considered.



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Network Coding




Towards Wireless Network Coding

Network coding is done at the Networklayer. For wireless networks (no graph represen-tation), network coding at the PHYlayer should be considered.

Network Coding

Linear Network Coding is optimal for a multicast network. Many other networks may

require nonlinear network coding.


i ib d i d/ k C di


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Wireless Distributed Computation

Principles

Turn the broadcast property of thewireless channel into a capacityboostingadvantage.Instead of considering the interference as a nuisance, each relay converts an interferingsignal into a combination of simultaneously transmitted codewords named equations.


Di t ib t d ti d/ N t k C di


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Principles


Compute-and-ForwardNodes are required to decode noiseless linear equations of the transmitted messagesusing the noisy linear combinations provided by the channel. The destination, givenenough linear combinations, can solve the linear system for its desired messages.




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Principles


Compute-and-ForwardNodes are required to decode noiseless linear equations of the transmitted messagesusing the noisy linear combinations provided by the channel. The destination, givenenough linear combinations, can solve the linear system for its desired messages.

Generalization

Decode at each node a function of the transmitted data (can be non linear) and transmit

it. TowardsWireless Distributed Computation.


Security in Networks


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Outline

1 Tools

2 Networks



5 Teams




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Physical Security

Example of the Gaussian Wiretap Channel

A B

E

N1

N0




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y

Physical Security

Example of the Gaussian Wiretap Channel

A B

E

N1

N0

Secrecy Capacity

Cs=

log

1+

P

N0

log

1+

P

N1

+


Teams


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Outline

1 Tools

2 Networks



5 Teams


Teams


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Teams

CEA - LIST

INRIA Paris-Rocquencourt

Telecom ParisTech - LTCI

LIX

LSS

Telecom SudParis - SAMOVAR

E3S - Supelec


Documents

Comex Task1