Rate-Distortion Behavior of the Plenacoustic Function

Author

Robert L. Konsbruck

Introduction

Wireless sensor networks consist of a large number of small, low power devices, equipped with limited processing and communication capabilities, which measure a physical phenomenon in some region of interest. The goal is typically to reconstruct the measured physical field (e.g. temperature, pressure, light) at an intelligent central unit to within some prescribed accuracy, and this at the lowest possible cost on the communication link and power consumption by the sensors. We investigate the role of physical laws in source coding problems appearing in typical sensor network applications with the aim of quantifying the potential gains in terms of rate-distortion behavior that exploiting these laws can provide and also of devising practical strategies to approach the theoretical bounds.

Current and Future Research

We consider the rate-distortion problem for recording a spatio-temporal acoustic field in some region, which is generated by sound sources at a distant location. Sensors equipped with microphones in the recording region sample the sound field, quantize the samples, and transmit the compressed samples to a central base station, which produces an estimate of the original sound field at any point in the recording region. The recorded field is the solution of the acoustic wave equation with appropriate boundary conditions and a driving function determined by the sound sources. In other words, it is the result of the spatio-temporal convolution of the source field with the Green’s function of the wave equation, which is also called the plenacoustic function (PAF). The interesting observation is that for temporally bandlimited sources, the recorded sound field is essentially bandlimited in space and, thus, it can be sampled with a finite microphone array. Moreover, the spectral support in space of the PAF is small at low temporal frequencies, and it increases linearly with the temporal frequency. We study the influence of the characteristics of the PAF on the performance of distributed coding schemes and analyze coding strategies that are adapted to the particular spectral shape of the PAF.

Collaborations

Martin Vetterli, Emre Telatar (EPFL – Information Theory Laboratory (LTHI)).

Project Period

December 2004 – ongoing.

Funding Source

LCAV.