Zero-delay source-channel coding with a low-resolution ADC front end

Motivated by the practical constraints arising in emerging sensor network and Internet-of-Things (IoT) applications, the zero-delay transmission of a Gaussian measurement over a real single-input multiple-output (SIMO) additive white Gaussian noise (AWGN) channel is studied with a low-resolution analog-to-digital converter (ADC) front end. Joint optimization of the encoder and the decoder mapping is tackled under both the mean squared error (MSE) distortion and the distortion outage probability (DOP) criteria, with an average power constraint on the channel input. Optimal encoder and decoder mappings are identified for a one-bit ADC front end under both criteria. For the MSE distortion, the optimal encoder mapping is shown to be non-linear in general, while it tends to a linear encoder in the low signal-to-noise ratio (SNR) regime, and to an antipodal digital encoder in the high SNR regime. This is in contrast to the optimality of linear encoding at all SNR values in the presence of a full-precision front end. For the DOP criterion, it is shown that the optimal encoder mapping is piecewise constant and can take only two opposite values when it is non-zero. For both the MSE distortion and the DOP criteria, necessary optimality conditions are then derived for K-level ADC front ends as well as front ends with multiple one-bit ADCs. These conditions are used to obtain numerically optimized solutions. Extensive numerical results are also provided in order to gain insights into the structure of the optimal encoding and decoding mappings.