On Hypothesis Testing Against Independence with Multiple Decision Centers

A distributed binary hypothesis testing problem is studied with one observer and two decision centers. The type-II error exponents region is derived for testing against independence when the observer communicates with the two decision centers over one common and two individual noise-free bit pipes. When there is only a common noise-free bit pipe, the type-II error exponents region is derived for testing against conditional independence. Finally, when the observer can communicate to the two decision centers over a discrete memoryless broadcast channel, an achievable type-II error exponents region is derived for testing against conditional independence. The last type-II error exponent is obtained by splitting the observations into subblocks, having the transmitter apply hybrid joint source-channel coding with side-information independently to each subblock, and having each receiver apply a Neyman-Pearson test jointly over the subblocks. This decision approach avoids introducing further error exponents due to the binning or the decoding procedures.