On The Capacity of Wireless Networks: The Relay Case

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On The Capacity of Wireless Networks The Relay
Case

• M. Gastpar, M. Vetterli

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Outline

• Introduction, Info. Theory and Networks
• The Gaussian Relay Network
• Capacity of Gaussian Relay Network
• Upperbound
• Lowerbound
• Asymptotic Capacity
• Conclusion

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Wireless Relay Networks

• Gupta, Kumar assumed point-to-point coding,
  excluding MAC, BC, etc
• Gives aggregate cap. bit-meters/sec
• or roughly O(1) bit/sec
• Here, one active source-destination pair, other
  nodes help them to communicate
• Same physical assumptions
• Paper demonstrates O(log n) bit/sec asymp. cap.

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Physical Model
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Information Theory Networks

• Multiple Access
• Broadcast, degraded case
• Relay, degraded case
• Not many concrete conclsuions
• Asymptotic Results

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Gaussian Relay Network

• The Network Model
• n nodes located uniformly in a disk of unit area
• In each time slot, each node either transmits or
  receives

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Further assumptions

• There is a dead zone around source and
  destination nodes
• Realistic, no pointy node
• The source node may send only half of the time
• Not necessary

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Capacity of Gaussian Relay Network

• Upperbound by max flow min cut thm.
• Lowerbound by uncoded transmission and separation
  theorem
• They coincide asymptotically for large n !

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Upperbound on Capacity

• Broadcast cut
• Capacity cannot be greater
• than a 1 X n-1 MIMO s

• Notes
• s are bounded from above
• Expected value of upperbound
• scales by log n

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Lower Bound on Capacity- I

• Separation theorem, gives the lower bound
• for any scheme achieving
• Pick up a Gaussian source and squared-error
  distortion measure
• Send the Gaussian signal without coding over the
  channel to relays
• Relays scale the signal and send it to the Rec.
• Receiver does linear processing

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Lower Bound on Capacity- II
Favorable power allocation, simplifies the
calculations
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Asymptotic Capacity- I
For any realization of the channel and by this
setup capacity asymptotically tends to
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Asymptotic Capacity- II

• Behavior of the convergence of upper and lower
  bounds with n

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Conclusion

• Network Coding Helps O(log n) instead of O(1)
• Some of the assumptions not necessary
• Simple encoding and decoding can do great when
  source and channel are matched