1Oct. 6, 2004 SECON 2004

An Information-theoretic View of Connectivity in Large Wireless Networks

Xin LiuDepartment of Computer Science

Univ. of California, Davis

Joint work with R. Srikant

Oct. 6, 2004 SECON 2004 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

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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.

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System Model

A regular grid network with unreliable nodes

Planar

Active Node

Inactive Node

Linear

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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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System Model Cont’d AWGN channel Signal attenuation model

>1. Asymptotic bounds

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Objective 1

What is the guaranteed data rate? for any single active sensor node with other active nodes as helpers given the topology.

Active NodeInactive Node

d Sink

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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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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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Upper Bound

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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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Lower Bound

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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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Linear Network Upper bound

((log(n))-2+1)

Lower bound O((log(n))-2)

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Impact of n

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Impact of p

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Planar Networks

Upper bound ((log(n))-+1)

Lower bound O((log(n))-)

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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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To-do list

Gap between upper and lower bounds Random deployed networks Fading channels

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System Model

A regular grid network with unreliable nodes

Linear Network

Planar Network