Asymptotically Optimal Decision Rules for Joint Detection and Source Coding

The problem of joint detection and lossless source coding is considered. We derive asymptotically optimal decision rules for deciding whether or not a sequence of observations has emerged from a desired information source, and to compress it if has. In particular, our decision rules asymptotically m...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 60; no. 11; pp. 6787 - 6795
Main Author: Merhav, Neri
Format: Journal Article
Language:English
Published: New York IEEE 01.11.2014
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Asymptotic methods
Asymptotic properties
Coding
Coding theory
Compressing
Cost engineering
Data compression
Decision analysis
False alarms
Information theory
Joints
Linear programming
Minimization
Optimization
Probability
Source coding
Testing
Vectors
misdetection
universal schemes
source coding
hypothesis testing
false alarm
Error exponent
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:The problem of joint detection and lossless source coding is considered. We derive asymptotically optimal decision rules for deciding whether or not a sequence of observations has emerged from a desired information source, and to compress it if has. In particular, our decision rules asymptotically minimize the cost of compression in the case that the data have been classified as desirable, subject to given constraints on the two kinds of the probability of error. In another version of this performance criterion, the constraint on the false alarm probability is replaced by a constraint on the cost of compression in the false alarm event. We then analyze the asymptotic performance of these decision rules. We also derive universal decision rules for the case where the underlying sources (under either hypothesis or both) are unknown, and training sequences from each source may or may not be available. Finally, we discuss how our framework can be extended in several directions.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2014.2352300