Nonlinear coordination is an essential property of the complex functioning of the autonomic nervous system. Therefore, the coupled behavior of heart rate fluctuations (HRF) and respiratory movements (RM) was analyzed on the basis of their joint reconstruction in phase space. Independence measures of complexity and predictability were approximated from the correlation integrals which enabled the strength of cardiorespiratory couplings to be quantified. These measures were validated in a simulation study of two coupled nonlinear oscillators in dependence on their coupling strength and respective synchronization effects. The cardiorespiratory coordination during quiet sleep and active sleep of newborn piglets was quantified by means of the proposed independence measures of complexity and predictability. The difference of those measures between the sleep states investigated was more significant than the difference of the respective linear coherence peaks.