A/D conversion with imperfect quantizers

This paper analyzes mathematically the effect of quantizer threshold imperfection commonly encountered in the circuit implementation of analog-to-digital (A/D) converters such as pulse code modulation (PCM) and sigma-delta (SigmaDelta) modulation. SigmaDelta modulation, which is based on coarse quantization of oversampled (redundant) samples of a signal, enjoys a type of self-correction property for quantizer threshold errors (bias) that is not shared by PCM. Although "classical" SigmaDelta modulation is inferior to PCM in the rate-distortion sense, this robustness feature is believed to be one of the reasons why SigmaDelta modulation is preferred over PCM in A/D converters with imperfect quantizers. Motivated by these facts, other encoders are constructed in this paper that use redundancy to obtain a similar self-correction property, but that achieve higher order accuracy relative to bit rate compared to classical SigmaDelta. More precisely, two different types of encoders are introduced that exhibit exponential accuracy in the bit rate (in contrast to the polynomial-type accuracy of classical SigmaDelta) while possessing the self-correction property