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Poisson channel with binary Markov input and average sojourn time constraint

Sinzger, M. and Gehri, M. and Koeppl, H. (2020):
Poisson channel with binary Markov input and average sojourn time constraint.
In: ISIT'20 - International Symposium on Information Theory, virtual online conference, 21.-26. June 2020, [Online-Edition: https://2020.ieee-isit.org/],
[Conference or Workshop Item]

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. OFFfavoring 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 ONfavoring local optima.

Item Type: Conference or Workshop Item
Erschienen: 2020
Creators: Sinzger, M. and Gehri, M. and Koeppl, H.
Title: Poisson channel with binary Markov input and average sojourn time constraint
Language: English
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. OFFfavoring 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 ONfavoring local optima.

Divisions: 18 Department of Electrical Engineering and Information Technology
18 Department of Electrical Engineering and Information Technology > Institute for Telecommunications > Bioinspired Communication Systems
18 Department of Electrical Engineering and Information Technology > Institute for Telecommunications
Interdisziplinäre Forschungsprojekte
Interdisziplinäre Forschungsprojekte > Centre for Synthetic Biology
Event Title: ISIT'20 - International Symposium on Information Theory
Event Location: virtual online conference
Event Dates: 21.-26. June 2020
Date Deposited: 03 Apr 2020 12:28
Official URL: https://2020.ieee-isit.org/
Alternative keywords:
Alternative keywordsLanguage
Poisson channel, gene expression, binary Markov, average sojourn time, filtering, bandwidth constraintEnglish
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