A causal algorithmic framework quantifying cross-channel phase-amplitude transfer entropy was proposed to measure long-range transmission dynamics between frontal and occipital brain areas during sleep. To this end, a noise-assisted multivariate empirical mode decomposition method was used to guarantee the consistent scales across multivariate signals. On the other side, transfer entropy was applied to measure information transfers from a low-frequency phase to a high-frequency amplitude across different brain regions. Our results showed δ phase may modulate either θ or α amplitude. The frontal cortex transferred information to the occipital brain area more than its inverse direction during Awake and N3 sleep stages, whereas N1 was more likely of serving as a transition state. On the other side, the information flow transferred from the occipital area to the frontal cortex surpassed its inverse flow in the N2 sleep stage. The proposed causal algorithmic framework facilitated identifying information flow and driving force across brain regions in sleep.