Kernel methods constitute a category of machine learning algorithms extensively employed in the realm of classification, regression, identification, and other tasks. Our paper addresses the challenging problem of identifying the finite impulse response (FIR) of single-input single-output nonlinear systems under the influence of perturbations and binary-valued measurements. To overcome this challenge, we exploit two algorithms that leverage the framework of reproducing kernel Hilbert spaces (RKHS) to accurately identify the impulse response of the Proakis C channel. Additionally, we introduce the application of these kernel methods for estimating binary output data of nonlinear systems. We demonstrate the efficacy of kernel adaptive filters for identifying nonlinear systems with binary output measurements through experimental results presented in this work.