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

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 bit rate and sensing-related network overhead rate simultaneously go to zero. A general condition for the optimization of the rate of decay of the MSE upper-bound with sensor density is derived. Specific MSE versus sensor density decay rates are illustrated for the constant and Lipschitz-1 fields with the former attaining order-optimal scaling behavior.