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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

    4 / 15Comex- Task 1

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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