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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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slide1

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

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

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.

approach1
Approach

. . .

. . .

. . .

second flow component
Second flow component

. . .

. . .

. . .

hilbert schmidt decomposition of operator
Hilbert-Schmidt decomposition of operator

G

Singular values have a phase transition at the critical value

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

slide24

To be continued…

The endless enigma (Salvador Dali)

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

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