Poisson channel with binary Markov input and average sojourn time constraint
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.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Nonparametric Bayesian Factor Analysis for Dynamic Count Matrices
A gamma process dynamic Poisson factor analysis model is proposed to factorize a dynamic count matrix, whose columns are sequentially observed count vectors. The model builds a novel Markov chain that sends the latent ga…
Data AugmentationBlind Construction of Angular Power Maps in Massive MIMO Networks
Channel state information (CSI) acquisition is a challenging problem in massive multiple-input multiple-output (MIMO) networks. Radio maps provide a promising solution for radio resource management by reducing online CSI…
Bayesian Image Restoration for Poisson Corrupted Image using a Latent Variational Method with Gaussian MRF
We treat an image restoration problem with a Poisson noise chan- nel using a Bayesian framework. The Poisson randomness might be appeared in observation of low contrast object in the field of imaging. The noise observati…
Image RestorationActivity of any neuron with delayed feedback stimulated with Poisson stream is non-Markov
For a class of excitatory spiking neuron models with delayed feedback fed with a Poisson stochastic process, it is proven that the stream of output interspike intervals cannot be presented as a Markov process of any orde…
Predicting Lifespan of Ground-to-Air Multipath Components in mmWave UAV Channels
In mobile ground-to-air (GA) propagation channels, the birth and death of multipath components (MPCs) are frequently observed, and the wide-sense stationary uncorrelated scattering (WSSUS) assumption does not always hold…
Time Series