One-bit Distributed Sensing and Coding for Field Estimation in Sensor Networks

TL;DR

This paper introduces a novel distributed sensing scheme using one-bit quantizers for accurate field reconstruction in sensor networks, achieving near-zero error with increasing sensor density under certain conditions.

Contribution

It develops a new quantization and reconstruction method for noisy one-bit sensor data, providing theoretical guarantees and optimal scaling behavior.

Findings

MSE can be driven to zero with increasing sensor density.

The scheme achieves order-optimal MSE scaling for spatially constant fields.

Per-sensor bitrate and network overhead can vanish as sensor density increases.

Abstract

This paper formulates and studies a general distributed field reconstruction problem using a dense network of noisy one-bit randomized scalar quantizers in the presence of additive observation noise of unknown distribution. A constructive quantization, coding, and field reconstruction scheme is developed and an upper-bound to the associated mean squared error (MSE) at any point and any snapshot is derived in terms of the local spatio-temporal smoothness properties of the underlying field. It is shown that when the noise, sensor placement pattern, and the sensor schedule satisfy certain weak technical requirements, it is possible to drive the MSE to zero with increasing sensor density at points of field continuity while ensuring that the per-sensor bitrate and sensing-related network overhead rate simultaneously go to zero. The proposed scheme achieves the order-optimal MSE versus sensor density scaling behavior for the class of spatially constant spatio-temporal fields.