Nonparametric threshold decision rule, coverings, and some consequences

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.