Joint source-channel coding with one-bit ADC front end

This paper considers the zero-delay transmission of a Gaussian source over an additive white Gaussian noise (AWGN) channel with a one-bit analog-to-digital converter (ADC) front end. The optimization of the encoder and decoder is tackled under both the mean squared error (MSE) distortion and the outage distortion criteria with an average power constraint. For MSE distortion, the optimal transceiver is identified over the space of symmetric encoders. This result demonstrates that the linear encoder, which is optimal with a full-precision front end, approaches optimality only in the low signal-to-noise ratio (SNR) regime; while, digital transmission is optimal in the high SNR regime. For the outage distortion criterion, the structure of the optimal encoder and decoder are obtained. In particular, it is shown that the encoder mapping is piecewise constant and can take only two opposite values when it is non-zero.