Decentralized Encoding for Linear Estimation of a Remote Source

N separated sensors transmit noisy observations of a source to a central processor for final estimation; local encoding of each observation is performed prior to transmission. The issue is to devise encoding-decoding schemes for this decentralized context. The present scheme is composed of N scalar quantizes, each with a corresponding decoder, and a linear combination of individual estimates. This structure ensures that the decoder size increases only linearly with N. Through an example involving 2 sensors with a Gaussian model of source and observations, this scheme is compared to a previously considered unconstrained decoding scheme and to a distortion-rate bound.