2016/12/01 by Christoph Kawan, Serdar Yüksel, Kawan, Christoph +1
Biochemistry, Genetics and Molecular Biology · #FOS: Computer and information sciences #FOS: Mathematics #Gene Regulatory Network Analysis #Information Theory (cs.IT) #Optimization and Control (math.OC) #Single-cell and spatial transcriptomics
paper · pdf · doi:10.48550/arxiv.1612.00564
openalex publication_date 2016/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of optimal zero-delay coding and estimation of a\nstochastic dynamical system over a noisy communication channel under three\nestimation criteria concerned with the low-distortion regime. The criteria\nconsidered are (i) a strong and (ii) a weak form of almost sure stability of\nthe estimation error as well as (ii) quadratic stability in expectation. For\nall three objectives, we derive lower bounds on the smallest channel capacity\nC0 above which the objective can be achieved with an arbitrarily small\nerror. We first obtain bounds through a dynamical systems approach by\nconstructing an infinite-dimensional dynamical system and relating the capacity\nwith the topological and the metric entropy of this dynamical system. We also\nconsider information-theoretic and probability-theoretic approaches to address\nthe different criteria. Finally, we prove that a memoryless noisy channel in\ngeneral constitutes no obstruction to asymptotic almost sure state estimation\nwith arbitrarily small errors, when there is no noise in the system. The\nresults provide new solution methods for the criteria introduced (e.g.,\nstandard information-theoretic bounds cannot be applied for some of the\ncriteria) and establish further connections between dynamical systems,\nnetworked control, and information theory, and especially in the context of\nnonlinear stochastic systems.\n