Distributed Hypothesis Testing With Variable-Length Coding

The problem of distributed testing against independence with variable-length coding is considered when the average and not the maximum communication load is constrained as in previous works. The paper characterizes the optimum type-II error exponent of a single-sensor single-decision center system g...

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Veröffentlicht in:IEEE journal on selected areas in information theory Jg. 1; H. 3; S. 681 - 694
Hauptverfasser: Salehkalaibar, Sadaf, Wigger, Michele
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Piscataway IEEE 01.11.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Codes
Coding
Communication
Computer Science
Constraints
discrete memoryless channels
distributed hypothesis testing
Error probability
Feedback
Information Theory
Memoryless systems
Sensor systems
Sensors
strong converse
Testing
Variable-length coding
ISSN:2641-8770, 2641-8770
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Zusammenfassung:The problem of distributed testing against independence with variable-length coding is considered when the average and not the maximum communication load is constrained as in previous works. The paper characterizes the optimum type-II error exponent of a single-sensor single-decision center system given a maximum type-I error probability when communication is either over a noise-free rate-<inline-formula> <tex-math notation="LaTeX">R </tex-math></inline-formula> link or over a noisy discrete memoryless channel (DMC) with stop-feedback. Specifically, let <inline-formula> <tex-math notation="LaTeX">\epsilon </tex-math></inline-formula> denote the maximum allowed type-I error probability. Then the optimum exponent of the system with a rate-<inline-formula> <tex-math notation="LaTeX">R </tex-math></inline-formula> link under a constraint on the average communication load coincides with the optimum exponent of such a system with a rate <inline-formula> <tex-math notation="LaTeX">R/(1-\epsilon) </tex-math></inline-formula> link under a maximum communication load constraint. A strong converse thus does not hold under an average communication load constraint. A similar observation also holds for testing against independence over DMCs. With variable-length coding and stop-feedback and under an average communication load constraint, the optimum type-II error exponent over a DMC of capacity <inline-formula> <tex-math notation="LaTeX">C </tex-math></inline-formula> equals the optimum exponent under fixed-length coding and a maximum communication load constraint when communication is over a DMC of capacity <inline-formula> <tex-math notation="LaTeX">C/(1-\epsilon) </tex-math></inline-formula>.
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ISSN:2641-8770
2641-8770
DOI:10.1109/JSAIT.2020.3039839