Optimal Causal Rate-Constrained Sampling for a Class of Continuous Markov Processes
Optimal Causal Rate-Constrained Sampling for a Class of Continuous Markov Processes
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DOI：
10.1109/tit.2021.3114142
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发表时间：
2020-02
影响因子：
2.5
通讯作者：
Nian Guo;V. Kostina
中科院分区：
文献类型：
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作者：
Nian Guo;V. Kostina
考虑以下通信场景。编码器观察一个随机过程，并在每秒传输的预期比特数的约束下，因果地决定何时传输以及传输什么。解码器使用接收到的码字来真实的实时地因果估计该过程。编码器和解码器在时间上是同步的。对于一类满足正则性条件的连续Markov过程，在速率约束下，找到了使端到端估计均方误差最小的最优编码和解码策略.我们表明，最佳的编码策略传输一个1位的码字，一旦过程创新通过两个阈值之一。最佳解码器从1位码字和码字生成时间戳中无噪声地恢复最后一个样本，并使用它来决定当前过程的运行估计，直到下一个码字到达。特别是，我们显示的最佳因果码的Ornstein-Uhlenbeck过程，并计算其失真率函数。此外，我们还证明了最佳因果码还可以最小化由连续马尔可夫过程驱动并由加性控制信号控制的连续时间控制系统的均方成本。
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.