For decentralized estimation of a remote source under communication co
nstraints, noisy observations taken by spatially separated sensors are
encoded before transmission to a central decision maker. As the obser
vations are not simultaneously available at a given site, the peripher
al encoders are to operate disjointly. This problem cannot be cast as
the classical one of encoding a remote source. Given that the peripher
al encoders are scalar quantizers, we consider several criteria for pa
rtitioning the space of observations and for reproducing the source wi
th minimum distortion. They differ in regard to the knowledge about th
e source-observations model, for example about the spatial correlation
among the observations, and in regard to the complexity of the decodi
ng operations, but all lead to an unifying design approach of cyclical
optimization. For a linear Gaussian source-observations model, adopti
ng the quadratic distortion measure, we carry out each design and eval
uate the performance of the various schemes in terms of achieved disto
rtion-rate pairs, allowing for some combined parametric variations of
the model. We also derive the optimum theoretically achievable perform
ance for the distributed and for the conventional (non-distributed) sc
heme in terms of distortion-rate bounds. The results demonstrate that
distributed encoding-decoding schemes, if properly designed, compare f
avorably to the non-distributed schemes.