Information-theoretic and physical limits on the capacity of wireless networks
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Information-theoretic and physical limits on the capacity of wireless networks. MASSIMO FRANCESCHETTI University of California at San Diego. P. Minero (UCSD), M. D. Migliore (U. Cassino). TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A A.

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MASSIMO FRANCESCHETTI University of California at San Diego

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Massimo franceschetti university of california at san diego

Information-theoretic and physical limits on the capacity of wireless networks

MASSIMO FRANCESCHETTI

University of California at San Diego

P. Minero (UCSD), M. D. Migliore (U. Cassino)

TexPoint fonts used in EMF.

Read the TexPoint manual before you delete this box.: AAAAA


Standing on the shoulder of giants

Standing on the shoulder of giants


The problem

The problem

  • Computers equipped with power constrained radios

  • Randomly located

  • Random source-destination pairs

  • Transmit over a common wireless channel

  • Possible cooperation among the nodes

  • Maximum per-node information rate (bit/sec) ?


Scaling approach

Scaling approach

  • All pairs must achieve the same rate

  • Consider the limit

IEEE Trans-IT (2000)


Information theoretic limits

Information-theoretic limits

  • Provide the ultimate limits of communication

  • Independent of any scheme used for communication


Classic approach

Classic Approach

  • Assume physical propagation model

  • Allow arbitrary cooperation among nodes

Xie KumarIEEE Trans-IT (2004)

Xue XieKumarIEEE Trans-IT (2005)

Leveque, TelatarIEEE Trans-IT (2005)

Ahmad Jovicic ViswanathIEEE Trans-IT (2006)

Gowaikar Hochwald HassibiIEEE Trans-IT (2006)

Xie KumarIEEE Trans-IT (2006)

Aeron SaligramaIEEE Trans-IT (2007)

FranceschettiIEEE Trans-IT (2007)

Ozgur Leveque PreissmannIEEE Trans-IT (2007)

Ozgur Leveque TseIEEE Trans-IT (2007)


Information theoretic truths

Information theoretic “truths”

High attenuation regime

Low attenuation regime without fading

Low attenuation regime with fading

No attenuation regime, fading only


Good research should shrink the knowledge tree

Good research should shrink the knowledge tree


There is only one scaling law

There is only one scaling law

This is a degrees of freedom limitation dictated by Maxwell’s physics and by Shannon’s theory of information. It is independent of channel models and cannot be overcome by any cooperative communication scheme.


Approach

Approach


Approach1

Approach

. . .

. . .

. . .


Information flow decomposition

Information flow decomposition

A

V

D

d


First flow component

First flow component

. . .

. . .


Second flow component

Second flow component

. . .

. . .

. . .


Second flow component1

O

Second flow component

M

D


Hilbert schmidt decomposition of operator

Hilbert-Schmidt decomposition of operator

G

Singular values have a phase transition at the critical value


Singular values of operator

Singular values of operator

G


Degrees of freedom theorem

O

Degrees of freedom theorem


The finishing touches

O

The finishing touches


Understanding the space resource

Understanding the space resource

Space is a capacity bearing object

Geometry plays a fundamental role in determining the number of degrees of freedom and hence the information capacity


Geometrical configurations

Geometrical configurations

In 2D the network capacity scales with the perimeter boundary of the network

In 3D the network capacity scales with the surface boundary of the network


A different configuration

A different configuration

Distribute nodes in a 3D volume of size

Nodes are placed uniformly on a 2Dsurface inside the volume


Different configurations

Different configurations


Massimo franceschetti university of california at san diego

To be continued…

The endless enigma (Salvador Dali)

A hope beyond a shadow of a dream (John Keats)


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