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Optimal Causal Rate-Constrained Sampling of the Wiener Process

Guo, Nian and Kostina, Victoria (2019) Optimal Causal Rate-Constrained Sampling of the Wiener Process. In: 2019 57th Annual Allerton Conference on Communication, Control, and Computing. IEEE , Piscataway, NJ, pp. 1090-1097. ISBN 978-1-7281-3151-1.

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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 makes real-time estimation of the process using causally received codewords. 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 unlock 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 D_(DET)(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.

Item Type:Book Section
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URLURL TypeDescription Paper ItemJournal Article
Guo, Nian0000-0003-4490-328X
Kostina, Victoria0000-0002-2406-7440
Additional Information:© 2019 IEEE. This work was supported in part by the National Science Foundation (NSF) under grant CCF-1751356.
Funding AgencyGrant Number
Subject Keywords:Causal lossy source coding, sequential estimation, sampling
Record Number:CaltechAUTHORS:20191004-133629184
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Official Citation:N. Guo and V. Kostina, "Optimal Causal Rate-Constrained Sampling of the Wiener Process," 2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton), Monticello, IL, USA, 2019, pp. 1090-1097. doi: 10.1109/ALLERTON.2019.8919710
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:99090
Deposited By: Tony Diaz
Deposited On:04 Oct 2019 20:57
Last Modified:16 Nov 2021 17:43

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