Functional Covering of Point Processes
Information Theory
2022-04-21 v1 math.IT
Abstract
We introduce a new distortion measure for point processes called functional-covering distortion. It is inspired by intensity theory and is related to both the covering of point processes and logarithmic loss distortion. We obtain the distortion-rate function with feedforward under this distortion measure for a large class of point processes. For Poisson processes, the rate-distortion function is obtained under a general condition called constrained functional-covering distortion, of which both covering and functional-covering are special cases. Also for Poisson processes, we characterize the rate-distortion region for a two-encoder CEO problem and show that feedforward does not enlarge this region.
Keywords
Cite
@article{arxiv.2204.09188,
title = {Functional Covering of Point Processes},
author = {Nirmal V. Shende and Aaron B. Wagner},
journal= {arXiv preprint arXiv:2204.09188},
year = {2022}
}