Exact Rate Exponent Tradeoff for New Classes of Distributed Hypothesis Testing Problems

Abstract

We characterize the exact rate--exponent tradeoff for new classes of one-way distributed hypothesis testing problems by demonstrating that a recent upper bound, derived via the auxiliary-receiver technique, coincides with known lower bounds. We achieve this by relaxing the upper bound on the type-II error exponent into a form that shares the same inner functional as Han's lower bound, differing only in the outer rate constraint. Furthermore, we prove that this upper bound is tight for testing against dependence and for the doubly symmetric binary source (DSBS) with crossover probabilities ${\kappa }_0$ under the null hypothesis and ${\kappa }_1$ under the alternative hypothesis, provided $0<{\kappa }_1<{\kappa }_0<\frac{1}{2}$. The characterization of the exact error exponent for the DSBS source holds for every communication rate $R\ge 0$.