Universal simulation with a fidelity criterion

We consider the problem of universal simulation of memoryless; sources and Markov sources, based on training sequence emitted from these sources. The objective is to maximize the conditional entropy of the simulated sequence given the training sequence, subject to a certain distance constraint between the probability distribution of the output sequence and the probability distribution of the input, training sequence. We derive a single-letter expression for the maximum conditional entropy and then propose a universal simulation scheme that asymptotically attains this maximum.