A Caltech Library Service

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

Guo, Nian and Kostina, Victoria (2021) Optimal Causal Rate-Constrained Sampling for a Class of Continuous Markov Processes. IEEE Transactions on Information Theory, 67 (12). pp. 7876-7890. ISSN 0018-9448. doi:10.1109/tit.2021.3114142.

[img] PDF - Submitted Version
See Usage Policy.


Use this Persistent URL to link to this item:


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 the expected number of 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. For a class of continuous Markov processes satisfying regularity conditions, we find the optimal encoding and decoding policies that minimize the end-to-end estimation mean-square error under the rate constraint. 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 to decide 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. Furthermore, we show that the optimal causal code also minimizes the mean-square cost of a continuous-time control system driven by a continuous Markov process and controlled by an additive control signal.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper ItemConference Paper
Guo, Nian0000-0003-4490-328X
Kostina, Victoria0000-0002-2406-7440
Additional Information:© 2021 IEEE. Manuscript received May 13, 2020; revised April 23, 2021; accepted September 4, 2021. Date of publication September 20, 2021; date of current version November 22, 2021. This work was supported by the National Science Foundation (NSF) under Grant CCF-1751356 and Grant CCF-1956386. An earlier version of this paper was presented in part at the 2020 IEEE International Symposium on Information Theory.
Funding AgencyGrant Number
Subject Keywords:Causal lossy source coding, sequential estimation, event-triggered sampling, zero-delay coding, rate-distortion theory, control
Issue or Number:12
Record Number:CaltechAUTHORS:20211222-322820000
Persistent URL:
Official Citation:N. Guo and V. Kostina, "Optimal Causal Rate-Constrained Sampling for a Class of Continuous Markov Processes," in IEEE Transactions on Information Theory, vol. 67, no. 12, pp. 7876-7890, Dec. 2021, doi: 10.1109/TIT.2021.3114142
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:112641
Deposited By: Tony Diaz
Deposited On:22 Dec 2021 21:50
Last Modified:22 Dec 2021 21:50

Repository Staff Only: item control page