  This paper proposes simple perfect samplers using monotone birth-and-death
processes (BD-processes), which draw samples from an arbitrary finite discrete
target distribution. We first construct a monotone BD-process whose stationary
distribution is equal to the target distribution. We then derive upper bounds
for the expected coalescence time of the copies of the monotone BD-process. We
also establish upper bounds for the expected values and tail probabilities of
the running times of two perfect samplers, which are Doubling CFTP and
Read-once CFTP using our monotone BD-process. The latter sampler can draw
samples exactly from unnormalized target distributions with little memory
consumption.
