Differential Properties of Information in Jump-diffusion Channels

TL;DR

This paper models communication channels with jump-diffusion processes, deriving new differential identities for entropy and mutual information that extend classical results to more complex stochastic processes.

Contribution

It introduces a novel jump-diffusion channel model and extends de Bruijn's identity and I-MMSE relation to general Markov processes.

Findings

Expresses mutual information using Fisher-type information and KL divergence

Extends classical identities to jump-diffusion and Markov processes

Provides series and integral forms for information measures

Abstract

We propose a channel modeling using jump-diffusion processes, and study the differential properties of entropy and mutual information. By utilizing the Kramers-Moyal and Kolmogorov-Feller equations, we express the mutual information between the input and the output in series and integral forms, presented by Fisher-type information and mismatched KL divergence. We extend de Bruijn's identity and the I-MMSE relation to encompass general Markov processes.