  Zero-delay transmission of a Gaussian source over an additive white Gaussian
noise (AWGN) channel is considered with a one-bit analog-to-digital converter
(ADC) front end and a correlated side information at the receiver. The design
of the optimal encoder and decoder is studied for two performance criteria,
namely, the mean squared error (MSE) distortion and the distortion outage
probability (DOP), under an average power constraint on the channel input. For
both criteria, necessary optimality conditions for the encoder and the decoder
are derived. Using these conditions, it is observed that the numerically
optimized encoder (NOE) under the MSE distortion criterion is periodic, and its
period increases with the correlation between the source and the receiver side
information. For the DOP, it is instead seen that the NOE mappings periodically
acquire positive and negative values, which decay to zero with increasing
source magnitude, and the interval over which the mapping takes non-zero
values, becomes wider with the correlation between the source and the side
information.
