Distributed Hypothesis Testing Against Dependence

@misc{wu2026distributed,
  title = {{Distributed Hypothesis Testing Against Dependence}},
  author = {Han Wu and Shun Watanabe},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.24403},
  eprint = {2608.24403},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.24403},
}

TY  - UNPB
TI  - Distributed Hypothesis Testing Against Dependence
AU  - Han Wu
AU  - Shun Watanabe
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2608.24403
UR  - https://arxiv.org/abs/2608.24403
AB  - We study distributed hypothesis testing and establish the exact error exponent in single-letter form for new testing problems. In distributed hypothesis testing, a receiver decides between ℋ_0:P_XY and ℋ_1:Q_XY based on Y^n and a rate-limited description of X^n. So far, such single-letter forms are known only for testing against independence, studied by Ahlswede and Csiszár, and testing against conditional independence, studied by Rahman and Wagner. In this paper, we study testing against dependence, where P_XY=P_XP_Y, and show that its error exponent is given by Han's exponent, which is established by single-letterizing a multi-letter version of Han's exponent. We also disprove a previous conjecture of Han claiming that the error exponent is given by the lautum information, as we show that Han's exponent can strictly exceed the latter. We then consider the Cartesian product of testing against dependence and testing against independence, and derive a single-letter characterization of its error exponent. We next study testing against conditional dependence, which is the dependence-testing counterpart of the setting studied by Rahman and Wagner. We derive a single-letter converse bound for the error exponent by introducing and solving a related setting where the side information is also available to the transmitter. We show that our converse bound is tight in some cases by using a conditional-coding version of the quantization scheme. Finally, we extend our converse method for testing against dependence to the general setting, and recover a recently established single-letter converse bound.
ER  -