An Information-theoretic View of Connectivity in Large Wireless Networks

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 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 SECON 2004

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. SECON 2004

4. Active Node Inactive Node System Model • A regular grid network with unreliable nodes Planar Linear SECON 2004

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. SECON 2004

6. System Model Cont’d • AWGN channel • Signal attenuation model • >1. • Asymptotic bounds SECON 2004

7. d Active Node Inactive Node Objective 1 • What is the guaranteed data rate? • for any single active sensor node • with other active nodes as helpers • given the topology. Sink SECON 2004

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. SECON 2004

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 SECON 2004

10. Upper Bound SECON 2004

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. SECON 2004

12. Lower Bound SECON 2004

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. SECON 2004

14. Linear Network • Upper bound • ((log(n))-2+1) • Lower bound • O((log(n))-2) SECON 2004

15. Impact of n SECON 2004

16. Impact of p SECON 2004

17. Planar Networks • Upper bound • ((log(n))-+1) • Lower bound • O((log(n))-) SECON 2004

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. SECON 2004

19. To-do list • Gap between upper and lower bounds • Random deployed networks • Fading channels Thank you! SECON 2004

20. System Model • A regular grid network with unreliable nodes Linear Network Planar Network SECON 2004