Source-channel coding for very-low bandwidth sources

We address the source-channel coding problem of a sensor observing a slowly time-varying Gaussian source and communicating its information to a receiver through a Gaussian channel. Due to the slowly time-varying characteristic of the source, we consider that the sensor is capable of using many channel dimensions per source symbol. Under an energy constraint per source realisation, we derive a theoretical lower bound on the MSE distortion as well as an analytical upper bound based on a practical coding scheme involving a linear uniform quantizer followed by an orthogonal modulation and a MAP receiver. Other coding schemes coupled with an MMSE estimator are also proposed and their performances are compared. An extension to the case where the sensor has the capability of encoding a sequence of N source components is studied and a general upper bound in that case is obtained.