论文标题
一类连续马尔可夫过程的最佳因果率约束抽样
Optimal Causal Rate-Constrained Sampling for a Class of Continuous Markov Processes
论文作者
论文摘要
考虑以下通信方案。编码器观察到一个随机过程，并在因素限制每秒传输的位置数量的情况下，因果决定何时以及要传输什么。解码器使用接收的代码字实时估计该过程。编码器和解码器随时间同步。对于满足规律性条件的一类连续马尔可夫流程，我们发现最佳编码和解码策略最小化了速率约束下的端到端估计均值误差。我们表明，一旦流程创新通过了两个阈值之一，最佳编码策略将传输$ 1 $的代码字。最佳解码器无噪音从1位代码字和代码字制成的时间戳中恢复最后一个示例，并使用它来确定当前过程的运行估计，直到下一个代码字到达为止。特别是，我们显示了Ornstein-Uhlenbeck过程的最佳因果代码，并计算其失真率函数。此外，我们表明，最佳因果代码还可以最大程度地减少由连续的马尔可夫过程驱动并由加法控制信号控制的连续时间控制系统的平均值成本。
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.
