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We study the problem of the reconstruction of a Gaussian field defined in [0,1] using N sensors deployed at regular intervals. The goal is to quantify the total data rate required for the reconstruction of the field with a given mean square distortion. We consider a class of two-stage mechanisms which (a) send information to allow the reconstruction of the sensor's samples within sufficient accuracy, and then (b) use these reconstructions to estimate the entire field. To implement the first stage, the heavy correlation between the sensor samples suggests the use of distributed coding schemes to reduce the total rate. Our main contribution is to demonstrate the existence of a distributed block coding scheme that achieves, for a given fidelity criterion for the sensor's measurements, a total information rate that is within a constant, independent of N, of the minimum information rate required by an encoder that has access to all the sensor measurements simultaneously. The constant in general depends on the autocorrelation function of the field and the desired distortion criterion for the sensor samples.