Hypothesis Testing Under Successive Refinement Communication Constraints

We investigate the distributed successive refinement (SR) hypothesis testing problem. Bivariate hypothesis $H_{0}$: $P_{XY}$ against $H_{1}$: $P_{X}P_{Y}$, i.e., test against independence is considered, when a remote sensor sends compressed information about data stream $X$ subject to SR coding constraints to a decision site, where data stream $Y$ can be observed directly. We show that this problem is closely related to the SR lossless one-helper problem and the SR pattern recognition problem. More precisely, the rate-type-two-error-exponent region of the SR hypothesis testing problem, the rate region of the SR one-helper problem and that of the SR pattern recognition problem can be reduced to essentially the same entropy characterization form, up to an isometry. Single letter solution is subsequently given in this unified framework, and this connection is further explored. Strong converse result is proved by generalizing the image size characterization technique, which shows the optimal type-two error exponents for SR hypothesis testing under fixed type-one error constraints are independent of the exact values of those constraints. The notion of successive refinability is defined, and somewhat surprisingly for large value of type-one error constraints, a source is alwayssuccessive refinablefor hypothesis testing.