Error bound of hypothesis testing with data compression

We discuss hypothesis testing with data compression in a multiterminal system. This case is different from the usual statistical case which can be solved using Stein´s lemma. We give a lower bound on the exponent of hypothesis testing error which is better than the bounds which have been previously derived, and give the sufficient rate for achieving Stein´s lemma. The lower-bound is obtained by constructing an encoding-decoding system