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Some properties of sequential predictors for binary Markov sources

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3 Author(s)
N. Merhav ; Dept. of Electr. Eng., Technion-Israel Inst. of Technol., Haifa, Israel ; M. Feder ; M. Gutman

Universal predictions of the next outcome of a binary sequence drawn from a Markov source with unknown parameters is considered. For a given source, the predictability is defined as the least attainable expected fraction of prediction errors. A lower bound is derived on the maximum rate at which the predictability is asymptotically approached uniformly over all sources in the Markov class. This bound is achieved by a simple majority predictor. For Bernoulli sources, bounds on the large deviations performance are investigated. A lower bound is derived for the probability that the fraction of errors will exceed the predictability by a prescribed amount Δ>0. This bound is achieved by the same predictor if Δ is sufficiently small

Published in:

IEEE Transactions on Information Theory  (Volume:39 ,  Issue: 3 )