Robust and practical analog-to-digital conversion with exponential precision
Beta-encoders with error correction were introduced by Daubechies, DeVore, Güntürk and Vaishampayan as an alternative to pulse-code modulation (PCM) for analog-to-digital conversion. An N -bit beta-encoder quantizes a real number by computing one of its N-bit truncated β-expansions where β ∈ (1, 2) determines the base of expansion. These encoders have (almost) optimal rate-distortion properties like PCM; furthermore, they exploit the redundancy of beta-expansions and thus they are robust with respect to quantizer imperfections. However, these encoders have the shortcoming that the decoder needs to know the value of the base of expansion β, a gain factor in the circuit used by the encoder, which is an impractical constraint. We present a method to implement beta-encoders so that they are also robust with respect to uncertainties of the value of β. The method relies upon embedding the value of β in the encoded bitstream.We show that this can be done without a priori knowledge of β by the transmitting party. Moreover the algorithm still works if the value of β changes (slowly) during the implementation. © 2006 IEEE.
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