  Delay constrained linear transmission (LT) strategies are considered for the
transmission of composite Gaussian measurements over an additive white Gaussian
noise fading channel under an average power constraint. If the channel state
information (CSI) is known by both the encoder and decoder, the optimal LT
scheme in terms of the average mean-square error distortion is characterized
under a strict delay constraint, and a graphical interpretation of the optimal
power allocation strategy is presented. Then, for general delay constraints,
two LT strategies are proposed based on the solution to a particular multiple
measurements-parallel channels scenario. It is shown that the distortion
decreases as the delay constraint is relaxed, and when the delay constraint is
completely removed, both strategies achieve the optimal performance under
certain matching conditions. If the CSI is known only by the decoder, the
optimal LT strategy is derived under a strict delay constraint. The extension
for general delay constraints is shown to be hard. As a first step towards
understanding the structure of the optimal scheme in this case, it is shown
that for the multiple measurements-parallel channels scenario, any LT scheme
that uses only a one-to-one linear mapping between measurements and channels is
suboptimal in general.
