Optimal Causal Rate-Constrained Sampling of the Wiener Process

Abstract

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 bits transmitted per second. A decoder uses the received codewords to causally estimate the process in real time. We aim to find the optimal encoding and decoding policies that minimize the end-to-end estimation mean-square error under the rate constraint. For * N. Guo and V. Kostina are with the

Stabilizing a linear system using phone calls

“…In the framework of control of dynamical systems over communication channels, it has recently been observed that event-triggering policies encoding information over time in a state-dependent fashion can exploit timing information for stabilization in addition to the information traditionally carried by data packets [13]- [22]. In a more general framework, this paper studied from an information-theoretic perspective the fundamental limitation of using only timing information for stabilization, independent of any transmission strategy.…”

“…Rather than performing periodic communication between the system and the controller, in event-triggered control communication occurs only as needed, in an opportunistic manner. In this setting, the timing of the triggering events can carry useful information about the state of the system, that can be used for stabilization [13]- [22]. In this context, it has been shown that the amount of timing information is sensitive to the delay in the communication channel.…”

“…through the timestamps of the symbols transmitted over the channel; the time is carrying the message. This formulation is motivated by recent works in event-triggering control, showing that the timing of the triggering events carries information that can be used for stabilization [13]- [22]. By encoding information in timing, stabilization can be achieved by transmitting additional data at a rate arbitrarily close to zero.…”

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

“…The optimality of the proposed schemes was not considered in [11]- [20]. In our previous work [21], we introduced an information-theoretic framework for studying jointly optimal sampling and quantization policies by considering a longterm average bitrate constraint. We showed that the optimal event-triggered sampling policy for the Wiener process remains a two-threshold policy even under a bitrate constraint, while the optimal deterministic (process-independent) sampling policy is uniform.…”

“…In the paper, we leverage the information-theoretic framework of our prior work [21], introduced in the context of the Wiener process, to study the jointly optimal sampling and quantization policies for the wider class of continuous-time processes introduced in Section 1.2. We prove that the optimal sampling policy is a two-threshold policy whether or not quantization is taken into account.…”