Various novel techniques for A/D conversion of signals subject to a fidelity criterion are presented, leading to optimum digital representations, in which each signal sample is not necessarily quantized to the closest reconstruction level. Quantization is treated as an optimization problem, and the tradeoffs among sampling rate, quantization stepsize, and quantization distortion are examined. It is shown that symmetric neural networks offer a natural means for efficient implementation of the proposed technique. Applications include digital image halftoning, as well as all forms of PCM coding and oversampled A/D conversion. It is shown that concepts and structures used in digital image halftoning are directly applicable to oversampled sigma-delta modulation of sound signals. A novel kind of parallel analog network is introduced and shown to be appropriate for this task. These networks contain a nonmonotonic nonlinearity in lieu of the sigmoid function and perform error diffusion in all directions. Ideas for massively parallel analog VLSI implementation are offered.< >