On the Reliability Function of Distributed Hypothesis Testing under Optimal Detection

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The distributed hypothesis testing problem with full side-information is studied. The trade-off (reliability function) between the two types of error exponents under limited rate is studied in the following way. First, the problem is reduced to the problem of determining the reliability function of channel codes designed for detection (in analogy to a similar result which connects the reliability function of distributed lossless compression and ordinary channel codes). Second, a single-letter random-coding bound based on a hierarchical ensemble, as well as a single-letter expurgated bound, are derived for the reliability of channel-detection codes. Both bounds are derived for a system which employs the optimal detection rule. We conjecture that the resulting random-coding bound is ensemble-tight, and consequently optimal within the class of quantization-and-binning schemes.

Original languageEnglish
Article number8684901
Pages (from-to)4940-4965
Number of pages26
JournalIEEE Transactions on Information Theory
Issue number8
StatePublished - Aug 2019


  • Binning
  • channel-detection codes
  • distributed hypothesis testing
  • error exponents
  • expurgated bounds
  • hierarchical ensembles
  • multiterminal data compression
  • random coding
  • side information
  • statistical inference
  • superposition codes

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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