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Markov Random Processes are not Recoverable After Quantization and Mostly not Recoverable From Samples

Marco, Daniel (2007) Markov Random Processes are not Recoverable After Quantization and Mostly not Recoverable From Samples. In: 2007 IEEE International Symposium on Information Theory. IEEE , Piscataway, NJ, pp. 2886-2890. ISBN 978-1-4244-1397-3. https://resolver.caltech.edu/CaltechAUTHORS:20170419-173738031

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Abstract

Markov random processes and general random processes are considered. It is shown that continuous-time, continuous-valued, wide-sense stationary, Markov random processes that have absolutely continuous second order distributions are not bandlimited. It is also shown that when these processes are strictly stationary and continuous almost surely, they cannot be recovered without error from their quantized versions. Further, it is shown that continuous-time, discrete-valued Markov random processes, which are uniformly bounded and satisfy an additional condition, can be recovered with zero average distortion from an appropriate set of samples for a general distortion measure. A similar result is shown for general continuous-time random processes with rth power distortion measure. Additionally, it is shown that under a milder condition on the Markov processes and a different condition on the sampling times (e.g., uniform sampling), such processes cannot be recovered with zero average distortion. Finally, the notion of information-singularity is extended to continuous-time random processes, and it is shown that both continuous- and discrete-time Markov processes are not information-singular.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/ISIT.2007.4557656DOIArticle
http://ieeexplore.ieee.org/document/4557656/PublisherArticle
Additional Information:© 2007 IEEE. This work was supported by the Center for the Mathematics of Information at California Institute of Technology.
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Funding AgencyGrant Number
Caltech Center for the Mathematics of InformationUNSPECIFIED
DOI:10.1109/ISIT.2007.4557656
Record Number:CaltechAUTHORS:20170419-173738031
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170419-173738031
Official Citation:D. Marco, "Markov Random Processes are not Recoverable After Quantization and Mostly not Recoverable From Samples," 2007 IEEE International Symposium on Information Theory, Nice, 2007, pp. 2886-2890. doi: 10.1109/ISIT.2007.4557656
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:76736
Collection:CaltechAUTHORS
Deposited By: Kristin Buxton
Deposited On:20 Apr 2017 04:38
Last Modified:15 Nov 2021 17:02

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