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CORR
2010
Springer

Lower bounds for the error decay incurred by coarse quantization schemes

13 years 3 months ago
Lower bounds for the error decay incurred by coarse quantization schemes
Several analog-to-digital conversion methods for bandlimited signals used in applications, such as quantization schemes, employ coarse quantization coupled with oversampling. The standard mathematical model for the error accrued from such methods measures the performance of a given scheme by the rate at which the associated reconstruction error decays as a function of the oversampling ratio . It was recently shown that exponential accuracy of the form O(2-) can be achieved by appropriate one-bit Sigma-Delta modulation schemes. However, the best known achievable rate constants in this setting differ significantly from the general information theoretic lower bound. In this paper, we provide the first lower bound specific to coarse quantization, thus narrowing the gap between existing upper and lower bounds. In particular, our results imply a quantitative correspondence between the maximal signal amplitude and the best possible error decay rate. Our method draws from the theory of larg...
Felix Krahmer, Rachel Ward
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2010
Where CORR
Authors Felix Krahmer, Rachel Ward
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