Universal delay-limited simulation

We consider the problem of universal delay-limited simulation of an unknown information source of a certain parametric family (e.g., the family of memoryless sources or Markov sources of a given order), given a training sequence from that source and a stream of purely random bits. In the delay-limited setting, the simulation algorithm generates a random sequence sequentially, by delivering one symbol for each training symbol that is made available after a given initial delay, whereas the random bits are assumed to be available on demand. The goal of universal simulation is that the probability law of the generated sequence be identical to that of the training sequence, with minimum mutual information between the random processes generating both sequences. We characterize the optimal delay-limited simulation scheme and upper-bound the expected number of random bits it consumes. As in the non-sequential case, this upper bound is related to the entropy rate of the source