| Paper: | SS-7.4 | ||
| Session: | Distributed Digital Signal Processing for Sensor Networking | ||
| Time: | Thursday, May 20, 10:15 - 10:30 | ||
| Presentation: | Special Session Lecture | ||
| Topic: | Special Sessions: Distributed Digital Signal Processing for Sensor Networking | ||
| Title: | RATE-DISTORTION PROBLEM FOR PHYSICS BASED DISTRIBUTED SENSING | ||
| Authors: | Baltasar Beferull-Lozano; Swiss Federal Institute of Technology (EPFL) | ||
| Robert Konsbruck; Swiss Federal Institute of Technology (EPFL) | |||
| Martin Vetterli; Swiss Federal Institute of Technology (EPFL) | |||
| Abstract: | We consider the rate-distortion problem for sensing the continuousspace-time physical temperature in a circular ring on which a heatsource is applied over space and time, and which is allowedto cool by radiation or convection. The heat source is modelled asa continuous space-time stochastic process which is bandlimited overspace and time. The temperature field is the result of a certaincontinuous space-time convolution of the heat source with theGreen's function corresponding to the heat equation, which isspace and time invariant. The temperature field is sampled atuniform spatial locations by a set of sensors and it has to bereconstructed at a base station. The goal is to minimize themean-square-error per second, for a given number of nats persecond, assuming ideal communication channels between sensors andbase station. We find a) the centralized $R^{\text{c}}(D)$function of the temperature field, where the base station canoptimally encode all the space-time samples jointly. Then, weobtain b) the $R^{\text{s-i}}(D)$ function, where each sensor,independently, encodes its samples optimally over time and c) the$R^{\text{st-i}}(D)$ function, where each sensor is constrained toencode also independently over time. We also study twodistributed prediction-based approaches: a) with perfect feedbackfrom the base station, where temporal predictionis performed at the base station and each sensor performsdifferential encoding, and b) without feedback, whereeach sensor locally performs temporal prediction. | ||
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