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

Guo, Nian; Kostina, Victoria

doi:10.1109/tit.2021.3114142

Cited by 12 publications

(7 citation statements)

References 38 publications

(83 reference statements)

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“…Then, threshold policies are shown optimal in this case, in which a new sample is acquired only if the expected age-penalty by the time it arrives surpasses a certain value. This paper extends [38] (and the related studies in [39,40]) to multiple OU processes.…”

Section: Introductionmentioning

confidence: 60%

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Timely Multi-Process Estimation Over Erasure Channels With and Without Feedback

Banawan¹,

Arafa²,

Seddik³

2023

Preprint

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We consider a multi-process remote estimation system observing K independent Ornstein-Uhlenbeck processes. In this system, a shared sensor samples the K processes in such a way that the long-term average sum mean square error (MSE) is minimized. The sensor operates under a total sampling frequency constraint f max . The samples from all processes consume random processing delays in a shared queue and then are transmitted over an erasure channel with probability . We study two variants of the problem: first, when the samples are scheduled according to a Maximum-Age-First (MAF) policy, and the receiver provides an erasure status feedback; and second, when samples are scheduled according to a Round-Robin (RR) policy, when there is no erasure status feedback from the receiver. Aided by optimal structural results, we show that the optimal sampling policy for both settings, under some conditions, is a threshold policy. We characterize the optimal threshold and the corresponding optimal long-term average sum MSE as a function of K, f max , , and the statistical properties of the observed processes. Our results show that, with an exponentially distributed service rate, the optimal threshold τ * increases as the number of processes K increases, for both settings. Additionally, we show that the optimal threshold is an increasing function of in the case of available erasure status feedback, while it exhibits the opposite behavior, i.e., τ * is a decreasing function of , in the case of absent erasure status feedback.

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Section: Introductionmentioning

confidence: 60%

“…Our recent work in [39] also focuses on characterizing the relationship of MSE and AoI, yet with the additional presence of coding and quantization. Reference [40] shows the optimality of threshold policies for tracking OU processes under rate constraints.…”

Section: Introductionmentioning

confidence: 99%

Timely Multi-Process Estimation Over Erasure Channels With and Without Feedback

Banawan¹,

Arafa²,

Seddik³

2023

Preprint

View full text Add to dashboard Cite

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“…Rabi et al [8] formulated the estimation of the scalar Wiener and scalar Ornstein-Uhlenbeck processes as an optimal multiple stopping time problem by discarding the signaling effect, and showed that the optimal triggering policy is symmetric threshold. Guo and Kostina [9] addressed the estimation of the scalar Wiener and scalar Ornstein-Uhlenbeck processes in the presence of the signaling effect, and obtained a result that matches with that in [8]. They also looked at the estimation of the scalar Wiener process with fixed communication delay in the presence of the signaling effect in [10], and obtained a similar structural result.…”

Section: Introductionmentioning

confidence: 86%

“…There are multiple works that are closely related to our study [5][6][7][8][9][10][11]. In these works, optimal triggering policies were characterized in settings that are different from ours.…”

Section: Introductionmentioning

confidence: 99%

Value of Information in Feedback Control: Global Optimality

Soleymani

Baras

Hirche

et al. 2023

IEEE Trans. Automat. Contr.

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In this chapter, we present our recent invention, i.e., the notion of the value of information-a semantic metric that is fundamental for networked control systems tasks. We begin our analysis by formulating a causal tradeoff between the packet rate and the regulation cost, with an encoder and a decoder as two distributed decision makers, and show that the valuation of information is conceivable and quantifiable grounded on this tradeoff. More precisely, we characterize an equilibrium, and quantify the value of information there as the variation in a value function with respect to a piece of sensory measurement that can be communicated from the encoder to the decoder at each time. We prove that, in feedback control of a dynamical process over a noiseless channel, the value of information is a function of the discrepancy between the state estimates at the encoder and the decoder, and that a data packet containing a sensory measurement at each time should be exchanged only if the value of information at that time is nonnegative. Finally, we prove that the characterized equilibrium is in fact globally optimal.

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“…packet-erasure channel in [5], [6], remote estimation of a scalar Markov process with symmetric noise distribution over an ideal channel in [9], remote estimation of a scalar autoregressive Markov process with symmetric noise distribution over an ideal channel, an i.i.d. packet-erasure channel, and a Gilbert-Elliott packeterasure channel in [10]- [12], remote estimation of the scalar Wiener and scalar Ornstein-Uhlenbeck processes over an ideal channel and a fixed-delay channel in [13], [14], remote estimation of the scalar Wiener process over a random-delay channel in [15], remote estimation of multiple random variables with arbitrary distributions over a collision channel in [16], [17], remote estimation of multiple random variables with arbitrary distributions over unicast and broadcast channels in [18], and remote estimation of two Gaussian random variables over a multi-access channel in [19]. These studies established certain characteristics such as a symmetric, asymmetric, or threshold structure of the optimal scheduling policy with respect to the estimation discrepancy.…”

Section: A Related Workmentioning

confidence: 99%

State Estimation over Delayed and Lossy Channels: An Encoder-Decoder Synthesis

Soleymani,

Baras,

Johansson

2024

IEEE Trans. Automat. Contr.

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This article examines the problem of state estimation over multi-terminal channels in an unreliable regime. More specifically, we consider two canonical settings. In the first setting, measurements of a common stochastic source need to be transmitted to two distinct remote monitors over a packet-erasure broadcast channel. In the second setting, measurements of two distinct stochastic sources need to be transmitted to a common remote monitor over a packet-erasure multi-access channel. For these networked systems, we uncover the fundamental performance limits in the sense of a causal tradeoff between the estimation error and the communication cost by identifying optimal encoding and decoding strategies. In the course of our analysis, we introduce two novel semantic metrics that play essential roles in state estimation over broadcast and multi-access channels. The first metric arising in the context of broadcast channels is the dissemination value of information, which quantifies the valuation of provisioning a piece of information to multiple receivers simultaneously. The second metric arising in the context of multiaccess channels is the prioritization value of information, which quantifies the valuation of provisioning a piece of information chosen from one out of multiple transmitters. Our findings certify that the optimal encoding and decoding strategies hinge on these semantic metrics.

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

Cited by 12 publications

References 38 publications

Timely Multi-Process Estimation Over Erasure Channels With and Without Feedback

Timely Multi-Process Estimation Over Erasure Channels With and Without Feedback

Value of Information in Feedback Control: Global Optimality

State Estimation over Delayed and Lossy Channels: An Encoder-Decoder Synthesis

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