On the Reliability Function of Distributed Hypothesis Testing Under Optimal Detection

The distributed hypothesis-testing problem with full side-information is studied. The trade-off (reliability function) between the type 1 and type 2 error exponents under limited rate is studied in the following way. First, the problem of determining the reliability function of distributed hypothesis-testing is reduced to the problem of determining the reliability function of channel-detection codes (in analogy to a similar result which connects the reliability of distributed compression and ordinary channel codes). Second, a random-coding bound based on an hierarchical ensemble, as well as an expurgated bound, are derived for the reliability of channel-detection codes. The resulting bounds are the first to be derived for quantization-and-binning schemes under optimal detection.

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