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 SECON 2004

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 SECON 2004

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 SECON 2004

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

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

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

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 SECON 2004

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

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

Upper Bound SECON 2004

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

Lower Bound SECON 2004

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

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

Impact of n SECON 2004

Impact of p SECON 2004

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

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

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

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