Optimal Causal Rate-Constrained Sampling of the Wiener Process
- Creators
- Guo, Nian
- Kostina, Victoria
Abstract
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.
Additional Information
© 2019 IEEE. This work was supported in part by the National Science Foundation (NSF) under grant CCF-1751356.Attached Files
Submitted - 1909.01317.pdf
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Additional details
- Eprint ID
- 99090
- DOI
- 10.1109/ALLERTON.2019.8919710
- Resolver ID
- CaltechAUTHORS:20191004-133629184
- CCF-1751356
- NSF
- Created
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2019-10-04Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field