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The objective of this research is to evaluate the ε-minimum overflow threshold of the Bayes codes for a Markov source. In the lossless variable-length source coding problem, typical criteria are the mean codeword length and the overflow probability. The overflow probability is the probability with which a codeword length per source symbol exceeds a… (More)

This paper considers universal lossless variable-length source coding problem and deals with one of the fundamental limits and pointwise asymptotics of the Bayes code for stationary ergodic finite order Markov sources. As investigation of the fundamental limits, we show upper and lower bounds of the minimum rate such that the probability which exceeds it is… (More)

We analyze the asymptotic properties of the cumulative logarithmic loss in the decision problem based on the Bayesian principle and explicitly identify the constant terms of the asymptotic equations as in the case of previous studies by Clarke and Barron and Gotoh et al. We assume that the set of models is given that identify a class of parameterized… (More)

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