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Nonparametric threshold decision rule, coverings, and some consequences

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1 Author(s)
T. Hashimoto ; Dept. of Electr. Eng., Univ. of Electro-Commun., Tokyo, Japan

Threshold decision is a decision rule for errors and erasures decoding such that the decoder accepts the decoded codeword if its likelihood is larger than a given threshold value. This decision rule involves a parameter that needs to be optimized. We propose a nonparametric version of threshold decision and show that this nonparametric threshold decision allows us to extend some results on decision rules known only for restricted cases: the relationship between the threshold decision and the rule based on error detection coding and the attainability of Forney's (1968, 1981) exponent by the likelihood-ratio test. These results are derived from a covering theorem which is closely related to the nonparametric threshold decision

Published in:

IEEE Transactions on Information Theory  (Volume:46 ,  Issue: 1 )