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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
3 Distributed computing and/or Network Coding
4 Security in 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
From Network Coding ...
XA XB
A, B
A, B A, B
Figure: The butterfly network
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Networks
From Network Coding ...
XA
XA
XA
XB
XB
XB
A, B
A, B A, B
Figure: The butterfly network
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Networks
From Network Coding ...
XA
XA
XA
XB
XB
XB
A, B
XA
XB
A, B A, B
Figure: The butterfly network
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Networks
From Network Coding ...
XA
XA
XA
XB
XB
XB
XA XB
A, B
XA
XB
A, B A, B
Figure: The butterfly network
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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
3 Distributed computing and/or Network Coding
4 Security in Networks
5 Teams
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Distributed computing and/or Network Coding
Network Coding
Network Coding PerformancesIncrease data rates
Minimize energy consumption
Respect the quality of service required by the application layer
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Distributed computing and/or Network Coding
Network Coding
Network Coding PerformancesIncrease data rates
Minimize energy consumption
Respect the quality of service required by the application layer
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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Distributed computing and/or Network Coding
Network Coding
Network Coding PerformancesIncrease data rates
Minimize energy consumption
Respect the quality of service required by the application layer
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.
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i ib d i d/ k C di
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Distributed computing and/or Network Coding
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.
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Di t ib t d ti d/ N t k C di
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Distributed computing and/or Network Coding
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.
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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Distributed computing and/or Network Coding
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Distributed computing and/or Network Coding
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.
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.
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Security in Networks
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Security in Networks
Outline
1 Tools
2 Networks
3 Distributed computing and/or Network Coding
4 Security in Networks
5 Teams
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Security in Networks
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Security in Networks
Physical Security
Example of the Gaussian Wiretap Channel
A B
E
N1
N0
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Security in Networks
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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
+
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Teams
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Outline
1 Tools
2 Networks
3 Distributed computing and/or Network Coding
4 Security in Networks
5 Teams
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Teams
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Teams
CEA - LIST
INRIA Paris-Rocquencourt
Telecom ParisTech - LTCI
LIX
LSS
Telecom SudParis - SAMOVAR
E3S - Supelec
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