βα-Encoders for A/D conversion

Abstract

The β-encoder, introduced as an alternative to binary encoding in A/D conversion, creates a quantization scheme robust with respect to quantizer imperfections by the use of a β-expansion, where 1 < β < 2. In this paper we introduce a more general encoder called the β-encoder, that can offer more flexibility in design and robustness without any significant drawback on the exponential rate of convergence of the obtained expansion. Although an extra multiplication is introduced, it needs not be very accurate. Mathematically, the βα-encoder gives rise to a dynamical system that is both very interesting and challenging.