Abstract
We address the problem of deterministic oversampling of bandlimited sensor fields in a distributed communication-constrained processing environment, where it is desired for a central intelligent unit to reconstruct the sensor field to maximum pointwise accuracy. We show, using a dither-based sampling scheme, that is is possible to accomplish this using minimal inter-sensor communication with the aid of a multitude of low-precision sensors. Furthermore, we show the feasibility of having a flexible tradeoff between the average oversampling rate and the Analog to Digital (A/D) quantization precision per sensor sample with respect to achieving exponential accuracy in the number of bits per Nyquist-period, thereby exposing a key underpinning “conservation of bits” principle. That is, we can distribute the bit budget per Nyquist-period along the amplitude-axis (precision of A/D converter) and space (or time or space-time) using oversampling in an almost arbitrary discrete-valued manner, while retaining the same reconstruction error decay profile. Interestingly this oversampling is possible in a highly localized communication setting, with only nearest-neighbor communication, making it very attractive for dense sensor networks operating under stringent inter-node communication constraints. Finally we show how our scheme incorporates security as a by-product due to the presence of an underlying dither signal which can be used as a natural encryption device for security. The choice of the dither function enhances the security of the network.
This research was supported by NSF under grant CCR-0219722 and DARPA under grant F30602-00-2-0538.
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References
R. J. Marks, II, Introduction to Shannon Sampling and Interpolation Theory. New York, USA: Springer-Verlag, 1990.
J. Chou, D. Petrovic, and K. Ramchandran, “Tracking and exploiting correlations in dense sensor networks,” in Asilomar Conference on Signals, Systems and Computers, (Pacific Grove, CA), Nov 2002.
Z. Cvetković and M. Vetterli, “Error-rate Characteristics of Oversampled Analog-to-Digital Conversion,” IEEE Trans. on Information Theory, vol. 44, pp. 1961–1964, Sep 1998.
I. Daubechies, Ten Lectures on Wavelets. Philadelphia: SIAM, 1992.
Z. Cvetković and I. Daubechies, “Single Bit oversampled A/D conversion with exponential accuracy in bit rate,” Proceeding DCC, pp. 343–352, March 2000.
Z. Cvetković, I. Daubechies, and B. F. Logan, “Interpolation of Bandlimited functions from quantized Irregular Samples,” Proceeding DCC, pp. 412–421, April 2002.
W. Rudin, Principles of Mathematical Analysis. USA: McGraw-Hill Companies, 1976.
G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities. London, UK: Cambridge University Press, 1959.
M. Vetterli, P. Marzilliano, and T. Blu, “Sampling Signals with Finite Rate of Innovation,” IEEE Trans. Signal Proc., pp. 1417–1428, June 2002.
P. Gupta and P. R. Kumar, “The Capacity of Wireless Networks,” IEEE Trans. on Information Theory, vol. IT-46, pp. 388–404, Mar. 2000.
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Ishwar, P., Kumar, A., Ramchandran, K. (2003). Distributed Sampling for Dense Sensor Networks: A “Bit-Conservation Principle”. In: Zhao, F., Guibas, L. (eds) Information Processing in Sensor Networks. IPSN 2003. Lecture Notes in Computer Science, vol 2634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36978-3_2
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DOI: https://doi.org/10.1007/3-540-36978-3_2
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