By Topic

Successive Refinement for Hypothesis Testing and Lossless One-Helper Problem

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Tian, C. ; AT&T Labs.-Res., Florham Park, NJ ; Jun Chen

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 straightforward operational meaning for the IB method. Connection to the pattern recognition problem, the notion of successive refinability, and two specific sources are also discussed. A strong converse for the SR-HT problem is proved by generalizing the image size characterization method, which shows the optimal type-two error exponents under constant type-one error constraints are independent of the exact values of those constants.

Published in:

Information Theory, IEEE Transactions on  (Volume:54 ,  Issue: 10 )