Poisson channel with binary Markov input and average sojourn time constraint
Abstract
A minimal model for gene expression, consisting of a switchable promoter together with the resulting messenger RNA, is equivalent to a Poisson channel with a binary Markovian input process. Determining its capacity is an optimization problem with respect to two parameters: the average sojourn times of the promoter's active (ON) and inactive (OFF) state. An expression for the mutual information is found by solving the associated filtering problem analytically on the level of distributions. For fixed peak power, three bandwidth-like constraints are imposed by lower-bounding (i) the average sojourn times (ii) the autocorrelation time and (iii) the average time until a transition. OFF-favoring optima are found for all three constraints, as commonly encountered for the Poisson channel. In addition, constraint (i) exhibits a region that favors the ON state, and (iii) shows ON-favoring local optima.
Cite
@article{arxiv.2101.01607,
title = {Poisson channel with binary Markov input and average sojourn time constraint},
author = {Mark Sinzger and Maximilian Gehri and Heinz Koeppl},
journal= {arXiv preprint arXiv:2101.01607},
year = {2021}
}
Comments
This article was accepted for publication by IEEE, ISIT 2020