Scalar quantization with noisy partitions and its application to Flash ADC design
Author(s)Wang, Da; Polyanskiy, Yury; Wornell, Gregory W.
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Motivated by recent circuit designs for Flash ADCs with imperfect comparators, we investigate the problem of scalar quantization with noisy partition points, where the partition point locations are perturbed from the designated values by noise during the placement process. For this problem setting, we derive a high resolution approximation for mean square error, and analyze the optimal partition point density accordingly. Our results indicate that it is necessary to take the effect of noise into account in the design process. In particular, we derive the optimal partition point density when the input distribution is Gaussian or uniform, and show when noise variance exceeds a certain threshold, a peculiar phase transition occurs and the optimal point density degenerates into a delta function at the origin. These theoretical results allow to optimize the design of flash ADCs and gain 1 bit in resolution over existing designs.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Proceedings of the 2014 IEEE International Symposium on Information Theory
Institute of Electrical and Electronics Engineers (IEEE)
Wang, Da, Yury Polyanskiy, and Gregory Wornell. “Scalar Quantization with Noisy Partitions and Its Application to Flash ADC Design.” 2014 IEEE International Symposium on Information Theory (June 2014).
Author's final manuscript