Converse coding theorem for the identification via multiple access channels

In this paper we consider the identification (ID) via multiple access channels (MAC). Steinberg (1998) proved that in the general MAC the ID capacity region is equal to the ordinary transmission capacity region. In this paper we give an alternative proof for the converse coding theorem for the ID via MAC. We estimate two types of error probabilities of identification for rates outside the capacity region, deriving some function which serves as a lower bound of the sum of two error probabilities of identification. The result of Steinberg immediately follows from this result.