Generation of random bits from Poisson processes

In a recent work, Bernardini and Rinaldo generalize and attempt to improve upon Elias method to obtain unbiased random bits from a geometric distribution resulted from a Poisson process. As a response, we analyse the output rates of their method and compare with the original binary Elias method applied on a Bernoulli process resulted from the same Poisson process, which turns out to be much simpler to implement and to have a higher output rate.