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2012 year, number 5

Errorless Readout of Random Discrete-Point Fields

A. L. Reznik, V. M. Efimov, A. A. Solov'ev, A. V. Torgov
Institute of Automation and Electrometry, Siberian Branch, Russian Academy of Sciences
Keywords: random division of the interval, analytical calculations on a computer, three-dimensional generalized Catalan numbers
Pages: 93-103


A closed analytical relation required to describe the reliability of readout of a random discrete-point field by integrators with two threshold levels is rigorously proved. The corresponding probabilistic problem is solved with the use of two nonstandard tricks: first, codes are developed for performing analytical computations on a computer; second, a new notion of "three-dimensional generalized Catalan numbers" is introduced and successfully applied.