1. An Information-theoretic View of Connectivity in Large Wireless Networks
Xin Liu
Department of Computer Science
Univ. of California, Davis
Joint work with R. Srikant
Oct. 6, 2004
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2. What’s new? Traditional approach: qualify connectivity.
Yes or No.
Far away nodes may still communicate.
“An ocean of possibilities”- from an information-theoretic viewpoint
Coherent relay, broadcast, multi-access, interference cancellation, network coding, etc.
Multi-path routing, multi-hop relay, etc.
Our approach: quantify connectivity
Network connectivity issue has attracted a lot of research attentions, including that of our previous speakers. Most work assume either a geographic location-based model or a SINR model. In the geographic model, a node is directly connected …. IN the SINR model, …. Questions being addressed include: whether or not a node, all nodes, a large portion of nodes are connected or not. Such approaches qualify connectivity, An analogy is to give a pass-no-pass grade in a course. We do not really know how good a student performs in the class. Such models well capture the current hardware and software status, especially small sensor nodes. ON the other hand, there are possibilities not being captured by such models. For instance, ..
IN our work, we want to take such possibilites into account. Basically, we want to quantify connectivity. Let me give a precise definition in the following slide.
Oct. 6, 2004
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3. Definition The network is connected at rate R, if
any single node
communicate with its randomly chosen destination node at rate R
assuming all other nodes are helpers.
For a sensor network, the destination can be the sink node.
There are a few key words in this definition. One pair, but any pair.
Given such a definition, we would like to address the connectivity property of a large sensor network. Let me first introduce the system model
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4. System Model A regular grid network with unreliable nodes Planar
Linear
Active Node
Inactive Node
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5. System Model Cont’d p: probability a node is active
Out of energy, out of sync, damaged, etc.
Can reflect the temporal property of a network
Pinv: average power constraint per node
Does not limit to multi-hop relay
Include possible approaches
Coherent relay, broadcast, multi-access, interference cancellation, etc.
Multi-path routing, multi-hop relay, etc.
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6. System Model Cont’d AWGN channel Signal attenuation model >1.
Asymptotic bounds
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7. Objective 1 What is the guaranteed data rate?
for any single active sensor node
with other active nodes as helpers
given the topology.
Sink
Active Node
Inactive Node d
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8. Objective 2 How large an area can be covered by n nodes?
given the desired data rate R
for each single active sensor node
with other active nodes as helpers.
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9. Applications Infrequent yet important communications
Surveillance network with rare events
Lower bound on data rate for ALL nodes
Isolated nodes are important in terms of information gathering and event detection
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10. Upper Bound
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11. Notes Some nodes may achieve higher rates.
Upper bound cannot be guaranteed for ALL.
Achievable rate is bounded by the total received power
With a certain probability, there exists an isolated node
An isolated node is a node far away from others
Rate is bounded.
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12. Lower Bound
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13. Notes Guaranteed lower bound Achievability
Divide the linear network into intervals
Each interval has at least one node
Multi-hop relay with interference cancellation.
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14. Linear Network Upper bound Lower bound ((log(n))-2+1) O((log(n))-2)
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15. Impact of n
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16. Impact of p
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17. Planar Networks Upper bound Lower bound ((log(n))-+1) O((log(n))-)
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18. Take-home Message Quantify connectivity
Connectivity is associated with guaranteed achievable data rate.
Applies to networks with infrequency communications
Applies to wireless networks with a p-2-p communication pattern.
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19. To-do list Thank you! Gap between upper and lower bounds
Random deployed networks
Fading channels
Thank you!
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20. System Model A regular grid network with unreliable nodes
Linear Network
Planar Network
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