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