The Golden Ratio Encoder

TL;DR

This paper introduces a robust Nyquist-rate A/D conversion algorithm based on a beta-encoder with the golden mean, achieving exponential accuracy despite component imperfections.

Contribution

It extends beta-encoder robustness to include imperfect analog multipliers and proposes a formal model and testing framework for algorithmic encoder robustness.

Findings

Achieves exponential accuracy at Nyquist rate with imperfect components

Extends beta-encoder robustness to gain imprecision in analog multipliers

Provides a formal computational model and robustness evaluation test bed

Abstract

This paper proposes a novel Nyquist-rate analog-to-digital (A/D) conversion algorithm which achieves exponential accuracy in the bit-rate despite using imperfect components. The proposed algorithm is based on a robust implementation of a beta-encoder where the value of the base beta is equal to golden mean. It was previously shown that beta-encoders can be implemented in such a way that their exponential accuracy is robust against threshold offsets in the quantizer element. This paper extends this result by allowing for imperfect analog multipliers with imprecise gain values as well. A formal computational model for algorithmic encoders and a general test bed for evaluating their robustness is also proposed.