Computer Science – Information Theory
Scientific paper
2010-12-14
Computer Science
Information Theory
some of the results were reported at ISIT2011
Scientific paper
The problem of filtering of finite--alphabet stationary ergodic time series is considered. A method for constructing a confidence set for the (unknown) signal is proposed, such that the resulting set has the following properties: First, it includes the unknown signal with probability $\gamma$, where $\gamma$ is a parameter supplied to the filter. Second, the size of the confidence sets grows exponentially with the rate that is asymptotically equal to the conditional entropy of the signal given the data. Moreover, it is shown that this rate is optimal.
Ryabko Boris
Ryabko Daniil
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