The β α-Encoders for Robust A/D Conversion

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 α-encoder, that can offer more flexibility in design and robustness without any significant drawback on the exponential rate of convergence of the obtained expansion. Mathematically, the β α-encoder gives rise to a dynamical system that is both very interesting and challenging.