# Mutual info between discrete and continuous RV with history dependence

I am looking for literature references/measures to compute the mutual information between a continuous variable (time series) and a binary variable (a temporal sequence of 0's/1's). Briefly, a time series x(t) is assumed to be picked from some statistical ensemble (known). At each time point t1, a 0 or 1 is picked based on a probability which depends on x(t <= t1), i.e., on the history of x upto t1. In such a case, is there some known measure to estimate how well the sequence of 0's/1's correlates with/reflects the time profile of x? Some help finding relevant references would be appreciated.