Two kinds of problems - multiterminal hypothesis testing and one-to-many lossy source coding - are investigated in a unified way. It is demonstrated that a simple key idea, which is developed by Iriyama for one-to-one source coding systems, can be applied to multiterminal source coding systems. In particular, general bounds on the error exponents for multiterminal hypothesis testing and one-to-many lossy source coding are given.

The multiterminal hypothesis testing problem with zero-rate constraint is considered. For this problem, an upper bound on the optimal error exponent is given by Shalaby and Papamarcou, provided that the positivity condition holds. Our contribution is to prove that Shalaby and Papamarcou's upper bound is valid under a weaker condition: (i) two remote observations have a common random variable in the sense of Gácks and Körner, and (ii) when the value of the common random variable is fixed, the conditional distribution of remaining random variables satisfies the positivity condition. Moreover, a generalization of the main result is also given.