Linear and non-linear montecarlo approximations of analog joint source-channel coding under generic probability distributions

A distributed estimation setting is considered, where a number of sensors transmit their observations of a physical phenomenon, described by one or more random variables, to a sink over noisy communication channels. The goal is to minimize a quadratic distortion measure (Minimum Mean Square Error - MMSE) under a global power constraint on the sensors´ transmissions. Both linear MMSE encoders and decoders, parametrically optimized in encoders´ gains, and non-linear parametric functional approximators (neural networks) are investigated and numerically compared, highlighting subtle differences in sensitivity and achievable performance.