In this work, a novel method is proposed for detecting bipolar discrete Return-to-Zero (RZ) signals in non-Gaussian noise with Excess Kurtosis for Information and Measurement Systems (IMS). The approach relies on describing random processes through moment–cumulant characteristics and on constructing stochastic decision rules (DRs) in polynomial form. Classical detection techniques, which rely on Gaussian noise assumptions, often prove insufficient under real-world conditions where the noises are characterized by such significant parameters as kurtosis and skewness. To overcome the mentioned constraints, higher-order statistics (HOS) are utilized — particularly third- and fourth-order moments and cumulants to achieve a more detailed characterization of non-Gaussian noise. Both linear (S = 1) and nonlinear (S = 3) DRs are developed and optimized using a moment-based quality criterion aimed at reducing Type I and Type II error probabilities. Simulation results demonstrate that accounting for excess kurtosis significantly enhances detection performance. In particular, the nonlinear DRs show up to a threefold improvement in signal discrimination accuracy compared to tradi-tional Gaussian-based models.