Universal Simulation With Fidelity Criteria

We consider the problem of universal simulation of a memoryless source (with some partial extensions to Markov sources), based on a training sequence emitted from the source. 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, for several distance criteria, single-letter expressions for the maximum attainable conditional entropy as well as corresponding universal simulation schemes that asymptotically attain these maxima.