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

Guo, Nian; Kostina, Victoria

doi:10.1109/isit44484.2020.9174333

Cited by 13 publications

(16 citation statements)

References 23 publications

(48 reference statements)

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“…Prior art on remote estimation and optimal scheduling mostly considered a sampling frequency constraint, whereas in this work, we introduce a rate constraint. We leverage the information-theoretic framework of our prior work [26] to establish the jointly optimal causal sampling and quantization policies. We show that the optimal frequency-constrained causal sampling policy is a symmetric threshold sampling policy (Theorems 1-2).…”

Section: Discussionmentioning

confidence: 99%

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

Guo

Kostina

2021

IEEE Trans. Inform. Theory

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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.

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Section: Discussionmentioning

confidence: 99%

“…A part of this work will be presented at the 2020 IEEE International Symposium on Information Theory [26]; the conference version does not contain Section IV or any proofs.…”

Section: Contributionmentioning

confidence: 99%

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

Guo

Kostina

2021

IEEE Trans. Inform. Theory

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“…The SOI coding scheme also minimizes the mean-square cost of a stochastic plant driven by the Wiener process, and controlled via impulse control (Theorem 4). In our paper [37], we derive the optimal rate-constrained sampling policy for a class of continuous Markov processes satisfying symmetry conditions that the Wiener process meets, and we prove that the SOI code proposed in this paper remains optimal. Theorem 1 shows that the optimal threshold for the Wiener process is equal to 1 R .…”

Section: Discussionmentioning

confidence: 95%

“…Theorem 1 shows that the optimal threshold for the Wiener process is equal to 1 R . In [37], we show how to match the threshold to the statistics of the source more generally.…”

Section: Discussionmentioning

confidence: 99%

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Optimal Causal Rate-Constrained Sampling of the Wiener Process

Guo

Kostina

2022

IEEE Trans. Automat. Contr.

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We consider the following communication scenario. An encoder causally observes the Wiener process and decides when and what to transmit about it. A decoder estimates the process using causally received codewords in real time. We determine the causal encoding and decoding policies that jointly minimize the mean-square estimation error, under the long-term communication rate constraint of R bits per second. We show that an optimal encoding policy can be implemented as a causal sampling policy followed by a causal compressing policy. We prove that the optimal encoding policy samples the Wiener process once the innovation passes either 1 R or 1 R , and compresses the sign of the innovation (SOI) using a 1-bit codeword. The SOI coding scheme achieves the operational distortion-rate function, which is equal to D op (R) = 1 6R . Surprisingly, this is significantly better than the distortion-rate tradeoff achieved in the limit of infinite delay by the best non-causal code. This is because the SOI coding scheme leverages the free timing information supplied by the zero-delay channel between the encoder and the decoder. The key to unlocking that gain is the event-triggered nature of the SOI sampling policy. In contrast, the distortion-rate tradeoffs achieved with deterministic sampling policies are much worse: we prove that the causal informational distortion-rate function in that scenario is as high as DDET(R) = 5 6R . It is achieved by the uniform sampling policy with the sampling interval 1 R . In either case, the optimal strategy is to sample the process as fast as possible and to transmit 1-bit codewords to the decoder without delay. We show that the SOI coding scheme also minimizes the mean-square cost of a continuous-time control system driven by the Wiener process and controlled via rate-constrained impulses.

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Age of Information: An Introduction and Survey

Yates

Sun

Brown

et al. 2021

IEEE J. Select. Areas Commun.

617

251

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

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. We

Cited by 13 publications

References 23 publications

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

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

Optimal Causal Rate-Constrained Sampling of the Wiener Process

Age of Information: An Introduction and Survey

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