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 single-letter random-coding bound based on an hierarchical ensemble, as well as a single-letter expurgated bound, are derived for the reliability of channel-detection codes. Both bounds are derived for the optimal detection rule. We believe that the resulting bounds are ensemble-tight, and hence optimal within the class of quantization-and-binning schemes. Index Terms Binning, channel-detection codes, distributed hypothesis-testing, error exponents, expurgated bounds, hierarchical ensembles, multiterminal data compression, random coding, side information, statistical inference, superposition codes.