Rigorous analysis of quantization error of an A/D converter based on β-map

A non-binary analog-to-digital converter (ADC) based on β-expansion, called a β-encoder, can reportedly achieve robustness against large process variation and widespread environment change. The quantization error of the β-encoder is not uniformly distributed, which makes mean squared error (MSE) evaluation difficult. In this work, an analysis method for giving the upper bound of the MSE of the quantization error is proposed. We also gave an evaluation of signal-to-noise-ratio (SNR), which is effective for designing β-encoders.