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Optimal Causal Rate-Constrained Sampling for a Class of Continuous Markov Processes

Guo, Nian and Kostina, Victoria (2020) Optimal Causal Rate-Constrained Sampling for a Class of Continuous Markov Processes. In: 2020 IEEE International Symposium on Information Theory (ISIT). IEEE , Piscataway, NJ, pp. 2456-2461. ISBN 978-1-7281-6432-8. https://resolver.caltech.edu/CaltechAUTHORS:20200214-105617315

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Abstract

Consider the following communication scenario. An encoder observes a stochastic process and causally decides when and what to transmit about it, under a constraint on bits transmitted per second. A decoder uses the received codewords to causally estimate the process in real time. The encoder and the decoder are synchronized in time. We aim to find the optimal encoding and decoding policies that minimize the end-to-end estimation mean-square error under the rate constraint. For a class of continuous Markov processes satisfying regularity conditions, we show that the optimal encoding policy transmits a 1-bit codeword once the process innovation passes one of two thresholds. The optimal decoder noiselessly recovers the last sample from the 1-bit codewords and codeword-generating time stamps, and uses it as the running estimate of the current process, until the next codeword arrives. In particular, we show the optimal causal code for the Ornstein-Uhlenbeck process and calculate its distortion-rate function.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/ISIT44484.2020.9174333DOIArticle
https://arxiv.org/abs/2002.01581arXivDiscussion Paper
ORCID:
AuthorORCID
Guo, Nian0000-0003-4490-328X
Kostina, Victoria0000-0002-2406-7440
Additional Information:© 2020 IEEE. This work was supported in part by the National Science Foundation (NSF) under grant CCF-1751356.
Funders:
Funding AgencyGrant Number
NSFCCF-1751356
Subject Keywords:Causal lossy source coding, sequential estimation, event-triggered sampling, zero-delay coding
Record Number:CaltechAUTHORS:20200214-105617315
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200214-105617315
Official Citation:N. Guo and V. Kostina, "Optimal Causal Rate-Constrained Sampling for a Class of Continuous Markov Processes," 2020 IEEE International Symposium on Information Theory (ISIT), Los Angeles, CA, USA, 2020, pp. 2456-2461, doi: 10.1109/ISIT44484.2020.9174333
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101306
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:14 Feb 2020 20:45
Last Modified:23 Nov 2020 23:06

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