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Hypothesis testing with multiterminal data compression

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The multiterminal hypothesis testing H: XY against \overline{H}: \overline{X}\overline{Y} is considered where X^{n} (\overline{X}^{n}) and Y^{n} (\overline{Y}^{n}) are separately encoded at rates R_{1} and R_{2} , respectively. The problem is to determine the minimum \beta _{n} of the second kind of error probability, under the condition that the first kind of error probability \alpha _{n} \leq \epsilon for a prescribed 0 < \epsilon < 1 . A good lower bound \theta_{L}(R_{1}, R_{2}) on the power exponent \theta (R_{1}, R_{2},\epsilon)= \lim inf_{n \rightarrow \infty }(-1/n \log \beta _{n}) is given and several interesting properties are revealed. The lower bound is tighter than that of Ahlswede and Csiszár. Furthermore, in the special case of testing against independence, this bound turns out to coincide with that given by them. The main arguments are devoted to the special case with R_{2} = \infty corresponding to full side information for Y^{n}(\overline{Y}^{n}) . In particular, the compact solution is established to the complete data compression cases, which are useful in statistics from the practical point of view.

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Information Theory, IEEE Transactions on  (Volume:33 ,  Issue: 6 )