Rigorous estimates of quantization error for A/D converters based on beta-map

Abstract

A β-encoder, a non-binary analog-to-digital converter that is based on the β-expansion, is reported to be robust to large process variations and widespread environment fluctuations. However, the quantization error of the β-encoder is complicatedly distributed and hard to be estimated due to the chaotic nature of the β-transformation. In this work, we propose an analysis method for determining an upper bound of the mean squared error of the quantization. We also provide an evaluation of the signal-to-quantization-noise ratio, which is useful for designing β-encoders.