Functional Covering of Point Processes

TL;DR

This paper introduces a new distortion measure called functional-covering distortion for point processes, derives the rate-distortion function for Poisson processes, and analyzes the CEO problem under this framework.

Contribution

It proposes a novel distortion measure for point processes, derives the rate-distortion function with feedforward, and characterizes the CEO problem region for Poisson processes.

Findings

Derived the distortion-rate function for Poisson processes.

Characterized the rate-distortion region for the two-encoder CEO problem.

Showed feedforward does not enlarge the CEO region for Poisson processes.

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.