Twice-universal simulation of Markov sources and individual sequences

Abstract-- The problem of universal simulation given a training sequence is studied both in a stochastic setting and for individual sequences. In the stochastic setting, the training sequence is assumed to be emitted by a Markov source of unknown order, extending previous work where the order is assumed known and leading to the notion of twice-universal simulation. A simulation scheme, which partitions the set of sequences of a given length into classes, is proposed for this setting and shown to be asymptotically optimal. This partition extends the notion of type classes to the twice-universal setting. In the individual sequence scenario, the same simulation scheme is shown to generate sequences which are statistically similar, in a strong sense, to the training sequence, for statistics of any order, while essentially maximizing the uncertainty on the output.

• Type: Journal
• Year: 2010
• Where: TIT
• Authors: Alvaro Martín, Neri Merhav, Gadiel Seroussi, Marcelo J. Weinberger
• Keywords: Education, Simulation, Stochastic Setting, TIT 2010, Training Sequence