Hypothesis testing for arbitrarily varying source with exponential-type constraint

Hypothesis testing for an arbitrarily varying source (AVS) is considered. We determine the best asymptotic exponent of the probability of error of the second kind when the first kind error probability is less than 2^-nr. This result generalizes the well-known theorem of Hoeffding (1965), Blahut (1974), Csiszar and Longo (1971) for hypothesis testing with an exponential-type constraint. As a corollary in information theory, the best asymptotic error exponent and the r-optimal rate (the minimum compression rate when the error probability is less than 2^-nr, r⩾0) of AVS coding are determined