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Twice-Universal Simulation of Markov Sources and Individual Sequences

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4 Author(s)
Martin, A. ; Inst. de Comput., Univ. de la Republica, Montevideo, Uruguay ; Merhav, N. ; Seroussi, G. ; Weinberger, M.J.

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.

Published in:

Information Theory, IEEE Transactions on  (Volume:56 ,  Issue: 9 )