Successive Refinement for Hypothesis Testing and Lossless One-Helper Problem

Abstract--We investigate two closely related successive refinement (SR) coding problems: 1) In the hypothesis testing (HT) problem, bivariate hypothesis H0 : PXY against H1 : PXPY , i.e., test against independence is considered. One remote sensor collects data stream X and sends summary information, constrained by SR coding rates, to a decision center which observes data stream Y directly. 2) In the one-helper (OH) problem, X and Y are encoded separately and the receiver seeks to reconstruct Y losslessly. Multiple levels of coding rates are allowed at the two sensors, and the transmissions are performed in an SR manner. We show that the SR-HT rate-error-exponent region and the SR-OH rate region can be reduced to essentially the same entropy characterization form. Single-letter solutions are thus provided in a unified fashion, and the connection between them is discussed. These problems are also related to the information bottleneck (IB) problem, and through this connection we provide a...

• Type: Journal
• Year: 2008
• Where: TIT
• Authors: Chao Tian, Jun Chen
• Keywords: Entropy Characterization Form, Related Successive Refinement, SR-HT Rate-error-exponent Region, TIT 2008