Stable single-bit noise-shaping quantizer based on data coding into optimized binary vectors

This paper presents data coding techniques for a stable single-bit noise-shaping quantizer, which has a cascade structure of a multi-bit ΣΔ modulator (ΣΔM) and a binary interpolator. The binary interpolator chooses a pre-optimized binary vector for each input sample and successively generates the chosen binary vector as an output binary sequence. The binary vectors can have different lengths. The paper also proposes two methods to evaluate and bound output errors of a binary interpolator. A multi-bit ΣΔM is designed to cause no overload for all possible input signals whose amplitudes are bounded to a specified level, and thus the ΣΔM rigorously guarantees the stability condition. In a design example, we have evaluated SNDRs and a noise spectrum and then confirmed that our stable quantizer can sharply shape output noise spectra.