Zero-delay source-channel coding with a 1-Bit ADC front end and correlated receiver side information

Zero-delay transmission of a Gaussian source over an additive white Gaussian noise (AWGN) channel is considered with a 1-bit analog-to-digital converter (ADC) front end and correlated side information at the receiver. The design of the optimal encoder and decoder is studied for two different 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, which are then used to numerically obtain encoder and decoder mappings that satisfy these conditions. 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. Finally, inspired by the mentioned properties of the NOE mappings, parameterized encoder mappings with a small number of degrees of freedom are proposed for both distortion criteria, and their performance is compared with that of the NOE mappings.