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-digltal (A/D) converters such as pulse code modulation (PCM) and sigma-delta (∑Δ) modulation. ∑Δ 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" ∑Δ modulation is inferior to PCM in the rate-distortion sense, this robustness feature is believed to be one of the reasons why ∑Δ 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 ∑Δ. 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 ∑Δ) while possessing the self-correction property.