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Paper IDT.3.1
Paper Title Poisson channel with binary Markov input and average sojourn time constraint
Authors Mark Sinzger, Maximilian Gehri, Heinz Koeppl, Technische Universität Darmstadt, Germany
Session T.3: Information Theory and Biology
Presentation Lecture
Track Topics in Information Theory
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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 exploiting the link with filtering theory. 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.

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2021 IEEE International Symposium on Information Theory

11-16 July 2021 | Melbourne, Victoria, Australia

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