Math @ Duke

Publications [#287176] of Ingrid Daubechies
Papers Published
 Daubechies, I; Yilmaz, Ö, Robust and practical analogtodigital conversion with exponential precision,
IEEE Transactions on Information Theory, vol. 52 no. 8
(2006),
pp. 35333545, ISSN 00189448 [doi]
(last updated on 2017/12/17)
Abstract: Betaencoders with error correction were introduced by Daubechies, DeVore, Güntürk and Vaishampayan as an alternative to pulsecode modulation (PCM) for analogtodigital conversion. An N bit betaencoder quantizes a real number by computing one of its Nbit truncated βexpansions where β ∈ (1, 2) determines the base of expansion. These encoders have (almost) optimal ratedistortion properties like PCM; furthermore, they exploit the redundancy of betaexpansions 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 betaencoders 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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