Statistics of chaotic binary sequences

Statistical properties of binary sequences generated by a class of ergodic maps with some symmetric properties are discussed on the basis of an ensemble-average technique. We give a simple sufficient condition for such a class of maps to produce a fair Bernoulli sequence, that is, a sequence of independent and identically distributed (i.i.d.) binary random variables. This condition is expressed in terms of binary function, which is a generalized version of the Rademacher function for the dyadic map.