Abstract
Samples from a high-dimensional first-order auto-regressive process generated by an independently and identically distributed random innovation sequence are observed by a sender which can communicate only finitely many bits per unit time to a receiver. The receiver seeks to form an estimate of the process value at every time instant in real-time. We consider a time-slotted communication model in a slow-sampling regime where multiple communication slots occur between two sampling instants. We propose a successive update scheme which uses communication between sampling instants to refine estimates of the latest sample and study the following question: Is it better to collect communication of multiple slots to send better refined estimates, making the receiver wait more for every refinement, or to be fast but loose and send new information in every communication opportunity? We show that the fast but loose successive update scheme with ideal spherical codes is universally optimal asymptotically for a large dimension. However, most practical quantization codes for fixed dimensions do not meet the ideal performance required for this optimality, and they typically will have a bias in the form of a fixed additive error. Interestingly, our analysis shows that the fast but loose scheme is not an optimal choice in the presence of such errors, and a judiciously chosen frequency of updates outperforms it.
Highlights
We consider the setting of real-time decision systems based on remotely sensed observations
We restricted our treatment to an AR[1] process with uncorrelated components. This restriction is for clarity of presentation, and some of the results can be extended to AR[1]
The decoder will be replaced by a Kalman-like filter in the manner of [35]
Summary
We consider the setting of real-time decision systems based on remotely sensed observations In this setting, the decision maker needs to track the remote observations with high precision and in a timely manner. The decision maker needs to track the remote observations with high precision and in a timely manner These are competing requirements, since high precision tracking will require larger number of bits to be communicated, resulting in larger transmission delay and increased staleness of information. Towards this larger goal, we study the following problem. A sensor draws a sample from this process, periodically once every s time-slots In each of these time-slots, the sensor can send nR bits to a center.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.